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STEPS: Semantic-Contract-Guided Scheduling for LLM-Assisted Natural-Language-Driven Edge AI Services
arXiv:2606.09537v1 [cs.NI] 8 Jun 2026
Houyi Qi, Graduate Student Member, IEEE, Minghui Liwang, Senior Member, IEEE, Xianbin Wang, Fellow, IEEE, and Seyyedali Hosseinalipour, Senior Member, IEEE
Abstract—Networked AI services are increasingly delivered through edge infrastructures to support latency-sensitive and resource-intensive applications. As a result, edge user/service scheduling has become a critical mechanism for determining where and how AI services are executed under limited communication and computing resources. Nevertheless, existing edge scheduling frameworks typically assume that service requirements are explicitly specified as numerical quantities/constraints, such as latency bounds, energy budgets, or cost limits. In practice, however, users often express their service expectations through ambiguous and context-dependent natural-language descriptions (e.g., “finish quickly” or “save energy”), creating a fundamental gap between user intent and resource-constrained scheduling decisions. Bridging this semantic-to-optimization gap is particularly challenging in dynamic edge environments with time-varying resources, workloads, and execution conditions. To address this challenge, we propose semantic–contract–guided edge potential scheduling (STEPS), a natural-language-driven scheduling framework for networked AI services. STEPS introduces semantic contracts as executable interfaces between user-side semantics and edge-side decision making. Specifically, a large language model (LLM)-assisted semantic parser interprets naturallanguage requests and extracts semantic service levels together with confidence scores, which are subsequently converted into service preferences, fulfillment bounds, and semantic uncertainty. Based on these contracts, STEPS formulates edge scheduling as a contract-guided potential game that jointly determines executionnode selection, computing-resource provisioning, and bandwidth allocation. STEPS further incorporates fulfillment-driven adaptation by constructing feedback signals from semantic-request drift, fulfillment drift, fulfillment pressure, and admission pressure, which are used to dynamically regulate semantic admission, contract conservativeness, and edge coordination. Moreover, we characterize the exact-potential-game structure of the STEPS scheduling problem, establish the existence of pure-strategy Nash equilibria, and prove convergence and stability properties of the associated scheduling and adaptation processes. Extensive experiments demonstrate that STEPS improves semantic-contract fulfillment, reduces contract-guided service loss, and maintains robust adaptation under ambiguous natural-language requests and non-stationary networked AI environments. Index Terms—Networked AI, Natural Language-Driven Scheduling, Semantic Contract, Adaptive Optimization, Edge Intelligence, Potential Game.
I. I NTRODUCTION ECENT advances in artificial intelligence (AI) and computing technologies have led to the emergence of networked AI, where AI models are deployed and coordinated
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H. Qi ([email protected]) and M. Liwang (minghuiliwang@ tongji.edu.cn) are with the Shanghai Research Institute for Intelligent Autonomous Systems, State Key Laboratory of Autonomous Intelligent Unmanned Systems, Frontiers Science Center for Intelligent Autonomous Systems, and Department of Control Science and Engineering, Tongji University, Shanghai, China. X. Wang ([email protected]) is with the Department of Electrical and Computer Engineering, Western University, Ontario, Canada. S. Hosseinalipour ([email protected]) is with the Department of Electrical Engineering, University at Buffalo-SUNY, USA.
across end-edge-cloud integrated infrastructures to enable real-time inference, context-aware perception, and adaptive decision-making for various intelligent services, such as industrial automation, smart healthcare, autonomous driving, and immersive human-machine interaction [1]–[3]. Unlike conventional cloud-centric AI services, networked AI operates over the distributed and time-varying end-edge-cloud continuum, where communication (e.g., data transmission) and computation (e.g., modeling training and inference) are tightly coupled with execution feedback loops. In this context, edge computing provides a natural substrate of edge services for networked AI (E4NetAI), enabling latency-sensitive tasks to be executed closer to end users and thus reducing end-to-end service delay [4], [5]. Motivated by this premise, a major body of work on E4NetAI has focused on distributed device/service scheduling and network orchestration schemes at the network edge [2], [6]. However, such works largely follow a parameterdriven paradigm that requires users to explicitly specify lowlevel quantitative requirements, such as delay tolerances, energy budgets, payment limits, and preference weights in order to obtain proper device scheduling and network orchestration schemes [6], [7]. This assumption is often unrealistic for nonexpert users who lack backgrounds in the detailed pipelines of innovative technologies. In fact, instead of calibrating maximum tolerable latency, energy budgets, payment limits, or preference-weight vectors, ordinary users mostly tend to express their subjective preferences and service expectations in natural language [8]–[10], e.g., “finish this task as quickly as possible without incurring excessive cost”. This indicates that the user interaction mode of E4NetAI services is shifting from expert-oriented parameter configuration toward humancentric semantic interaction. While this shift lowers the access barrier to networked AI services for the users, it also poses a deeper semantic-grounding challenge to the pipeline of networked services: how to transform vague, implicit, and uncertain natural language-based user intents into executable and optimizable service specifications that are consistent with edge resource constraints. To address the aforementioned challenge on naturallanguage-driven network management, recent advances in intent-based networking (IBN) and large language models (LLMs) provide new opportunities. Specifically, IBN translates high-level user/operator intents into network policies and configurations [11]–[13], while LLM-assisted network orchestration enables natural language interpretation, policy generation, and automated service configuration [8], [14]. Nevertheless, directly applying existing IBN and LLM-assisted orchestration techniques to E4NetAI remains insufficient. This is because while IBN and LLMs are effective at interpreting high-level user/operator intents and generating service policies, they do not inherently provide an optimization-compatible
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representation that can reliably bridge ambiguous user semantics and resource-constrained edge decision-making. More specifically, first, natural-language requests are inherently ambiguous and context-dependent, making direct translation into mixed discrete-continuous device/service scheduling variables, such as computing allocations, bandwidth assignments, or execution-node selections, unreliable and inconsistent [15]. Second, unlike traditional intent translation tasks, E4NetAI user/service scheduling must operate under tightly coupled communication-computation constraints, such as limited computing capacity, bandwidth availability, queue states, and timevarying wireless channel conditions [3], [6]. Consequently, semantic intents must be grounded into executable specifications that explicitly account for resource feasibility and cross-layer dependencies. Third, E4NetAI environments are inherently non-stationary, where user semantic preferences, service demands, resource availability, and execution performance continuously evolve over time [16]. However, existing intent-translation and LLM-assisted orchestration approaches primarily focus on one-shot intent interpretation and policy generation, offering limited mechanisms for adapting service decisions according to the fulfillment outcomes of previously executed semantic requests. These challenges reveal a fundamental gap between natural-language intent understanding and edge optimization under system constraints, namely that user intents expressed in natural language cannot be directly consumed by edge schedulers and must instead be transformed into an intermediate representation that preserves semantic meaning while remaining compatible with resource-constrained optimization. Furthermore, because execution outcomes may deviate from user expectations under dynamic network conditions, this representation must also support feedback-driven adaptation over time. This motivates the introduction of a semantic contract as an executable interface between user-side semantics and edge-side decision making. Building upon this motivation, we develop a unified semantic-contract framework that bridges intent interpretation and execution through contract-based decision evolution. Realizing such a framework requires addressing several fundamental challenges spanning semantic grounding, contract-guided scheduling, and fulfillment-driven adaptation. Accordingly, we distill the following three research questions (RQs) that guide our design. • RQ 1: How can unstructured natural language service intents be systematically grounded into a structured and constraint-consistent decision representation for E4NetAI? Addressing this question is non-trivial because naturallanguage service requests are inherently ambiguous, qualitative, and context-dependent, whereas edge schedulers require precise representations that can be evaluated and optimized under resource constraints. Moreover, while existing IBN and LLM-assisted orchestration approaches can translate user intents into high-level policies or control directives [8], [11], they still lack an explicit intermediate representation that simultaneously preserves semantic meaning and enables optimizationcompatible decision making. Therefore, a key challenge is to establish an executable interface between user-side semantics and edge-side scheduling decisions while maintaining feasibility under system performance, cost, and execution constraints. • RQ 2: How can semantic contracts reshape the structure of edge scheduling under tightly coupled constraints and
semantic uncertainty? Addressing this question is non-trivial because, once natural-language intents are transformed into semantic contracts, service requirements are no longer represented solely by fixed numerical constraints. Instead, they become preference-aware, uncertainty-aware, and fulfillmentoriented objectives that must be simultaneously considered during user/service scheduling. Consequently, conventional edge scheduling formulations, which primarily optimize resource utilization or quality-of-service metrics under predefined constraints [6], [17], are no longer directly applicable. Therefore, a key challenge is to design a scheduling framework that jointly determines execution placement, computingresource provisioning, and bandwidth allocation while consistently accounting for semantic-contract requirements, resource limitations, and semantic uncertainty. • RQ 3: How can post-execution contract-satisfaction feedback enable principled adaptation in non-stationary E4NetAI systems? Addressing this question is non-trivial because E4NetAI operates in highly dynamic environments, where user preferences, service demands, resource availability, and execution conditions continuously evolve over time. Nevertheless, existing adaptive optimization and drift-aware learning approaches primarily focus on observable variations in data distributions, network states, or model performance [16]. As a result, they largely overlook the mismatch between semanticcontract expectations and realized service outcomes, which can only be evaluated after task execution. Subsequently, a key challenge is to construct meaningful contract-satisfaction feedback signals and distinguish between changes originating from user-side semantic evolution (i.e., semantic-request drift, where the characteristics and expectations expressed in user requests change over time) and changes caused by systemside execution conditions (i.e., fulfillment drift, where contractsatisfaction outcomes vary due to fluctuations in resources, network conditions, or service performance). To answer the above RQs, we propose semantic–contract– guided edge potential scheduling (STEPS), one of the first natural-language-driven scheduling frameworks for E4NetAI. Specifically, to address RQ1, STEPS introduces semantic contracts as an executable interface between natural-language intents and edge service decisions. Specifically, in STEPS, an LLM-assisted semantic parser interprets user requests and extracts semantic service levels together with a confidence score that quantifies the reliability of the semantic interpretation, which are then converted into service preferences, fulfillment bounds, and semantic uncertainty, thereby enabling optimization-compatible decision making. To address RQ 2, STEPS formulates a semantic-contract-guided edge scheduling problem under coupled communication-computation constraints, where edge association, computation provisioning, and bandwidth coordination are jointly optimized through a distributed potential-game-based equilibrium. To address RQ 3, STEPS evaluates post-execution contract fulfillment and constructs feedback signals to update semantic admission, contract conservativeness, price coordination, and edge coordination gain. Our main contributions can be summarized as follows. • We propose STEPS, which is one of the first semanticcontract-based adaptive scheduling framework for naturallanguage-driven E4NetAI. STEPS establishes one of the first closed-loop pipelines from natural language service requests
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to semantic abstraction, contract-guided edge scheduling, postexecution contract-satisfaction evaluation, and fulfillmentdriven adaptation. Further, through introducing the semantic contract as an executable intermediate interface, STEPS bridges user-side natural language semantics and resourceconstrained edge optimization. • We design an LLM-empowered semantic-contract generation engine that converts natural language requests into optimization-compatible service contracts. Specifically, an LLM-assisted semantic parser analyzes each request and extracts semantic service levels (e.g., delay sensitivity, energy sensitivity, cost sensitivity, and trustworthiness requirements) together with a confidence score that quantifies the reliability of the semantic interpretation. Based on these extracted semantics, interpretable mapping rules combine user requirements, task attributes, and system-side context to construct a semantic contract consisting of service preferences, fulfillment bounds, and semantic uncertainty. The resulting contract serves as an executable representation of user intent that can be directly incorporated into edge scheduling decisions. By restricting the LLM to semantic interpretation rather than resource optimization, the proposed framework avoids relying on unconstrained LLM-generated resource allocations while preserving interpretability and optimization consistency. • We develop a contract-guided edge scheduling engine for distributed execution-node selection and resource allocation in E4NetAI. Guided by the semantic contracts generated from user requests, the proposed engine jointly determines taskexecution placement, computing-resource provisioning, and bandwidth allocation while respecting communication and computation resource constraints. The scheduling objective explicitly captures the tradeoff among service delay, energy consumption, monetary cost, trustworthiness-for-execution, and semantic-contract fulfillment. To efficiently solve the resulting high-dimensional optimization problem, we reformulate each time-slot scheduling problem as an exact potential game and develop an asynchronous best-response mechanism for distributed equilibrium computation. This design enables scalable and contract-aware scheduling without requiring centralized optimization across all users and edge servers. • We design a contract-satisfaction feedback and adaptive optimization engine for non-stationary E4NetAI. Rather than adapting solely to changes in data distributions or network conditions, the proposed engine evaluates how well executed services satisfy their semantic contracts and converts these outcomes into feedback signals. Specifically, it captures changes in user-side service requirements (i.e., semantic-request drift), variations in achieved contract-satisfaction outcomes caused by execution conditions (i.e., contract-fulfillment drift), and instantaneous fulfillment pressure arising from contract violations, while separately using admission pressure to regulate the acceptance of highly uncertain requests. Based on these feedback signals, the engine dynamically updates semanticadmission thresholds, contract conservativeness factors, and edge-coordination gains. This design enables fulfillmentdriven adaptation and sustained scheduling performance under evolving user semantics, resource availability, and service conditions. • We provide theoretical analysis and extensive evaluations of STEPS. On the theoretical side, we characterize the exactpotential-game structure of the contract-guided scheduling
problem and establish key properties of the proposed framework, including the existence of pure-strategy Nash equilibrium, finite-step convergence of the asynchronous bestresponse dynamics, and boundedness of the feedback-driven adaptive update process. These results provide theoretical guarantees on the stability and computability of the proposed scheduling framework. On the experimental side, extensive evaluations demonstrate that STEPS improves semanticcontract fulfillment, reduces contract-guided service loss, and maintains robust adaptation under ambiguous natural-language requests, semantic uncertainty, and non-stationary network conditions. II. L ITERATURE R EVIEW In the following, we review the literature across three interrelated domains: (i) IBN and LLM-assisted service orchestration, (ii) edge AI service scheduling and provisioning, and (iii) drift-aware adaptive optimization. Throughout the review, we emphasize the fundamental differences between these existing research directions and the semantic-contractguided paradigm adopted by STEPS. Table I summarizes our discussions. (i) IBN and LLM-Assisted Service Orchestration: IBN serves as an important paradigm for simplifying network management by allowing users/operators to express high-level service intents instead of manually specifying low-level configurations [11], [18]. Within this paradigm, existing research has primarily focused on translating user intents into network policies, service descriptors, and management actions through processes such as intent decomposition, policy generation, service configuration, and closed-loop assurance. Recent advances in LLMs have further expanded the capabilities of intent-driven orchestration by enabling natural-language understanding and automated decision support. For example, Mekrache et al. [18] proposed an LLM-centric intent-based management architecture for next-generation networks that supports intent decomposition, translation, activation, and assurance. Mekrache and Ksentini [8] further studied LLM-enabled intent-driven service configuration, where natural language intents are translated into network service descriptors to reduce the need for manually constructing structured configuration templates. At a larger operational scale, Wang et al. [19] developed a multiagent LLM framework that decomposes complex network management workflows into coordinated subtasks executed by multiple agents. Beyond traditional network management, recent studies have extended intent-driven paradigms toward computing and edge-service environments. For example, Akbari et al. [20] investigated LLM-assisted intent-based computing across the compute continuum (i.e., edge servers and cloud resources), where user-defined intents are monitored and handled through diagnosis and reconfiguration. Qin et al. [14] explored the integration of generative AI and intentdriven wireless communications to facilitate more natural interactions between users and communication systems. Sun et al. [15] proposed an agentic-AI-based edge service scheduling framework that maps user intents into resource-oriented representations and leverages generative meta-learning to improve cross-scenario generalization. Although these prior studies have explored LLM-enabled and intent-driven orchestration, they predominantly treat natural-language inputs as mechanisms for generating policies, configurations, management
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TABLE I S UMMARY OF REPRESENTATIVE RELATED WORKS AND OUR PROPOSED METHOD . Reference
Research Field
[8], [18]
IBN + LLM orchestration
[19] [15], [20] [21], [22] [17] [24], [25] [26]
Summary of Contribution
Developed LLM-assisted intent management and service configuration methods that translate high-level natural language intents into network/service descriptors and management actions. Multi-agent LLM + network Proposed a multi-agent LLM framework for network management, where complex workflows are management decomposed and executed with existing tools and validation mechanisms. Intent-driven compute/edge Explored intent-driven resource management and edge service scheduling by mapping user intents into scheduling resource-related representations or agentic scheduling processes.
Edge-cloud generative AI
Surveyed mobile edge generative AI and LLM services, covering cloud-edge infrastructure, service lifecycle, edge deployment, inference, caching, and resource challenges. Device-edge co-inference Jointly optimized AI model splitting and wireless resource scheduling for device-edge collaborative inference under inference latency constraints. Edge AI/LLM inference Optimized compression offloading, quantization, and communication-computation resource scheduling scheduling for edge-based vision or generative LLM inference services.
Online FL + concept drift
Designed an online federated learning framework with non-stationarity detection and adaptation to improve learning performance under concept drift. [16], [27] O-RAN + adaptive optimiza- Investigated drift handling and online resource scheduling in O-RAN to reduce service-level-agreement tion violations, improve resource utilization, and adapt to time-varying network conditions/states. [28], [29] Wireless/model drift detec- Developed drift detection and online adaptation methods for wireless receivers or 6G AI/ML models tion under channel variation, data drift, label drift, or concept drift. STEPS (our Semantic contract + adaptive Introduced semantic contract as an executable interface between natural language requests and edge method) edge scheduling service scheduling, enabling contract-guided scheduling and fulfillment-driven adaptive optimization.
actions, or scheduling directives. As a result, they provide limited support for representing user requests as uncertaintyaware semantic requirements that can be directly incorporated into resource-constrained optimization. In contrast, our work introduces semantic contracts as executable interfaces between user-side semantics and edge-side scheduling decisions, enabling interpretable semantic grounding, contract-guided optimization, and fulfillment-driven adaptation within a unified framework. (ii) Edge AI Service Scheduling and Provisioning: Edge intelligence have been widely studied to support latencysensitive and computation-intensive AI services by bringing computation closer to end users. With the rapid development of generative AI and foundation models, edge networks are increasingly regarded as key infrastructure for delivering realtime and personalized AI services under limited communication and computing resources [2], [21]–[23]. Consequently, a significant body of research has focused on how to efficiently schedule AI workloads across devices, edge servers, and cloud resources. In particular, to improve service efficiency under resource constraints, existing studies have explored a variety of edge-AI scheduling and orchestration mechanisms, including model placement and partitioning, inference offloading, model compression and quantization, and communicationcomputation co-design. For example, Li and Bi [17] jointly optimized AI model partitioning and wireless resource allocation for device-edge collaborative inference. Xiao et al. [24] studied a content-aware compression and offloading framework for efficient edge-based vision inference. Zhang et al. [25] investigated resource-efficient deployment of generative LLM inference at the network edge by jointly optimizing quantization and resource scheduling under heterogeneous latency and accuracy requirements. Although these studies provide effective solutions for edge-AI services, they generally assume that service requirements are explicitly stated and available in the form of explicit numerical specifications, such as latency bounds, accuracy targets, energy budgets, or resource limits. This assumption is restrictive in natural-
language-driven E4NetAI, where user requests are often expressed through qualitative and ambiguous descriptions rather than numerical parameters. In contrast, our work explicitly addresses the semantic-to-optimization gap by transforming natural-language requests into semantic contracts that directly guide resource-constrained service provisioning at the network edge. (iii) Drift-Aware and Adaptive Optimization: Adaptive optimization, online learning, and drift-aware response adaptation have attracted growing attention in non-stationary learning and networked systems. The common objective of these approaches is to detect changes in system behavior and subsequently adapt learning models or control policies to maintain performance over time. In this domain, existing studies primarily focus on observable changes in data distributions, model performance, network conditions, or resource states. For example, Ganguly and Aggarwal [26] developed an online federated learning framework integrating drift detection, adaptive updating, and multi-scale learning to improve performance under concept drift. Gudepu et al. [27] proposed a driftmanagement framework for Open Radio Access Network (O-RAN), that incorporates drift detection, drift analysis, and adaptive mitigation mechanisms to reduce service-levelagreement violations and improve resource utilization. Kalntis et al. [16] studied adaptive service provisioning for virtualized base stations in O-RAN with online learning, where resourcecontrol decisions are updated according to time-varying network conditions/states. Uzlaner et al. [28] developed a modular drift-detection framework that determines when and which components of a deep learning-based receiver should be retrained under dynamic channel conditions. Ameur et al. [29] further designed a dual self-attention mechanism for detecting data drift, label drift, and concept drift in 6G networks. Although these studies enhance robustness and adaptability in non-stationary environments, their considered adaptation signals are predominantly derived from observable system characteristics, such as data distributions, model performance, channel conditions, and network states. In contrast, natural-
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𝑒 𝑗 ∈ E denotes an ES. For 𝑒 𝑗 , we let 𝐹 𝑗(𝑡 ) and 𝐵 (𝑡𝑗 ) denote its available computing capacity and bandwidth capacity at timeslot 𝑡, respectively. For UD side, we use 𝐹𝑖loc, (𝑡 ) to denote the local computing capacity of UD 𝑢 𝑖 . Besides, each EN is associated with a trustworthiness-for-execution (T4E) edge, (𝑡 ) score, where 𝜎 𝑗 ∈ [0, 1] denotes the T4E score of
Fig. 1. STEPS framework for natural-language-driven E4NetAI. Naturallanguage service requests are first transformed into semantic contracts, which then guide edge scheduling. Execution feedback further drives fulfillmentaware adaptive parameter updates for subsequent scheduling rounds.
language-driven E4NetAI introduces an additional source of non-stationarity arising from evolving user semantics and their resulting fulfillment outcomes. Consequently, the impact of semantic-request drift (i.e., changes in the characteristics and expectations expressed in user requests) and fulfillment drift (i.e., changes in contract-satisfaction outcomes caused by variations in execution conditions) remains largely unexplored. Our work addresses this gap by jointly modeling semanticrequest drift, fulfillment drift, and instantaneous fulfillment pressure, and leveraging these signals to drive fulfillmentaware scheduling adaptation. III. S EMANTIC -C ONTRACT S YSTEM M ODEL AND P ROBLEM F ORMULATION As illustrated in Fig. 1, STEPS operates over a time-varying E4NetAI system, operating over a time-slotted horizon T = {1, 2, . . . , 𝑇 }. At each timeslot U (𝑡 ) , the edge service platform (ESP) observes the system context and receives user device (UD) requests characterized by task attributes and naturallanguage service descriptions. The descriptions are parsed into semantic service levels with associated confidence, and further instantiated as semantic contracts capturing user preferences, fulfillment bounds, and semantic uncertainty. The contracts are subsequently calibrated under uncertainty and incorporated into edge execution decisions. Based on this semantic-contract framework, this section presents the system model, defines the service metrics, and formulates the long-term contract-guided scheduling problem. A. Time-Slotted Edge Service Platform We consider an ESP formed by a set of geographically distributed edge servers (ESs), denoted by E = {𝑒 1 , 𝑒 2 , . . . , 𝑒 | E | }, which collaboratively deliver E4NetAI services. To account for network dynamics, at each timeslot 𝑡 ∈ T , we use U (𝑡 ) to denote the set of UDs that submit service requests to the platform. Upon receiving a request, the platform determines whether the associated task should be executed locally by the originating UD or delegated to an ES for remote execution. To facilitate analysis, we rename all the UDs and ESs as execution nodes (ENs) collected by E0 = {𝑒 0 } ∪ E, where 𝑒 0 denotes local execution at the requesting UD and each
loc, (𝑡 ) 𝑒 𝑗 , while 𝜎𝑖,0 ∈ [0, 1] represents that the local one of UD 𝑢 𝑖 ’s device. Note that a larger value indicates a stronger capability of satisfying T4E requirements1 . The system-side context observed at timeslot 𝑡 is denoted by 𝜉 (𝑡 ) , which may include edge loads, queue states, wireless channel states, available resources, corresponding prices, and historical fulfillment records. This context is maintained by the ESP rather than provided by UDs, and is used for semantic-contract generation, contract-guided scheduling, and adaptive optimization.
B. Natural-Language Request and Semantic Contract At each timeslot 𝑡, each UD 𝑢 𝑖 ∈ U (𝑡 ) submits a service request consisting of a task attribute vector 𝑞 𝑖(𝑡 ) and its associated service-expectation description (SED) L𝑖(𝑡 ) , represented by (𝑞 𝑖(𝑡 ) , L𝑖(𝑡 ) ). The task attribute vector is defined as 𝑞 𝑖(𝑡 ) = (𝑑𝑖(𝑡 ) , 𝑐 𝑖(𝑡 ) ), where 𝑑𝑖(𝑡 ) denotes the input data size and 𝑐 𝑖(𝑡 ) denotes the computation workload required for task completion. Together, they characterize the basic resource demand of service. The SED L𝑖(𝑡 ) expresses user service expectations at a semantic level. Rather than specifying low-level operational parameters, users describe their expected service outcomes, such as “I do not have much time and budget", "my phone is running out of power". Unlike conventional edge scheduling frameworks that rely on user-specified numerical constraints and preference parameters, this formulation uses SEDs as the user-side semantic input and leaves their conversion into operational requirements to the semantic-contract interface. Specifically, the SED L𝑖(𝑡 ) is processed by an LLM-assisted semantic parser, which does not directly output continuous resource parameters or scheduling actions. Rather, it extracts semantic service levels and parsing confidence, represented (𝑡 ) ), where ℓ𝑖D, (𝑡 ) , as y𝑖(𝑡 ) = (ℓ𝑖D, (𝑡 ) , ℓ𝑖E, (𝑡 ) , ℓ𝑖M, (𝑡 ) , ℓ𝑖S, (𝑡 ) , 𝑐conf, 𝑖 S, (𝑡 ) M, (𝑡 ) E, (𝑡 ) denote the delay-sensitivity level, ℓ𝑖 , ℓ𝑖 , and ℓ𝑖 energy-sensitivity level, monetary-cost sensitivity level, and (𝑡 ) T4E requirement level, respectively. The term 𝑐conf, ∈ [0, 1] 𝑖 represents the parsing confidence score. In this way, the LLM is constrained to semantic interpretation, while the extracted levels and confidence scores are converted into optimizationcompatible contract parameters through interpretable mapping rules. As one unique aspects, we design semantic contract, as the key interface that converts parsed natural language semantics into optimization-compatible service requirements. Based on the semantic feature vector y𝑖(𝑡 ) , task attributes 𝑞 𝑖(𝑡 ) , and system-side context 𝜉 (𝑡 ) , the ESP generates a semantic contract for UD 𝑢 𝑖 at timeslot 𝑡 as C𝑖(𝑡 ) = Fsc (y𝑖(𝑡 ) , 𝑞 𝑖(𝑡 ) ; 𝜉 (𝑡 ) ) = (w𝑖(𝑡 ) , g𝑖(𝑡 ) , 𝜌𝑖(𝑡 ) ), where Fsc (·) denotes the semantic-contract generation function. The semantic contract C𝑖(𝑡 ) consists of three components: preferences w𝑖(𝑡 ) , fulfillment bounds g𝑖(𝑡 ) , 1 In this paper, trust is not modeled as a standalone security subsystem; instead, it is incorporated as one dimension of semantic-contract fulfillment during task execution.
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and semantic uncertainty 𝜌𝑖(𝑡 ) . The LLM-assisted parser only extracts semantic levels and parsing confidence, while all continuous contract parameters are generated by interpretable mapping rules that incorporate task attributes and system-side context. This design avoids directly asking the LLM to output physically constrained resource scheduling parameters. In particular, the preference vector w𝑖(𝑡 ) = D, (𝑡 ) E, (𝑡 ) M, (𝑡 ) S, (𝑡 ) [𝑤 𝑖 , 𝑤𝑖 , 𝑤𝑖 , 𝑤𝑖 ] specifies what UD cares about in scheduling, where the four elements represent the relative importance of delay, energy consumption, monetary cost, and T4E, respectively. Let ℓˆ𝑖k, (𝑡 ) ∈ [0, 1] denote the normalized semantic level of dimension 𝑘 ∈ {D, E, M, S}. The preference weights are generated as (𝑡 ) 𝑤 k, =Í 𝑖
exp(𝜃 𝑤 ℓˆ𝑖k, (𝑡 ) ) ˆr, (𝑡 ) ) r∈ {D,E,M,S} exp(𝜃 𝑤 ℓ𝑖
,
k ∈ {D, E, M, S}. (1)
The parameter 𝜃 𝑤 ≥ 0 controls the sensitivity of preference Í (𝑡 ) differentiation. These weights satisfy 𝑘 ∈ {D,E,M,S} 𝑤 k, = 𝑖 (𝑡 ) k, (𝑡 ) = ≥ 0. The fulfillment-bound vector g𝑖 1 and 𝑤 𝑖 max, (𝑡 ) min, (𝑡 ) max, (𝑡 ) (𝑡 ) ] specifies what must be , 𝑆 , 𝑀 , 𝐸 [𝐷 max, 𝑖 𝑖 𝑖 𝑖 (𝑡 ) , 𝐸 𝑖max, (𝑡 ) , fulfilled during service execution. Here, 𝐷 max, 𝑖 𝑀𝑖max, (𝑡 ) , and 𝑆𝑖min, (𝑡 ) denote the maximum tolerable delay, maximum tolerable energy consumption, maximum acceptable monetary cost, and minimum T4E level, respectively. Before generating these bounds, the ESP obtains lightweight reference service indicators under the current context, denoted by 𝐷¯ 𝑖(𝑡 ) , 𝐸¯ 𝑖(𝑡 ) , 𝑀¯ 𝑖(𝑡 ) , and 𝑆¯𝑖(𝑡 ) . These reference indicators are pre-scheduling estimates of the service metrics defined in Sec. III-C, and can be computed using a default policy 𝜋 ref , such as local execution, nearest-edge execution, or historical average execution under 𝜉 (𝑡 ) . They are not post-execution observations and therefore do not introduce circular dependence. Then, the fulfillment bounds are generated as (𝑡 ) 𝐷 max, = 𝐷¯ 𝑖(𝑡 ) 𝛿D ( ℓˆ𝑖D, (𝑡 ) ), 𝑖 𝑀 max, (𝑡 ) = 𝑀¯ (𝑡 ) 𝛿M ( ℓˆM, (𝑡 ) ),
𝐸 𝑖max, (𝑡 ) = 𝐸¯ 𝑖(𝑡 ) 𝛿E ( ℓˆ𝑖E, (𝑡 ) ), 𝑆𝑖min, (𝑡 ) = [𝑆0 + 𝛿S ℓˆ𝑖S, (𝑡 ) ] 10 . 𝑖 𝑖 𝑖 (2) Here, [𝑥] 10 = min{max{𝑥, 0}, 1} denotes the projection of 𝑥 onto [0, 1]. The functions 𝛿D (·), 𝛿E (·), and 𝛿M (·) are nonincreasing mapping functions. For example, a higher delaysensitivity level leads to a smaller 𝛿D ( ℓˆ𝑖D, (𝑡 ) ) and hence a tighter delay bound2 . The semantic uncertainty 𝜌𝑖(𝑡 ) ∈ [0, 1] measures how reliable and context-compatible the semantic interpretation is. It jointly captures parsing unreliability of the SED and context inconsistency of the corresponding service request: h i1 (𝑡 ) 𝜌𝑖(𝑡 ) = 𝛼𝑐 (1 − 𝑐conf, ) + 𝛼 𝑥 𝑟 𝑖ctx, (𝑡 ) , (3) 𝑖 0
where 𝛼𝑐 ≥ 0 and 𝛼 𝑥 ≥ 0 are weighting coefficients, and 𝑟 𝑖ctx, (𝑡 ) ∈ [0, 1] denotes the context-inconsistency risk. A larger 𝜌𝑖(𝑡 ) indicates that the request is more uncertain or less compatible with the current system state. To make the context-
inconsistency risk computable, we define h i1 𝑟 𝑖ctx, (𝑡 ) = 𝜔D 𝜈𝑖D, (𝑡 ) + 𝜔E 𝜈𝑖E, (𝑡 ) + 𝜔M 𝜈𝑖M, (𝑡 ) + 𝜔S 𝜈𝑖S, (𝑡 ) , 0 (4) where 𝜔D , 𝜔E , 𝜔M , 𝜔S ≥ 0 are weighting coefficients. The mismatch terms are given by # #+ " (𝑡 ) " (𝑡 ) (𝑡 ) + 𝐸¯ 𝑖 − 𝐸 𝑖max, (𝑡 ) 𝐷¯ 𝑖 − 𝐷 max, D, (𝑡 ) E, (𝑡 ) 𝑖 𝜈𝑖 , 𝜈𝑖 , = = (𝑡 ) 𝐷 max, 𝐸 𝑖max, (𝑡 ) 𝑖 #+ " (𝑡 ) h i+ 𝑀¯ 𝑖 − 𝑀𝑖max, (𝑡 ) M, (𝑡 ) S, (𝑡 ) min, (𝑡 ) ¯ (𝑡 ) . 𝜈𝑖 , 𝜈 = = 𝑆 − 𝑆 𝑖 𝑖 𝑖 𝑀𝑖max, (𝑡 ) (5) Here, [𝑥] + = max{𝑥, 0}. Therefore, 𝑟 𝑖ctx, (𝑡 ) becomes large when the SED implies stringent service requirements that are difficult to satisfy under the current network and edgeresource state. Due to the inherent ambiguity and contextual variability of natural-language requests, semantic contracts are calibrated before scheduling. Let 𝛽 (𝑡 ) ≥ 0 denote the conservativeness factor at timeslot 𝑡, where larger values imply more conservative fulfillment bounds. These calibrated bounds do not represent the users’ original service intents, but rather scheduling-stage safety margins introduced to mitigate semantic uncertainty. Execution is still evaluated using the original semantic contract g𝑖(𝑡 ) . For each UD 𝑢 𝑖 , we define the calibrated fulfillment bounds as emax, (𝑡 ) = 𝐷 𝑖 e max, (𝑡 ) = 𝑀 𝑖
(𝑡 ) 𝐷 max, 𝑖
, (𝑡 )
1 + 𝛽 (𝑡 ) 𝜌𝑖
𝑀𝑖max, (𝑡 ) 1 + 𝛽 (𝑡 ) 𝜌𝑖(𝑡 )
,
e𝑖 max, (𝑡 ) = 𝐸
𝐸 𝑖max, (𝑡 ) 1 + 𝛽 (𝑡 ) 𝜌𝑖(𝑡 )
,
𝑆e𝑖min, (𝑡 ) = [𝑆𝑖min, (𝑡 ) + 𝛽 (𝑡 ) 𝜌𝑖(𝑡 ) ] 10 .
(6) e max, (𝑡 ) , and 𝑆emin, (𝑡 ) are the emax, (𝑡 ) , 𝑀 emax, (𝑡 ) , 𝐸 Here, 𝐷 𝑖 𝑖 𝑖 𝑖 scheduling-stage delay, energy, monetary-cost, and T4E bounds, respectively. When the semantic uncertainty 𝜌𝑖(𝑡 ) is high, the system tightens delay, energy, and cost planning bounds and raises the T4E requirement, thereby reserving a larger safety margin for execution. We further define a semantic admission threshold 𝜏 𝜌, (𝑡 ) ∈ [0, 1], which specifies the maximum acceptable semantic uncertainty at timeslot 𝑡. Let schedulable UD set be U s, (𝑡 ) = {𝑢 𝑖 ∈ U (𝑡 ) | 𝜌𝑖(𝑡 ) ≤ 𝜏 𝜌, (𝑡 ) }, and only UDs in U s, (𝑡 ) can participate in the subsequent contract-guided scheduling process. To avoid overstating fulfillment performance by simply filtering uncertain requests, the evaluation will explicitly report the semantic admission ratio together with execution metrics. Apparently, if U s, (𝑡 ) = ∅, no scheduling is performed in timeslot 𝑡. C. Edge Execution and Contract-Guided Service Loss For each UD 𝑢 𝑖 ∈ U s, (𝑡 ) , we define a binary EN selection variable 𝑥𝑖,(𝑡𝑗) ∈ {0, 1}, where 𝑥 𝑖,(𝑡𝑗) = 1 indicates that UD 𝑢 𝑖 ’s task is executed at EN 𝑒 𝑗 ∈ E0 , and we have ∑︁ 𝑥 𝑖,(𝑡𝑗) = 1, ∀𝑢 𝑖 ∈ U s, (𝑡 ) . (7) 𝑒 𝑗 ∈ E0
2 In experiments, these mapping functions can be implemented by fixed
lookup tables corresponding to low, medium, and high semantic levels.
For each ES 𝑒 𝑗 ∈ E, 𝑓𝑖,(𝑡𝑗) ≥ 0 and 𝑏 𝑖,(𝑡 𝑗) ≥ 0 denote computing and bandwidth resources allocated to UD 𝑢 𝑖 , respectively. The
7
edge capacity constraints in a centralized formulation are ∑︁ ∑︁ 𝑥𝑖,(𝑡𝑗) 𝑓𝑖,(𝑡𝑗) ≤ 𝐹 𝑗(𝑡 ) , 𝑥 𝑖,(𝑡𝑗) 𝑏 𝑖,(𝑡 𝑗) ≤ 𝐵 (𝑡𝑗 ) , ∀𝑒 𝑗 ∈ E. (8) 𝑢𝑖 ∈ U s, (𝑡 )
Besides, the resource constraints are 𝑥 𝑖,(𝑡𝑗) 𝑓min ≤ 𝑓𝑖,(𝑡𝑗) ≤ 𝑥𝑖,(𝑡𝑗) 𝐹 𝑗(𝑡 ) , 𝑥𝑖,(𝑡𝑗) 𝑏 min ≤ 𝑏 𝑖,(𝑡 𝑗) ≤ 𝑥𝑖,(𝑡𝑗) 𝐵 (𝑡𝑗 ) , (𝑡 ) loc (𝑡 ) (𝑡 ) loc, (𝑡 ) (𝑡 ) 𝑥 𝑖,0 𝑓min ≤ 𝑓𝑖,0 ≤ 𝑥𝑖,0 𝐹𝑖 , 𝑏 𝑖,0 = 0,
(9)
loc are minimum nonzero resource where 𝑓min , 𝑏 min , and 𝑓min packages. When 𝑥𝑖,(𝑡𝑗) = 0, both the lower and upper bounds force the corresponding resource scheduling to zero; when 𝑥𝑖,(𝑡𝑗) = 1, the allocated resources are strictly positive. This avoids undefined delay or rate expressions for selected ENs. For edge execution, the uplink transmission rate between UD 𝑢 𝑖 and ES 𝑒 𝑗 is during timeslot 𝑡
𝑝 𝑖(𝑡 ) ℎ𝑖,(𝑡 𝑗) ª © 𝑅𝑖,(𝑡𝑗) = 𝑏 𝑖,(𝑡 𝑗) log2 1 + ®, 𝑁0 𝑏 𝑖,(𝑡 𝑗) ¬ «
if 𝑥𝑖,(𝑡𝑗) = 1.
(10)
Here, 𝑝 𝑖(𝑡 ) denotes the transmit power of UD 𝑢 𝑖 , ℎ𝑖,(𝑡 𝑗) shows the channel gain, and 𝑁0 is the noise power spectral density. To keep the service metrics well-defined only on the selected EN, we define the total service delay directly as 𝑐 𝑖(𝑡 ) (𝑡 ) 𝑓𝑖,0 +𝜖
+
(𝑡 ) 𝑐 (𝑡 ) © 𝑑 ª 𝑥𝑖,(𝑡𝑗) (𝑡 )𝑖 + (𝑡 )𝑖 + 𝑄 (𝑡𝑗 ) ® , 𝑅 +𝜖 𝑓𝑖, 𝑗 + 𝜖 𝑒𝑗 ∈E « 𝑖, 𝑗 ¬
∑︁
(11) where 𝜖 > 0 is a sufficiently small constant for numerical stability, and 𝑄 (𝑡𝑗 ) denotes the pre-decision queueing delay observed at ES 𝑒 𝑗 at the beginning of timeslot 𝑡. The small constant 𝜖 does not affect the physical interpretation because selected actions always satisfy positive minimum resourcepackage constraints. For local execution, the energy consump(𝑡 ) 2 ) , where 𝜅𝑢 is the effective tion is modeled as 𝜅 𝑢 𝑐 𝑖(𝑡 ) ( 𝑓𝑖,0 switched-capacitance coefficient of UD 𝑢 𝑖 ’s device. While energy consumption of edge execution is mainly caused by uplink transmission. Thus, the total energy consumption is (𝑡 ) 2 (𝑡 ) 𝐸 𝑖(𝑡 ) = 𝑥𝑖,0 𝜅 𝑢 𝑐 𝑖(𝑡 ) ( 𝑓𝑖,0 ) +
∑︁ 𝑒𝑗 ∈ E
(𝑡 ) (𝑡 ) (𝑡 ) 𝑝 𝑖 𝑑 𝑖
𝑥 𝑖, 𝑗
𝑅𝑖,(𝑡𝑗) + 𝜖
.
(12)
(𝑡 ) Besides, 𝜆f,𝑗 (𝑡 ) and 𝜆b, denote the unit prices of com𝑗 puting and bandwidth resources at ES 𝑒 𝑗 , respectively, which are treated as system-side scheduling parameters at timeslot 𝑡. The monetary cost of UD 𝑢 𝑖 is 𝑀𝑖(𝑡 ) = Í (𝑡 ) f, (𝑡 ) (𝑡 ) (𝑡 ) (𝑡 ) 𝑓𝑖, 𝑗 + 𝜆b, 𝑏 𝑖, 𝑗 . Finally, the achieved T4E 𝑒 𝑗 ∈ E 𝑥 𝑖, 𝑗 𝜆 𝑗 𝑗 edge, (t) (𝑡 ) (𝑡 ) loc, (t) Í level of UD 𝑢 𝑖 is 𝑆𝑖 = 𝑥𝑖,0 𝜎𝑖,0 + 𝑒 𝑗 ∈ E 𝑥𝑖,(𝑡𝑗) 𝜎 𝑗 . Here, edge, (t)
emax, (𝑡 ) (1 + 𝑧 D, (𝑡 ) ), 𝐷 𝑖(𝑡 ) ≤ 𝐷 𝑖 𝑖 e max, (𝑡 ) (1 + 𝑧 M, (𝑡 ) ), 𝑀𝑖(𝑡 ) ≤ 𝑀 𝑖 𝑖
𝑢𝑖 ∈ U s, (𝑡 )
(𝑡 ) 𝐷 𝑖(𝑡 ) = 𝑥 𝑖,0
These variables satisfy
𝜎𝑗 is interpreted as T4E score maintained by the ESP based on historical service fulfillment, EN availability, and audit records, rather than as a standalone security subsystem. These service metrics provide the physical execution outcomes against which semantic contracts will be evaluated. The semantic contract specifies both preferences and fulfillment bounds. To characterize possible violations of calibrated fulfillment bounds during scheduling, we introduce nonnega(𝑡 ) (𝑡 ) (𝑡 ) (𝑡 ) tive slack variables 𝑧D, , 𝑧 E, , 𝑧 M, , and 𝑧S, for delay, 𝑖 𝑖 𝑖 𝑖 energy consumption, monetary cost, and T4E, respectively.
emax, (𝑡 ) (1 + 𝑧 E, (𝑡 ) ), 𝐸 𝑖(𝑡 ) ≤ 𝐸 𝑖 𝑖 𝑆emin, (𝑡 ) − 𝑆 (𝑡 ) ≤ 𝑧S, (𝑡 ) . 𝑖
𝑖
(13)
𝑖
Accordingly, the semantic-contract violation degree is defined (𝑡 ) (𝑡 ) (𝑡 ) (𝑡 ) (𝑡 ) as Ωsc, = 𝜁D 𝑧D, + 𝜁E 𝑧 E, + 𝜁M 𝑧M, + 𝜁S 𝑧S, , where 𝜁D , 𝑖 𝑖 𝑖 𝑖 𝑖 𝜁E , 𝜁M , and 𝜁S are nonnegative violation weights. Based on the calibrated semantic contract, the contract-guided service loss of UD 𝑢 𝑖 at timeslot 𝑡 is formulated as (𝑡 ) 𝐽𝑖(𝑡 ) = 𝑤 D, 𝑖
(𝑡 ) E, (𝑡 ) 𝐸 𝑖 + 𝑤 𝑖 emax, (𝑡 ) emax, (𝑡 ) 𝐷 𝐸
𝐷 𝑖(𝑡 )
𝑖
(𝑡 ) + 𝑤 M, 𝑖
𝑖
(14)
𝑀𝑖(𝑡 )
(𝑡 ) (𝑡 ) + 𝑤 S, (1 − 𝑆𝑖(𝑡 ) ) + 𝜂Ωsc, , 𝑖 𝑖 max, (𝑡 ) e 𝑀𝑖
where 𝜂 ≥ 0 is the weight of semantic-contract violation. The first three terms quantify normalized delay, energy, and monetary cost, the fourth term measures the soft loss caused by insufficient T4E, and the last term penalizes fulfillmentbound violations. D. Problem Formulation (𝑡 ) E, (𝑡 ) M, (𝑡 ) S, (𝑡 ) ⊤ ] denote the , 𝑧𝑖 , 𝑧𝑖 , 𝑧𝑖 Let z𝑖(𝑡 ) = [𝑧 D, 𝑖 semantic-contract violation vector of UD 𝑢 𝑖 at timeslot 𝑡. We formulate the long-term semantic-contract-guided scheduling problem as problem P: 𝑇
P: s.t.
1 ∑︁ {x (𝑡 ) ,f (𝑡 ) ,b (𝑡 ) ,z (𝑡 ) }𝑡 ∈T 𝑇 𝑡=1 min
∑︁
𝐽𝑖(𝑡 )
(7) holds for task assignment, (8), (9) hold for resource feasibility, (13) holds for calibrated contract fulfillment, 𝑥𝑖,(𝑡𝑗) ∈ {0, 1}, z𝑖(𝑡 ) ⪰ 0,
(15)
𝑢𝑖 ∈ U s, (𝑡 )
(15a) (15b) (15c)
∀𝑢 𝑖 ∈ U s, (𝑡 ) , ∀𝑒 𝑗 ∈ E0 , ∀𝑡 ∈ T , (15d)
∀𝑢 𝑖 ∈ U s, (𝑡 ) , ∀𝑡 ∈ T .
(15e)
In P, the objective minimizes the time-average contractguided service loss of all UDs 𝑢 𝑖 ∈ U s, (𝑡 ) over the whole time horizon. Constraint (15a) represents the task-assignment requirement, ensuring that each schedulable task is assigned to exactly one EN, either the local device or one ES. Constraint (15b) collects the resource-feasibility requirements, including edge-capacity limits and resource-selection coupling. Specifically, the edge-capacity constraint in (8) ensures that the aggregate computing and bandwidth demands at each ES do not exceed its available capacities, while the coupling constraint in (9) guarantees that resources are allocated only to selected ENs. Constraint (15c) enforces calibrated semanticcontract fulfillment, where the slack vector z𝑖(𝑡 ) quantifies possible violations of delay, energy-consumption, monetarycost, and T4E bounds. Constraints (15d) and (15e) specify the binary EN selection variables and the nonnegative violation vector, respectively. Problem P represents a long-term mixed-integer nonlinear optimization problem due to binary EN selection, coupled communication-computation service provision, and nonlinear delay-rate relationships. Therefore, directly solving P is challenging, motivating the STEPS developed next.
8
IV. D ESIGN OF STEPS In this section, we introduce STEPS, an online distributed framework for semantic-contract-guided edge scheduling. STEPS decomposes the long-term stochastic problem into perslot decisions. In each timeslot, a UD is referred to as an admitted UD if its natural-language service request passes semantic admission and is allowed to enter the subsequent edge scheduling stage. Each admitted UD then determines its EN and resource configuration according to its semantic contract and the instantaneous edge congestion state. The resulting execution outcomes are then fed back to adapt semantic admission, contract conservativeness, resource-price coordination, and edge coordination gain. In this manner, STEPS establishes a closed-loop framework that integrates semantic-contract generation, distributed edge scheduling, and fulfillment-driven adaptive optimization. A. Per-Slot Penalized Surrogate and Potential Game Directly solving P over the entire time horizon requires future information on UDs’ requests, wireless channels, edge workloads, and resource availability, as well as centralized coordination across all UDs and ESs. This is impractical for online E4NetAI systems with time-varying service demands and resource states [17], [25]. Accordingly, STEPS adopts a slot-wise online decision structure based only on the currently observed system state. Given the current state, each UD’s direct service loss can be determined by its own EN and resource-package decision, while competition among UDs for limited resources is captured through ES-side congestion penalties. In this way, the capacity coupling among UDs is transformed into a penalized surrogate form that can be locally perceived and distributedly optimized, following the principle of congestion games and resource pricing [30], [31]. To further support distributed implementation with finite action spaces, computing and bandwidth resources are discretized into finite resource packages [25]. Each UD 𝑢 𝑖 ∈ U s, (𝑡 ) first selects an intended EN and the corresponding resource-package combination according to its semantic contract and the current system state. The ESP then performs the final feasibility check and allocation realization based on the actual resource capacities and possible conflicts. Based on this modeling, we next define the feasible action space of each UD and construct the per-slot potential game. Definition 1. (Action Space of UDs in STEPS) For each UD 𝑢 𝑖 ∈ U s, (𝑡 ) , its action is denoted by 𝑎 𝑖(𝑡 ) = (𝑒 𝑖(𝑡 ) , 𝑟 𝑖f, (𝑡 ) , 𝑟 𝑖b, (𝑡 ) ), where 𝑒 𝑖(𝑡 ) ∈ E0 is the selected EN, 𝑟 𝑖f, (𝑡 ) is the intended computing-resource package, and 𝑟 𝑖b, (𝑡 ) is the intended bandwidth-resource package. Since local execution does not consume uplink bandwidth to an ES, the feasible action space is defined as edge, (𝑡 )
A𝑖(𝑡 ) = A𝑖loc, (𝑡 ) ∪ A𝑖
,
(16) edge, (𝑡 )
where A𝑖loc, (𝑡 ) = {(𝑒 0 , 𝑟 f , 0) | 𝑟 f ∈ R 𝑖loc,f, (𝑡 ) }, and A𝑖 = f, (𝑡 ) b, (𝑡 ) loc,f, (𝑡 ) f b f b {(𝑒 𝑗 , 𝑟 , 𝑟 ) | 𝑒 𝑗 ∈ E, 𝑟 ∈ R 𝑖, 𝑗 , 𝑟 ∈ R 𝑖, 𝑗 }. Here, R 𝑖 , R 𝑖,f, (𝑡𝑗 ) , and R 𝑖,b,𝑗(𝑡 ) are finite resource-package sets. Each action 𝑎 𝑖(𝑡 ) can be mapped to the EN selection variable 𝑥 𝑖,(𝑡𝑗) and the intended resource-package values.
Given an action profile a (𝑡 ) = (𝑎 𝑖(𝑡 ) )𝑢𝑖 ∈ U s, (𝑡 ) , the intended computing and bandwidth loads of ES 𝑒 𝑗 as ∑︁ 𝐿 f,𝑗 (𝑡 ) (a (𝑡 ) ) = 1{𝑒 𝑖(𝑡 ) = 𝑒 𝑗 }𝑟 𝑖f, (𝑡 ) , 𝑢𝑖 ∈ U s, (𝑡 )
∑︁
(𝑡 ) (𝑡 ) 𝐿 b, (a ) = 𝑗
(17)
1{𝑒 𝑖(𝑡 ) = 𝑒 𝑗 }𝑟 𝑖b, (𝑡 ) .
𝑢𝑖 ∈ U s, (𝑡 )
where 1{·} is the indicator function. For each candidate action, STEPS evaluates how well the resulting service outcome matches the calibrated semantic contract. Specifically, the action-dependent slack terms are computed as " (𝑡 ) 𝑧 D, (𝑎 𝑖 ) = 𝑖
emax, (𝑡 ) 𝐷 𝑖 "
(𝑡 ) 𝑧 M, (𝑎 𝑖 ) = 𝑖
𝐷 𝑖(𝑡 ) (𝑎 𝑖 ) 𝑀𝑖(𝑡 ) (𝑎 𝑖 ) e max, (𝑡 ) 𝑀 𝑖
#+ −1 #+ −1
" (𝑡 ) , 𝑧E, (𝑎 𝑖 ) = 𝑖
𝐸 𝑖(𝑡 ) (𝑎 𝑖 ) emax, (𝑡 ) 𝐸 𝑖
#+ −1
,
h i+ (𝑡 ) , 𝑧S, (𝑎 𝑖 ) = 𝑆e𝑖min, (𝑡 ) −𝑆𝑖(𝑡 ) (𝑎 𝑖 ) . 𝑖
(18) The corresponding action-dependent semantic-contract viola(𝑡 ) (𝑡 ) (𝑡 ) tion degree is Ωsc, (𝑎 𝑖 ) = 𝜁D 𝑧 D, (𝑎 𝑖 ) + 𝜁E 𝑧E, (𝑎 𝑖 ) + 𝑖 𝑖 𝑖 S, (𝑡 ) (𝑡 ) (𝑎 ). This design avoids introducing (𝑎 ) + 𝜁 𝑧 𝜁M 𝑧 M, 𝑖 𝑖 S 𝑖 𝑖 separate continuous slack variables inside the finite game. Based on the above action-dependent quantities, the contractguided service loss of UD 𝑢 𝑖 is defined as (𝑡 ) 𝐻𝑖(𝑡 ) (𝑎 𝑖(𝑡 ) ) = 𝑤 D, 𝑖
(𝑡 ) + 𝑤 M, 𝑖
𝑀𝑖(𝑡 ) (𝑎 𝑖(𝑡 ) ) e max, (𝑡 ) 𝑀 𝑖
𝐷 𝑖(𝑡 ) (𝑎 𝑖(𝑡 ) ) emax, (𝑡 ) 𝐷 𝑖
(𝑡 ) + 𝑤 E, 𝑖
𝐸 𝑖(𝑡 ) (𝑎 𝑖(𝑡 ) ) emax, (𝑡 ) 𝐸 𝑖
(𝑡 ) (𝑡 ) + 𝑤 S, 1 − 𝑆𝑖(𝑡 ) (𝑎 𝑖(𝑡 ) ) + 𝜂Ωsc, (𝑎 𝑖(𝑡 ) ). 𝑖 𝑖
(19) Here, the first four terms evaluate delay, energy consumption, monetary cost, and T4E fulfillment under the semantic contract, while the last term penalizes explicit contract violation. The above service loss captures the UD-side semantic objective. To further discourage excessive concentration of UDs on the same ES, we introduce edge-side congestion penalties. Unlike capacity constraints, these penalties can be evaluated locally from aggregate intended loads and can therefore be incorporated into distributed best-response updates. For 𝑒 𝑗 , the resource congestion penalties are defined as 2 2 𝛾b 𝐿 b, (𝑡 ) − 𝜚 f , Γ 𝑗 (𝐿) = (𝑡 ) − 𝜚 b , (𝑡 ) 2 𝐹𝑗 𝐵𝑗 + +
𝛾 Γf,𝑗 (𝑡 ) (𝐿) = f 2
𝐿
(20) where [𝑥] + = max{𝑥, 0}, 𝛾f and 𝛾b are nonnegative penalty coefficients, and 𝜚f , 𝜚b ∈ (0, 1] are target utilization thresholds. When 𝜚 f = 𝜚b = 1, the penalty is activated only after overload. When 𝜚f and 𝜚b are smaller than one, the system proactively discourages high-utilization ESs before hard overload occurs. With the user-side loss and edge-side congestion terms in place, we can now formalize the per-slot distributed scheduling interaction as a game. Definition 2. (Contract-Guided Scheduling Game) At each timeslot 𝑡, the contract-guided scheduling game is defined as G (𝑡 ) = U s, (𝑡 ) , {A𝑖(𝑡 ) }𝑢𝑖 ∈ U s, (𝑡 ) , {J𝑖 (𝑡 ) }𝑢𝑖 ∈ U s, (𝑡 ) , (21) where U s, (𝑡 ) is the player set, A𝑖(𝑡 ) is the finite action set of UD 𝑢 𝑖 , and J𝑖 (𝑡 ) is the scheduling cost of UD 𝑢 𝑖 .
9
For a given action profile, the scheduling cost of UD 𝑢 𝑖 is J𝑖
(𝑡 )
(𝑡 ) (𝑎 𝑖(𝑡 ) , a−𝑖 ) = 𝐻𝑖(𝑡 ) (𝑎 𝑖(𝑡 ) ) + (1 + 𝜒 (𝑡 ) )ΔΓ𝑖f, (𝑡 ) + (1 + 𝜒 (𝑡 ) )ΔΓ𝑖b, (𝑡 ) ,
(22) (𝑡 ) where a−𝑖 denotes the actions of all UDs except 𝑢 𝑖 , and 𝜒 (𝑡 ) is the edge coordination gain. For local execution with 𝑒 𝑖(𝑡 ) = 𝑒 0 , we set ΔΓ𝑖f, (𝑡 ) = ΔΓ𝑖b, (𝑡 ) = 0. For edge execution, let 𝑒 𝑗𝑖 = 𝑒 𝑖(𝑡 ) denote the ES selected by UD 𝑢 𝑖 . The marginal congestion costs are given by ΔΓ𝑖f, (𝑡 ) = Γf,𝑗𝑖(𝑡 ) 𝐿 f,𝑗𝑖(𝑡 ) (a (𝑡 ) ) − Γf,𝑗𝑖(𝑡 ) 𝐿 f,𝑗𝑖(𝑡 ) (a (𝑡 ) ) − 𝑟 𝑖f, (𝑡 ) , (𝑡 ) b, (𝑡 ) (𝑡 ) b, (𝑡 ) b, (𝑡 ) (𝑡 ) b, (𝑡 ) ΔΓ𝑖b, (𝑡 ) = Γb, 𝐿 (a ) − Γ 𝐿 (a ) − 𝑟 . 𝑗𝑖 𝑗𝑖 𝑗𝑖 𝑗𝑖 𝑖
(23) The marginal-cost design in (22) allows the selfish bestresponse dynamics of UDs to be aligned with a global potential function [32], [33]. Specifically, the potential function of G (𝑡 ) is defined as Φ (𝑡 ) (a (𝑡 ) ) =
∑︁
+ (1 + 𝜒
)
∑︁ h
i (𝑡 ) (𝑡 ) (𝑡 ) Γf,𝑗 (𝑡 ) 𝐿 f,𝑗 (𝑡 ) (a (𝑡 ) ) + Γb, 𝐿 b, (a ) . 𝑗 𝑗
𝑒𝑗 ∈E
(24) The first term in Φ (𝑡 ) aggregates the contract-guided service losses of admitted UDs, while the second term penalizes edgeside resource congestion. Therefore, minimizing the potential function corresponds to improving a distributed penalized surrogate of the capacity-constrained per-slot scheduling problem. The potential game produces an intended action profile. Since intended resource packages may still exceed resource capacities when the system is highly congested, the ESP performs a final feasibility-realization step before actual task execution. Let afin, (𝑡 ) denote the final action profile returned by the game. For each ES 𝑒 𝑗 , define the resource realization factors as (𝑡 ) 𝐹𝑗 , 𝐿 f,𝑗 (𝑡 ) (afin, (𝑡 ) ) > 0, min 1, f, (𝑡 ) 𝐿 𝑗 (afin, (𝑡 ) ) (25) 𝜅 f,𝑗 (𝑡 ) = f, (𝑡 ) fin, (𝑡 ) 1, (a ) = 0, 𝐿 𝑗 and (𝑡 ) 𝐵𝑗 (𝑡 ) fin, (𝑡 ) min 1, , 𝐿 b, (a ) > 0, b, (𝑡 ) fin, (𝑡 ) (𝑡 ) 𝑗 𝐿𝑗 (a ) 𝜅 b, = 𝑗 (𝑡 ) fin, (𝑡 ) 1, ) = 0. 𝐿 b, (a 𝑗 The realized service provision is then given by (𝑡 ) 𝑓𝑖,(𝑡𝑗) = 1{𝑒 fin, = 𝑒 𝑗 }𝜅 f,𝑗 (𝑡 ) 𝑟 𝑖f,fin, (𝑡 ) , 𝑖 (𝑡 ) (𝑡 ) b,fin, (𝑡 ) 𝑏 𝑖,(𝑡 𝑗) = 1{𝑒 fin, = 𝑒 𝑗 }𝜅 b, 𝑟𝑖 , 𝑖 𝑗
𝑒 𝑗 ∈ E.
(26)
(27)
For local execution, the realized local computing resource (𝑡 ) (𝑡 ) is given by 𝑓𝑖,0 = 1{𝑒 fin, = 𝑒 0 }𝑟 𝑖f,fin, (𝑡 ) , and no uplink 𝑖 (𝑡 ) bandwidth is allocated, i.e., 𝑏 𝑖,0 = 0. After UDs select their intended ES and resource packages, the ESP finalizes the actual resource scheduling under physical capacity constraints. Specifically, the final allocation satisfies ∑︁ ∑︁ 𝑓𝑖,(𝑡𝑗) ≤ 𝐹 𝑗(𝑡 ) , 𝑏 𝑖,(𝑡 𝑗) ≤ 𝐵 (𝑡𝑗 ) , ∀𝑒 𝑗 ∈ E. (28) 𝑢𝑖 ∈ U s, (𝑡 )
B. Fulfillment-Driven Feedback and Adaptive Optimization After task execution under the final feasible allocation, the system observes the actual service outcomes and evaluates whether the original semantic contract is fulfilled [18], [20]. (𝑡 ) Different from Ωsc, , which is used during scheduling with 𝑖 calibrated bounds, the post-execution deviation is evaluated using the original fulfillment bounds in g𝑖(𝑡 ) . Specifically, the fulfillment deviation of admitted UD 𝑢 𝑖 is defined as " (𝑡 ) Ωful, = 𝜁D 𝑖
𝑢𝑖 ∈ U s, (𝑡 )
The final feasible allocation in (27) is then used to evaluate execution delay, energy consumption, monetary cost, and T4E
(𝑡 ) 𝐷 𝑖(𝑡 ) − 𝐷 max, 𝑖 (𝑡 ) 𝐷 max, 𝑖
" + 𝜁M
𝐻𝑖(𝑡 ) (𝑎 𝑖(𝑡 ) )
𝑢𝑖 ∈ U s, (𝑡 ) (𝑡 )
fulfillment. Thus, the potential game generates distributed tentative decisions, whereas the final allocation step ensures physical feasibility before execution.
#+
" + 𝜁E
# max, (𝑡 ) +
𝑀𝑖(𝑡 ) − 𝑀𝑖
𝑀𝑖max, (𝑡 )
𝐸 𝑖(𝑡 ) − 𝐸 𝑖max, (𝑡 )
#+
𝐸 𝑖max, (𝑡 ) h
+ 𝜁S 𝑆𝑖min, (𝑡 ) − 𝑆𝑖(𝑡 )
(29) i+ .
The semantic-contract fulfillment degree is then defined as (𝑡 ) ). A larger 𝜑𝑖(𝑡 ) indicates better fulfillment, 𝜑𝑖(𝑡 ) = exp(−Ωful, 𝑖 (𝑡 ) and 𝜑𝑖 = 1 means that no fulfillment violation occurs. To support adaptive optimization in non-stationary E4NetAI environments, STEPS distinguishes two types of drift signals, motivated by recent studies on concept drift, model drift, and online adaptation in dynamic networked AI systems [26]–[28]. The first signal captures how user-side semantic requirements change over time, while the second signal captures how the system’s contract-fulfillment capability varies after execution. Definition 3. (Semantic request drift) Semantic request drift measures the temporal variation of user-side semantic requirements induced by generated semantic contracts. It captures changes in service preferences, fulfillment-bound stringency, and semantic uncertainty, and is computed over all incoming UDs to avoid being hidden by semantic admission. To characterize semantic request drift, we first define the semantic state of UD 𝑢 𝑖 as i⊤ h (30) s𝑖(𝑡 ) = (w𝑖(𝑡 ) ) ⊤ , ( ḡ𝑖(𝑡 ) ) ⊤ , 𝜌𝑖(𝑡 ) , where ḡ𝑖(𝑡 ) is the normalized version of the fulfillment-bound vector g𝑖(𝑡 ) . The average semantic state over all incoming UDs is given by ( Í (𝑡 ) 1 (𝑡 ) | > 0, (𝑡 ) | 𝑢 ∈ U (𝑡 ) s𝑖 , |U (𝑡 ) | U s̄all = (𝑡 −1) 𝑖 (31) s̄all , |U (𝑡 ) | = 0. Let 𝑊 new and 𝑊 old denote the recent and historical time windows, respectively. For early timeslots where a full historical window is not yet available, STEPS uses the available samples to initialize the window averages. The semantic request drift is defined as (𝑡 ) Δsem =
1 |𝑊 new |
∑︁ 𝜏 ∈𝑊 new
(𝜏) s̄all −
∑︁ 1 (𝜏) s̄all |𝑊 old | old 𝜏 ∈𝑊
.
(32)
2
Definition 4. (Fulfillment drift) Fulfillment drift measures the temporal variation of the system’s ability to satisfy generated semantic contracts. Different from semantic request drift, which reflects user-side requirement changes, fulfillment
10
drift is evaluated from post-execution contract deviations and reflects changes in runtime service capability. For each timeslot, we first compute the average fulfillment pressure among admitted UDs: ( Í ful, (𝑡 ) 1 , |U s, (𝑡 ) | > 0, (𝑡 ) s, (𝑡 ) | 𝑢𝑖 ∈ U s, (𝑡 ) Ω𝑖 | U 𝑃ful = (33) 0, |U s, (𝑡 ) | = 0. The fulfillment drift is then defined as the window-level change of fulfillment pressure: (𝑡 ) Δful =
1 |𝑊 new |
∑︁
(𝜏) 𝑃ful −
𝜏 ∈𝑊 new
∑︁ 1 (𝜏) 𝑃ful . old |𝑊 | old
(34)
Beyond the two drift signals, STEPS also accounts for instantaneous pressure in the feedback design. The fulfillment (𝑡 ) pressure 𝑃ful in (33) reflects the current contract-violation burden among admitted UDs. However, only using admitted UDs may hide the pressure caused by rejected high-uncertainty requests. Therefore, STEPS further introduces the semantic admission pressure as ( s, (𝑡 ) 1 − | |UU (𝑡 ) | | , |U (𝑡 ) | > 0, (𝑡 ) 𝑃adm = (35) 0, |U (𝑡 ) | = 0. Based on the above drift and fulfillment-pressure signals, the fulfillment-side non-stationary feedback signal is defined as (36)
where 𝛼𝑠 ≥ 0, 𝛼 𝑓 ≥ 0, and 𝛼 𝑝 ≥ 0 are weighting coefficients. The first two terms capture window-level semantic-request and fulfillment-capability changes, while the third term captures the instantaneous fulfillment pressure among admitted UDs. (𝑡 ) The semantic admission pressure 𝑃adm is not merged into (𝑡 ) Ψful ; instead, it is used as a separate admission-relaxation signal to avoid excessive rejection of semantically uncertain requests. After each timeslot, the ESP updates resource prices for the next timeslot according to the intended resource demand reflected by the game-output action profile before feasibility realization. This allows the price signal to capture latent resource pressure even when the final feasible allocation is capped by physical capacities. Specifically, we have f
𝜆f,𝑗 (t+1) = 𝜆f,𝑗 (𝑡 ) + 𝜇f (1 + 𝜒 (𝑡 ) )
𝜆max 𝐿 f,𝑗 (𝑡 ) (afin, (𝑡 ) ) − 𝐹 𝑗(𝑡 ) , f 𝐹 𝑗(𝑡 ) 𝜆min b
(37)
𝜆max (𝑡 ) fin, (𝑡 ) 𝐿 b, (a ) − 𝐵 (𝑡𝑗 ) b, (𝑡 ) 𝑗 b, (t+1) (𝑡 ) 𝜆𝑗 = 𝜆 𝑗 + 𝜇b (1 + 𝜒 ) . b 𝐵 (𝑡𝑗 ) 𝜆min
Here, 𝜇f and 𝜇b are price-update stepsizes, and [·] 𝜆𝜆max denotes min projection onto the corresponding price interval. The updated prices are used in the next timeslot and do not affect the monetary-cost settlement of the current timeslot. A larger 𝜒 (𝑡 ) makes resource-price feedback more sensitive to overload, thereby strengthening edge-side coordination under stronger non-stationarity. Finally, STEPS updates the semantic admission threshold, contract conservativeness, and edge coordination gain accord-
(𝑡 )
(𝑡 )
Input: Task attributes {𝑞𝑖 } , SED { L𝑖 } , system context 𝜉 (𝑡 ) , edge states, f, (𝑡 ) b, (𝑡 ) prices {𝜆 𝑗 , 𝜆 𝑗 } , adaptive control parameters 𝜏 𝜌, (𝑡 ) , 𝛽 (𝑡 ) , 𝜒 (𝑡 ) , and maximum round number 𝐼max . (𝑡 ) , f (𝑡 ) , b (𝑡 ) } , updated prices, and updated 2 Output: Scheduling decisions {x parameters 𝜏 𝜌, (t+1) , 𝛽 (t+1) , 𝜒 (t+1) . 3 for 𝑡 = 1 to 𝑇 do 4 for 𝑢𝑖 ∈ U (𝑡 ) do (𝑡 ) (𝑡 ) 5 Parse the SED L𝑖 into semantic levels and confidence y𝑖 ; (𝑡 ) 6 Generate semantic contract C𝑖 ; 7 8 9
𝜏 ∈𝑊
(𝑡 ) (𝑡 ) (𝑡 ) (𝑡 ) Ψful = 𝛼𝑠 Δsem + 𝛼 𝑓 Δful + 𝛼 𝑝 𝑃ful ,
Algorithm 1: Proposed STEPS 1
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
28 29 30
(𝑡 )
Construct U s, (𝑡 ) = {𝑢𝑖 ∈ U (𝑡 ) | 𝜌𝑖 ≤ 𝜏 𝜌, (𝑡 ) } ; for 𝑢𝑖 ∈ U s, (𝑡 ) do Calibrate contract bounds by (6); (𝑡 ) Construct finite action space A𝑖 by (16); Initialize action profile a (𝑡 ) (0) and set 𝑟 ← 0; repeat Set improved ← false; Visit UDs in U s, (𝑡 ) in an asynchronous order; for each visited UD 𝑢𝑖 do (𝑡 ) (𝑡 ) (𝑡 ) Evaluate J𝑖 in (22) for all 𝑎𝑖 ∈ A𝑖 ; star, (𝑡 ) (𝑡 ) (𝑡 ) (𝑡 ) 𝑎𝑖 ← arg min (𝑡 ) (𝑡 ) J𝑖 (𝑎𝑖 , a−𝑖 ) ; if J𝑖
(𝑡 )
star, (𝑡 )
𝑎 𝑖 (𝑡 )
∈A
𝑖
(𝑡 )
(𝑡 )
(𝑡 )
(𝑎𝑖 , a−𝑖 ) < J𝑖 (𝑎𝑖 , a−𝑖 ) then (𝑡 ) star, (𝑡 ) Update 𝑎𝑖 ← 𝑎𝑖 ; Set improved ← true; Update edge loads and congestion penalties by (17)–(20); 𝑟 ← 𝑟 + 1; until no improvement occurs in a full UD update round or 𝑟 = 𝐼max ; Set the final intended action profile as afin, (𝑡 ) ; Realize feasible service provision by (25)–(27); Execute scheduled tasks and observe execution service outcomes; Compute fulfillment feedback by (29), semantic and fulfillment drift by (32)–(34), admission pressure by (35), and fulfillment-side feedback by (36); Update edge prices for the next timeslot by (37); Update 𝜏 𝜌, (t+1) , 𝛽 (t+1) , and 𝜒 (t+1) by (38); Return: {x (𝑡 ) , f (𝑡 ) , b (𝑡 ) } , updated prices, and updated adaptive parameters.
ing to fulfillment-side feedback and admission pressure: h i 𝜏max (𝑡 ) (𝑡 ) 𝜏 𝜌, (𝑡+1) = 𝜏 𝜌, (𝑡 )− 𝜇𝜌 Ψful − Ψ0 + 𝜇 𝑎 𝑃adm − 𝑃adm,0 , 𝜏min h i 𝛽 max (𝑡 ) 𝛽 (𝑡+1) = 𝛽 (𝑡 ) + 𝜇 𝛽 Ψful − Ψ0 , (38) 𝛽min h i 𝜒max (𝑡 ) 𝜒 (𝑡+1) = 𝜒 (𝑡 ) + 𝜇 𝜒 Ψful − Ψ0 , 𝜒min
where Ψ0 denotes the acceptable fulfillment-side feedback level, 𝑃adm,0 denotes the acceptable admission-pressure level, (𝑡 ) and 𝜇 𝑎 is the admission-relaxation stepsize. When Ψful > Ψ0 , the system reacts to increased fulfillment pressure by tightening semantic admission, increasing contract conservativeness, and strengthening edge coordination. Meanwhile, when (𝑡 ) > 𝑃adm,0 , the semantic admission threshold is relaxed 𝑃adm to avoid excessive rejection of semantically uncertain requests. Therefore, fulfillment pressure and admission pressure affect 𝜏 𝜌, (𝑡 ) in opposite directions, while 𝛽 (𝑡 ) and 𝜒 (𝑡 ) are updated only according to fulfillment-side feedback. C. Solution Design At each timeslot, STEPS converts natural language requests into semantic contracts, solves a contract-guided potential game for admitted UDs, realizes feasible service provision, and updates prices and adaptive control parameters using execution feedback. Details are summarized in Alg. ??. Step 1. Semantic Contract Generation (lines 4–6): At the beginning of each timeslot, each UD submits its task attributes and associated SED. The LLM-assisted semantic
11
parser extracts semantic service levels and parsing confidence, based on which the semantic contract C𝑖(𝑡 ) is generated. Step 2. Semantic Admission and Contract Calibration (lines 7–10): The system constructs the schedulable UD set U s, (𝑡 ) according to the semantic uncertainty threshold 𝜏 𝜌, (𝑡 ) . For each admitted user, the original fulfillment bounds are calibrated using semantic uncertainty 𝜌𝑖(𝑡 ) and contract conservativeness 𝛽 (𝑡 ) , and the finite action space is constructed. Step 3. Potential Game and Asynchronous Best Response (lines 11–23): STEPS initializes the action profile and constructs the contract-guided potential game for admitted UDs. Then, UDs update their actions asynchronously. During each update, one admitted UD evaluates all candidate actions and selects the one that minimizes its scheduling cost J𝑖 (𝑡 ) . If the selected action reduces the current cost, the UD updates its action; otherwise, it keeps the current decision. The process repeats until no improvement occurs in a full UD update round or the maximum round number 𝐼max is reached. Step 4. Feasibility Realization and Execution (lines 24–26): The final action profile returned by the game specifies intended resource packages. Before execution, the ESP realizes these intended decisions into physically feasible computing and bandwidth scheduling. Then, the scheduled tasks are executed, and the actual delay, energy consumption, monetary cost, and T4E level are observed. Step 5. Execution Feedback (line 27): After execution, (𝑡 ) and the system computes the execution deviation Ωful, 𝑖 (𝑡 ) fulfillment degree 𝜑𝑖 for each admitted user. It then evaluates semantic request drift, fulfillment drift, fulfillment pressure, and admission pressure. Step 6. Adaptive Scheduling-Control Update (lines 28–29): The ESP first updates resource prices for the next timeslot according to the intended resource pressure. Then, the contract conservativeness and edge coordination gain are updated according to the fulfillment-side feedback signal, while the semantic admission threshold is updated by jointly considering fulfillment-side feedback and admission pressure. D. Computational Complexity The computational complexity of STEPS mainly comes from the asynchronous best-response process. For each UD 𝑢 𝑖 , the size of its action space is |A𝑖(𝑡 ) | = O |E0 ||R f ||R b | , where |R f | and |R b | denote the maximum sizes of computingresource and bandwidth-resource package sets. In each full update round, every admitted UD evaluates all candidate actions once. Therefore, if the maximum number of update rounds at timeslot 𝑡 is 𝐼max , the per-slot complexity is O 𝐼max |U s, (𝑡 ) ||E0 ||R f ||R b | . Semantic parsing and contract calibration are performed once per UD. Therefore, their additional complexity is linear in |U (𝑡 ) |, excluding the internal inference cost of the selected LLM parser. E. Key Properties We next present the key properties of STEPS. Since STEPS solves a penalized per-slot surrogate of P, the analysis applies to the surrogate game rather than the original long-horizon problem with hard capacity constraints. For brevity, the timeslot superscript (𝑡) is omitted, and all pre-decision states are
treated as fixed within each per-slot game; inter-user coupling arises only through congestion penalties. Theorem 1. (Exact Potential Property of STEPS) For each timeslot 𝑡, the contract-guided scheduling game G (𝑡 ) is an exact potential game with the potential function Φ (𝑡 ) (a (𝑡 ) ) defined in (24). Specifically, for any UD 𝑢 𝑖 ∈ U s, (𝑡 ) , fixed (𝑡 ) a−𝑖 , and any two feasible actions 𝑎 𝑖(𝑡 ) , b 𝑎 𝑖(𝑡 ) ∈ A𝑖(𝑡 ) , we (𝑡 ) (𝑡 ) (𝑡 ) (𝑡 ) (𝑡 ) (𝑡 ) (𝑡 ) have J𝑖 (b 𝑎 𝑖 , a−𝑖 ) − J𝑖 (𝑎 𝑖 , a−𝑖 ) = Φ (𝑡 ) (b 𝑎 𝑖(𝑡 ) , a−𝑖 )− (𝑡 ) Φ (𝑡 ) (𝑎 𝑖(𝑡 ) , a−𝑖 ). Proof. Consider an arbitrary timeslot and omit (𝑡) for brevity. Fix a−𝑖 and suppose that UD 𝑢 𝑖 changes its action from 𝑎 𝑖 to b 𝑎 𝑖 . Under the fixed-state convention, the local loss 𝐻 𝑘 (𝑎 𝑘 ) of any other UD 𝑢 𝑘 ≠ 𝑢 𝑖 is independent of 𝑢 𝑖 ’s action. Thus, the change in the aggregate local-loss term is simply 𝐻𝑖 (b 𝑎 𝑖 ) − 𝐻𝑖 (𝑎 𝑖 ). For the congestion part, the marginal congestion cost in (23) is exactly the increment of the corresponding edge congestion potential caused by UD 𝑢 𝑖 . Hence, the change in the computing congestion potential is ΔΓ𝑖f (b 𝑎 𝑖 , a−𝑖 ) −ΔΓ𝑖f (𝑎 𝑖 , a−𝑖 ), and the change in the bandwidth congestion potential is ΔΓ𝑖b (b 𝑎 𝑖 , a−𝑖 )−ΔΓ𝑖b (𝑎 𝑖 , a−𝑖 ). Combining these terms gives Φ(b 𝑎 𝑖 , a−𝑖 ) − Φ(𝑎 𝑖 , a−𝑖 ) = 𝐻𝑖 (b 𝑎 𝑖 ) − 𝐻𝑖 (𝑎 𝑖 ) + (1 + 𝜒) ΔΓ𝑖f (b 𝑎 𝑖 , a−𝑖 ) − ΔΓ𝑖f (𝑎 𝑖 , a−𝑖 ) + (1 + 𝜒) ΔΓ𝑖b (b 𝑎 𝑖 , a−𝑖 ) − ΔΓ𝑖b (𝑎 𝑖 , a−𝑖 ) = J𝑖 (b 𝑎 𝑖 , a−𝑖 ) − J𝑖 (𝑎 𝑖 , a−𝑖 ). This proves the exact potential property.
■
Theorem 2. (Existence of Pure-Strategy Nash Equilibrium) For each timeslot 𝑡, the contract-guided scheduling game G (𝑡 ) admits at least one pure-strategy Nash equilibrium. Proof. For each admitted user, A𝑖(𝑡 ) is finite because both the EN set and the resource-package sets are finite. Hence, Î the joint action space A (𝑡 ) = 𝑢𝑖 ∈ U s, (𝑡 ) A𝑖(𝑡 ) is finite. By (𝑡 ) Theorem 1, G is an exact potential game. Therefore, there exists at least one action profile astar, (𝑡 ) that minimizes Φ (𝑡 ) over A (𝑡 ) . If astar, (𝑡 ) were not a Nash equilibrium, some UD could unilaterally reduce its scheduling cost. By the exact potential property, this would strictly decrease Φ (𝑡 ) , contradicting the minimality of astar, (𝑡 ) . Thus, astar, (𝑡 ) is a pure-strategy Nash equilibrium [34]. ■ Theorem 3. (Finite-Step Convergence Under Uncapped Best Response) If the asynchronous best-response process is allowed to run until no unilateral improvement exists, it converges to a contract-stable pure-strategy Nash equilibrium in finite steps [33]. Proof. At each effective update, one UD changes its action only when the new action strictly reduces its scheduling cost. By Theorem 1, every such strict cost reduction induces a strict decrease in the potential function. Since the joint action space is finite, the potential function can take only finitely many values, and the process cannot revisit any previous joint action profile. Therefore, the number of effective updates is finite. When the process terminates, no admitted UD can further reduce its scheduling cost by unilateral deviation. Therefore, the terminal profile is a pure-strategy Nash equilibrium of the per-slot surrogate game. ■
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Note that with the iteration cap 𝐼max , the returned profile may be an approximate Nash equilibrium. Its (𝑡 ) residual unilateral improvement gap is measured by 𝜖NE = +
max𝑢𝑖 ∈ U s, (𝑡 ) J𝑖
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(𝑡 ) A smaller 𝜖 NE indicates a more stable finite-iteration output, (𝑡 ) and 𝜖NE = 0 corresponds to an exact Nash equilibrium.
Theorem 4. (Boundedness of Adaptive Control Parameters) For all timeslots, the adaptive control parameters satisfy 𝜏 𝜌, (𝑡 ) ∈ [𝜏min , 𝜏max ], 𝛽 (𝑡 ) ∈ [𝛽min , 𝛽max ], and 𝜒 (𝑡 ) ∈ [ 𝜒min , 𝜒max ]. If resource prices are updated with bounded projection, they also remain within their prescribed intervals. Proof. The updates in (38) use the projection operator [𝑥] 𝑏𝑎 = min{max{𝑥, 𝑎}, 𝑏}, whose output always lies in [𝑎, 𝑏]. Hence, 𝜏 𝜌, (𝑡 ) , 𝛽 (𝑡 ) , and 𝜒 (𝑡 ) remain within their prescribed intervals for all timeslots. The same argument applies to projected price updates in (37). ■ V. E VALUATIONS A. Experimental Settings 1) Synthetic Setting: STEPS is evaluated under both synthetic and trace-driven hybrid settings, with all results averaged over 30 independent Monte Carlo trials unless otherwise specified. The synthetic environment comprises randomly instantiated users, edge servers, wireless channels, computational resources, and edge AI inference tasks. Naturallanguage requests are generated from semantic templates spanning latency, energy, cost, and T4E requirements. To capture uncertainties in real requests and dynamic network environments, we inject ambiguous, conflicting, and out-ofscope requests with ratio 𝑟 unc ∈ [0, 0.5], and further introduce semantic-preference drift and workload fluctuations at selected timeslots. Semantic parsing is performed by a local LLM parser implemented with Ollama and Qwen3.5-4B. The parser outputs semantic service levels and parsing confidence, which are then used to generate semantic contracts. To ensure reproducibility, template-level parsing results are cached during evaluation. All experiments are conducted on a workstation equipped with a 12th Gen Intel Core i9-12900H CPU and an NVIDIA GeForce RTX 3060 GPU. Following representative edge-intelligence studies [15], [17], [19], [24], key parameters, LLM configuration, and STEPS settings are summarized in Table II. B. Benchmark Methods We compare STEPS with five representative benchmarks selected and adapted from closely related studies. (i) ParamOpt is a parameter-driven optimization baseline implemented following conventional edge AI resource scheduling studies [17]. It assumes that numerical service requirements, such as delay bounds, energy budgets, monetary-cost limits, and preference weights, are directly available from the groundtruth request templates. (ii) Direct-LLM is an LLM-enabled intent-translation baseline implemented following service configuration methods [8]. It directly maps natural language requests into scheduling parameters without explicitly modeling semantic uncertainty or contract calibration. (iii) DRLOpt is a hybrid DRL-and-optimization baseline following
TABLE II S IMULATION SETTINGS . Item Network topology
Setting 800 × 800 m2 area; | E | = 8 by default; 50–300 UDs. Wireless and comput- 𝑁0 = −174 dBm/Hz; bandwidth 20–40 MHz; ing resources transmit power 10–200 mW; local/edge CPU 0.5–2.0 / 20–80 GHz. Task and trust settings Data size 5–20 MB; workload 0.5–5.0 × 109 cycles; trust score 0.4–1.0. Semantic requests Four dimensions: delay, energy, monetary cost, and T4E; three levels: low, medium, high; 𝑟unc ∈ [0, 0.5]. Non-stationarity Semantic-preference shift and workload fluctuation with drift intensity 0.6. LLM parser Ollama + Qwen3.5-4B; cached template-level parsing. Parser confidence Average confidence 0.723; normal/uncertaintemplate confidence 0.828/0.357 on average. 𝜌 𝜌 STEPS configuration 𝜏0 = 0.86, 𝜏min = 0.55, 𝛽0 = 0.50, 𝜒0 = 1.5, 𝛾 𝑓 = 𝛾𝑏 = 10, resource packages {0.04, 0.08, 0.14}. Evaluation settings 𝑇 = 100; 30 Monte Carlo trials; 𝐼max = 20; violation tolerance 𝜖v = 0.10.
learning-aided edge resource scheduling studies [17]. A DRL policy first selects ENs and resource levels, after which an optimization-based repair step enforces capacity feasibility. (iv) Intent-Reconf is a violation-triggered intent management baseline following intent-driven resource management studies [20]. It monitors post-execution service violations and triggers corrective actions, such as task migration, resource scaling, or local fallback, rather than proactively calibrating semantic contracts before scheduling. (v) GAH is a generalizedassignment heuristic baseline following edge LLM scheduling studies [25]. It assigns service tasks to ENs under resourcecapacity constraints using a generalized assignment heuristic. We also evaluate two ablation variants of STEPS. NoCal removes semantic admission and uncertainty-aware calibration by setting 𝜏 𝜌, (𝑡 ) = 1 and 𝛽 (𝑡 ) = 0. NoEvo disables fulfillmentdriven evolution by fixing 𝜏 𝜌, (𝑡 ) = 1, 𝛽 (𝑡 ) = 𝛽0 , and 𝜒 (𝑡 ) = 𝜒0 , while retaining fixed uncertainty-aware calibration. C. Evaluation Protocol and Metrics For fair comparison, all methods are evaluated under the same network topology, task workloads, wireless conditions, edge resource states, and request templates. Fulfillment-related metrics are computed using the same template-derived semantic contracts and task attributes, rather than method-dependent internal bounds, to avoid biased self-assessment. Let I𝑚 = {(𝑖, 𝑡) | 𝑢 𝑖 is served under method 𝑚 at timeslot 𝑡} denote the served user–timeslot pairs of method 𝑚. For methods without semantic admission, all UDs are treated as admitted. 1) Semantic-contract fulfillment and admission: We use average fulfillment degree (AFD), contract violation rate (CVR), average contract-guided service loss (ACSL), and semantic admission ratio (SAR) to evaluate contract fulfillment and semantic admission behavior. Specifically, AFD𝑚 = (𝑡 ) 1 Í measures the average semantic-contract (𝑖,𝑡 ) ∈ I𝑚 𝜑𝑖 | I𝑚 | fulfillment degree, where a larger value indicates better fulfillment. To avoid over-counting negligible deviations, CVR Í (𝑡 ) is defined as CVR𝑚 = | I1𝑚 | (𝑖,𝑡 ) ∈ I𝑚 1{Ωful, > 𝜖v }, where 𝑖 𝜖 v = 0.10 unless otherwise specified. A smaller CVR indicates
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fewer significant contract violations. Since CVR only measures the frequency of threshold-exceeding fulfillment deviations, rather than their magnitude or the overall service quality, it is interpreted jointly with ACSL. In addition, ACSL𝑚 = (𝑡 ) 1 Í (𝑖,𝑡 ) ∈ I𝑚 𝐽𝑖,eval measures the contract-guided service loss | I𝑚 | computed using the reference preferences and original fulfillment bounds. Since STEPS includes semantic admission, s, (𝑡 ) Í we further report SAR𝑚 = 𝑇1 𝑇𝑡=1 | |UU𝑚(𝑡 ) | | to quantify the admission cost associated with fulfillment improvement. 2) Service efficiency and online scalability: We use average service delay (ASD) and running time (RT) to evaluate service efficiency and online scheduling overhead. ASD is defined Í as ASD𝑚 = | I1𝑚 | (𝑖,𝑡 ) ∈ I𝑚 𝐷 𝑖(𝑡 ) , where 𝐷 𝑖(𝑡 ) is the end-toend delay under the final feasible allocation. RT denotes the average computational time required to complete one per-slot scheduling decision, excluding semantic parsing time. In the scalability experiments, we jointly increase the numbers of UDs and ESs, and report AFD, ACSL, RT, and ASD under different problem scales. Additional overload-related indicators are reported only when needed for interpreting resourcecontention effects, but are not used as primary comparison metrics. 3) Non-stationary drift adaptation: To evaluate adaptation under non-stationary conditions, we introduce semanticpreference and workload shifts at timeslot 𝑡d . We report the moving-average AFD, CVR, and ACSL to characterize how different methods respond to such shifts over time. For a generic metric 𝑀 ∈ AFD, CVR, ACSL, its moving-average e𝑚(𝑡 ) = 1 Í 𝜏 ∈ W 𝑀𝑚( 𝜏 ) , where W𝑡 is value is defined as 𝑀 𝑡 | W𝑡 | the sliding window ending at timeslot 𝑡. Based on the movingaverage ACSL, the post-drift cumulative-average ACSL is Í𝑡 1 ( 𝜏 ) , 𝑡 ≥ 𝑡d . ACSL defined as PD-ACSL (𝑡 ) = 𝑡 −𝑡d +1
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A smaller PD-ACSL indicates lower accumulated post-drift service loss. These drift-oriented metrics are more informative than a strict recovery-time metric when full recovery is not always reached within the finite simulation horizon. D. Synthetic Experiments 1) Impact of Semantic Uncertainty: We first evaluate the robustness of different methods under increasing semantic uncertainty. As shown in Fig. 2, the uncertainty ratio 𝑟 unc specifies the fraction of ambiguous, conflicting, or out-ofscope natural language requests. Fig. 2(a) shows that the AFD of most methods decreases as 𝑟 unc increases, since uncertain requests make it more difficult to infer reliable service preferences and fulfillment bounds. Param-Opt and Direct-LLM achieve relatively high AFD under low uncertainty, as ParamOpt relies on template-provided numerical requirements and Direct-LLM directly translates natural language requests into scheduling parameters. However, their fulfillment performance degrades more rapidly as uncertainty increases. In contrast,
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STEPS maintains a more stable AFD by incorporating parsing confidence into semantic-contract generation and contractguided scheduling. Fig. 2(b) reports the CVR under the significant violation tolerance 𝜖v = 0.10. As the uncertainty ratio increases, most methods suffer from higher violation rates, indicating that ambiguous requests increase the likelihood of mismatch between inferred contracts and realized service outcomes. Since CVR only reflects the frequency of significant deviations, we further use ACSL to evaluate the severity of contract-guided service loss. Fig. 2(c) shows that STEPS consistently achieves the lowest ACSL across all uncertainty ratios. This result indicates that direct translation from natural language requests to scheduling parameters, as adopted by Direct-LLM, is vulnerable to semantic ambiguity. By introducing the semantic contract as an executable intermediate representation, STEPS jointly captures service preferences, fulfillment bounds, and semantic uncertainty, thereby reducing contract-guided service loss. Fig. 2(d) reports the SAR of different methods. Since methods without semantic admission accept tasks associated with all service requests, their SAR remains close to one. For STEPS, SAR slightly decreases as 𝑟 unc increases, indicating that semantic admission becomes more selective under higher uncertainty. Nevertheless, SAR remains high even when 𝑟 unc = 0.5, which confirms that the ACSL reduction is not achieved by excessively rejecting uncertain requests. 2) Scalability Under Different Problem Scales: We next evaluate the scalability of STEPS under different problem scales. Specifically, the four scales are defined as S1 : (|U (𝑡 ) |, |E |) = (50, 2), S2 : (100, 4), S3 : (200, 8), and S4 : (300, 12). These settings jointly increase the numbers of UDs and ESs, leading to progressively larger scheduling instances. Fig. 3(a) shows that STEPS maintains stable and high AFD across all scales. Compared with other baselines such as DRLOpt, Intent-Reconf, and GAH, STEPS achieves better fulfillment performance because it jointly considers semantic preferences, fulfillment bounds, and edge-side resource contention. Param-Opt and Direct-LLM also achieve favorable AFD due to their parameter-driven scheduling structures, but they do not explicitly account for semantic uncertainty or fulfillmentdriven contract evolution. Fig. 3(b) compares ACSL under different scales. STEPS achieves ACSL comparable to ParamOpt and Direct-LLM, while substantially outperforming DRLOpt, Intent-Reconf, and GAH. This verifies that contractguided scheduling can effectively control semantic-contract service loss in larger edge systems. The performance gap between STEPS and the non-contract baselines suggests that explicitly modeling semantic preferences, fulfillment bounds, and uncertainty is critical for natural-language-driven edge scheduling. Fig. 3(c) reports RT. As the problem scale increases, RT grows due to enlarged action spaces and stronger resource contention. STEPS incurs higher computational over-
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Fig. 3. Scalability under different problem scales: (a) AFD, (b) ACSL, (c) RT, and (d) ASD.
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head than lightweight baselines such as GAH and IntentReconf, but remains comparable to Param-Opt and DirectLLM. This indicates that introducing semantic contracts and asynchronous best-response updates remains computationally manageable for online scheduling, especially considering the substantial reduction in ACSL. Fig. 3(d) presents ASD. STEPS achieves delay close to Param-Opt and Direct-LLM, and significantly lower than DRL-Opt, Intent-Reconf, and GAH. This indicates that STEPS reduces semantic-contract service loss without causing excessive delay degradation. Overall, Fig. 3 demonstrates that STEPS remains scalable as the numbers of UDs and ESs increase, achieving a favorable balance among fulfillment quality, scheduling overhead, and service delay. 3) Adaptation Under Non-Stationary Drift: Finally, we evaluate the adaptation capability of different methods under non-stationary semantic and workload shifts. As shown in Fig. 4, a drift event is introduced at 𝑡d = 50, as marked by the vertical dashed line. After the drift, UD semantic preferences and workload conditions change, causing a mismatch between prior scheduling behavior and new fulfillment requirements. Fig. 4(a) shows the moving-average AFD over time. Before the drift, Param-Opt, Direct-LLM, and STEPS achieve relatively high fulfillment degrees. After the drift, all methods experience a clear AFD decrease, indicating that the drift alters the service-fulfillment conditions. STEPS maintains higher post-drift fulfillment performance because its adaptive control parameters are updated according to fulfillment feedback. Fig. 4(b) reports the moving-average CVR. The CVR increases after the drift for all methods, indicating that non-stationary semantic and workload changes introduce additional violation pressure. Since CVR reflects the occurrence rather than the magnitude of significant deviations, we further examine ACSL and post-drift cumulative-average ACSL. Fig. 4(c) shows that the ACSL of all methods increases after the drift. STEPS maintains one of the lowest ACSL values during the postdrift period and clearly outperforms DRL-Opt, Intent-Reconf, and GAH. This demonstrates that fulfillment-driven adaptive updates help adjust semantic admission, contract conservativeness, and edge coordination to the changing environment. Fig. 4(d) further reports post-drift cumulative-average ACSL.
TABLE III A BLATION STUDY, VALUES ARE REPORTED AS MEAN ± STANDARD DEVIATION . Method AFD↑ CVR↓ ACSL↓ SAR NoCal 0.267 ± 0.017 0.958 ± 0.011 15.647 ± 0.320 1.000 ± 0.000 NoEvo 0.277 ± 0.017 0.951 ± 0.013 15.568 ± 0.321 1.000 ± 0.000 STEPS 0.300 ± 0.017 0.948 ± 0.012 14.473 ± 0.340 0.905 ± 0.004
STEPS consistently achieves low cumulative-average ACSL throughout the post-drift period and clearly outperforms DRLOpt, Intent-Reconf, and GAH. Compared with Direct-LLM, STEPS sustains lower post-drift service loss by explicitly updating contract-related control parameters instead of using fixed semantic-to-parameter mappings. 4) Ablation Study: To examine the contribution of the key modules in STEPS, we conduct an ablation study under the default synthetic setting. As shown in Table III, NoCal removes semantic admission and uncertainty-aware contract calibration, while NoEvo retains semantic contracts and calibration but excludes fulfillment-driven adaptive updates. Table III shows that NoCal yields the lowest AFD and the highest ACSL, although it admits all requests. This indicates that directly using parsed semantic requirements without uncertainty-aware calibration can lead to inaccurate fulfillment targets and inefficient scheduling. NoEvo improves over NoCal, showing the benefit of fixed uncertainty-aware contract calibration. However, because all adaptive updates are disabled, NoEvo cannot adapt contract conservativeness or edge coordination according to fulfillment feedback, nor can it dynamically regulate semantic admission under changing uncertainty. The complete STEPS framework achieves the highest AFD and the lowest CVR and ACSL. Although its SAR is lower than those of NoCal and NoEvo, STEPS still maintains a high admission ratio while substantially reducing ACSL. This confirms that the performance gain is attributed to uncertainty-aware contract calibration and fulfillment-driven adaptation rather than excessive request rejection.
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TABLE IV T RACE - DRIVEN HYBRID EVALUATION ON THE M ELBOURNE CBD EUA TOPOLOGY. Method Param-Opt Direct-LLM DRL-Opt Intent-Reconf GAH STEPS
AFD↑ 0.3727 0.3587 0.2741 0.2748 0.2440 0.3688
CVR↓ 0.9506 0.9536 0.8905 0.8536 0.8604 0.9485
ACSL↓ 4.2859 4.3792 20.2877 22.7815 23.0266 4.2142
ASD↓ 1.3544 1.3923 3.0571 3.5088 3.6312 1.3832
RT↓ Post-ACSL↓ 1.3290 19.6168 1.3152 19.7405 0.1036 39.2660 0.1718 41.5401 0.0914 38.6770 1.2986 18.7764
E. Experiments on a Real-World Dataset To further validate STEPS under realistic spatial deployments, we conduct a trace-driven hybrid evaluation using the EUA dataset [35]. We select 300 UDs and 12 edge sites from the Melbourne CBD topology, where the average and maximum nearest-edge distances are 181.574 m and 367.711 m, respectively. Table IV presents the results on the Melbourne CBD trace. STEPS achieves the lowest ACSL and postdrift ACSL among all methods, demonstrating that semanticcontract-guided scheduling remains effective under realistic spatial distributions of UDs and edge sites. Although ParamOpt obtains a slightly higher AFD and lower ASD due to its access to template-derived numerical service requirements, STEPS reduces ACSL from 4.2859 to 4.2142 and postdrift ACSL from 19.6168 to 18.7764. Meanwhile, IntentReconf and GAH obtain lower CVR but much higher ACSL, indicating that CVR only measures the frequency of thresholdexceeding deviations and does not capture violation severity or overall contract-guided service quality. These results show that STEPS improves contract-guided service loss and postdrift robustness without introducing excessive scheduling time or service delay. Overall, the above results confirm that STEPS provides a robust and scalable approach for natural-language-driven E4NetAI. By introducing semantic contracts, uncertaintyaware calibration, and fulfillment-driven adaptive optimization, STEPS consistently reduces contract-guided service loss under semantic uncertainty, large-scale deployments, nonstationary drift, and the real-world trace, without incurring excessive admission rejection, delay degradation, or scheduling overhead. VI. C ONCLUSION In this paper, we proposed STEPS, a semantic-contractguided adaptive scheduling framework for natural-languagedriven E4NetAI. STEPS introduces the Semantic Contract as an executable interface between ambiguous natural language requests and resource-constrained edge scheduling, capturing service preferences, fulfillment bounds, and semantic uncertainty. Based on these contracts, we formulated contractguided scheduling under coupled communication-computation constraints and transformed the per-slot problem into an exact potential game, enabling distributed EN selection and service provision. To handle non-stationary environments, STEPS further uses execution feedback to update semantic admission, contract conservativeness, and edge coordination online. The theoretical analysis established the existence of a purestrategy equilibrium, finite-step convergence of the uncapped asynchronous best-response dynamics, and boundedness of the adaptive control parameters. Synthetic and trace-driven hybrid
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