Update for Decisions, Not Freshness: Goal-Oriented Status Updating and Selective Offloading at the Network Edge

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Update for Decisions, Not Freshness: Goal-Oriented Status Updating and Selective Offloading at the Network Edge

arXiv:2609.01082v1 [cs.DC] 1 Sep 2026

Jianpeng Qi, Qiyang Zhang, Chao Liu, Member, IEEE, Jing Sun, Yimei Liu, Yanwei Yu, Member, IEEE, Yingjie Wang, Member, IEEE, and Wei Ni, Fellow, IEEE

Abstract—In an edge–cloud collaborative edge-computing environment, an edge node (EN) must decide whether each user task should be executed locally, forwarded to a remote service (or cloud) node (SN), or rejected. The EN observes its local state directly but receives the SN state only through an intermittently refreshed cache. Status updating and task control therefore form an asynchronous closed loop under partial observability. Freshnessdriven schemes, including those based on Age of Information (AoI), do not directly value an update by its effect on subsequent task decisions. We propose C O SMO (Co-design of Semanticstate Management and Offloading), a cooperative event-driven reinforcement learning (RL) framework that coordinates semantic status management and selective offloading through realized task utility. C O SMO learns a compact representation of the heterogeneous SN service state. At the SN, a recurrent semiMarkov double deep Q-network (Double DQN) agent jointly selects send/no-send and the next decision interval. At the EN, a task-terminal off-policy value-learning agent makes hierarchical gate–route decisions from local observations and stale remote semantics. The agents maintain separate observations and value targets but share the same realized task-utility stream, without centralized execution. Across the evaluated workload families, C O SMO’s reported relative improvement in on-time completion rate over the best-performing competing method averages 18.6%– 21.2%. For capacity-aware decision accuracy across the three strict-overload points, the corresponding reported gains average 17.6%–17.9%. Index Terms—Mobile edge computing, computation offloading, goal-oriented status updating, age of information, deep reinforcement learning.

I. I NTRODUCTION

E

DGE computing increasingly relies on edge–cloud collaborative execution [1]. Each arriving task must be assigned to a local or remote service node that can process it within an acceptable delay. This assignment requires the dispatcher to compare local and remote service status, including service availability, queue backlog, and expected service delay. Local and remote service states differ in observability. The dispatcher observes its local state directly, and obtains remote state through a capacity-limited information link. Because this link cannot support continuous synchronization, the dispatcher caches the latest remote status. The cached view becomes stale as the remote service state evolves. The resulting stale-status dispatch problem requires task decisions based on incomplete and potentially outdated remote information. This local–remote dispatch setting has been studied extensively in mobile edge computing (MEC) [2]. Compute

Information Flow Task Flow

Service Node

Edge Node

01100 11001 10110

Network

01100 11001 10110

01100 11001 10110

Service Node

Decision

Local Processing

Autonomous Vehicle

T a s ks

Rejected

XR Glasses

Smartphone

Reject excess, protect the rest

Fig. 1. Information and task flows in goal-oriented status updating for CFN.

awareness in Compute-First Networking (CFN) and Computing Power Network (CPN) architectures provides a concrete instance of the stale-status problem [3]–[5]. As depicted in Fig. 1, user equipments (UEs) or end devices submit tasks to an edge node (EN), which acts as the dispatcher. The EN observes its own compute and queue state directly. By contrast, a remote service node (SN) is represented only by cached service status delivered over a separate information flow. For each arriving task, the EN chooses local execution, offloading to the SN, or rejection. Under overload (offeredload ratio ρ > 1), accepting every task can compromise the service quality of tasks that the system can serve. The EN therefore makes each choice from local observations and a potentially outdated SN view obtained through intermittent status updates [6]. The joint problem is to determine when the SN should refresh its status and how the EN should act on the cached information. Existing status-update methods commonly characterize update value through freshness. The age of information (AoI) and its variants quantify how outdated the receiver’s knowledge is and support status-update scheduling and monitoring [7]–[9]. More recently, goal-oriented and semantics-aware communication has shifted the focus from faithful source reproduction to information relevant to the receiver’s task [10]–[14]. The age of incorrect information provides a complementary criterion by measuring how long the cached value is wrong [15], [16]. These approaches provide distinct criteria for determining which status information to transmit. In the compute-aware service-offloading setting considered

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here, the update value depends on the downstream task decision rather than on freshness or state deviation alone [17]. A fresh status, or one that differs markedly from its cached copy, may still produce the same local/offload/reject action. Conversely, a small service-state change may alter the selected action. This gap motivates goal-oriented status updating: The SN should refresh its status when the new information is likely to improve downstream task handling, rather than only when the cached status is outdated or different. Realizing this goal-oriented view presents three challenges. First, the EN and SN operate under partial observability and information asymmetry. The EN makes each task decision from a cached SN status and never observes the SN’s instantaneous backlog. Meanwhile, the SN schedules updates without observing the EN’s local arrivals or queue. Neither of the agents has the complete information required to evaluate the joint decision. Second, updating and task decisions form a bidirectionally coupled closed loop, although they are triggered by different events. Each update influences EN task decisions until the next refresh. These decisions reshape the SN load and, in turn, affect when another update is useful. Optimizing either decision in isolation may therefore omit this feedback. Third, feedback arrives at two event horizons. The utility of an EN action becomes known only when the corresponding task reaches a terminal outcome. An SN update is instead evaluated from task utilities accumulated over the following decision interval and from the value of later intervals. The learning design must align a task-terminal EN return with a semi-Markov SN return without imposing a common artificial clock. In this paper, we formulate this asynchronous coupling as the control problem and propose C O SMO, a cooperative semantic-aware reinforcement learning (RL) framework. At each SN decision epoch, the SN maps its local service state into a compact representation and selects whether to transmit it and when to decide again. At each task arrival, the EN selects local execution, offloading, or rejection from its local observation and the latest cached semantic. The agents retain separate observations and value targets, while their rewards are derived from a common stream of realized task utilities. This event-driven coordination links what is transmitted, when it is transmitted, and how the EN uses the cached information for accept/reject and routing decisions. The contributions of this paper are summarized as follows. We formulate stale-state edge offloading as an asynchronous closed-loop control problem with two event clocks: SN status decisions and EN task arrivals. This formulation includes active rejection under overload and evaluates information by downstream task utility rather than freshness alone. • For the SN status-update decision, we design a temporal semantic decision network that uses cached semanticstate information, update age, and recent task feedback. A gated recurrent unit (GRU)-based dueling Double deep Qnetwork (Double DQN) head selects whether to transmit a semantic update and the next decision interval. A semi-

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Markov target uses interval-level rewards aggregated from downstream task utilities and update cost. • For the EN task-forwarding decision, we design a dualbranch state encoder and a hierarchical gate–route decision network. The gate first determines whether an arriving task should be accepted or rejected. The route head then selects local execution or SN offloading for accepted tasks. This hierarchy makes active rejection explicit under overload. The EN remains an off-policy RL agent, but its delayed task outcome forms a task-terminal value target rather than an inter-task bootstrap. • We evaluate the complete C O SMO framework across a range of load conditions and two arrival processes in ns-3. With the controlled single-EN/single-SN topology, we show end-to-end feasibility and improvements in ontime completion and capacity-aware decision accuracy, together with the status-update cost tradeoff relative to the compared freshness-driven and fixed-rule policies. The remainder of this paper is organized as follows. Section III presents the system model and problem formulation. Section IV elaborates on the goal-oriented co-design and its training procedure. Section V describes the experiments and results. The paper concludes with the limitations and directions for future work in Section VI. II. R ELATED W ORK We organize related work into three areas: Compute-aware service offloading, freshness- and goal-oriented status updating, and semantic-aware edge offloading. The first two areas separately address task assignment and remote state refresh. The third connects these decisions and motivates their joint design under stale information and overload. A. Compute-Aware Service Offloading CFN jointly schedules computation and connectivity to serve tasks across cloud, data-center, and edge tiers [1], [3]. Existing studies examine anycast-based service offloading in software-defined computing power networks [4], online scheduling of inference services with learning [6], and edge-enabled multi-user collaboration for interactive applications [5]. Load-aware multi-agent offloading partitions tasks among local devices, mobile LEO satellites, and a remote cloud data center based on current satellite resource and load states [18]. These studies largely assume that the controller or EN has sufficiently accurate node status and therefore focus on offloading or placement. In contrast, this paper considers pertask decisions based on stale, cached SN status. This setting requires the SN refresh schedule and EN task policy to be coordinated. B. Freshness and Goal-Oriented Updating A substantial body of work quantifies update utility through information freshness. AoI and its variants support update scheduling and monitoring [7], including pull-based or querydriven settings [8] and multi-source scheduling weighted by semantic importance [9]. Because freshness does not indicate

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whether a cached state is correct, the age of incorrect information measures how long that state remains wrong [15], [16]. Goal-oriented and semantics-aware communication moves closer to the receiver’s objective by prioritizing information relevant to the downstream task [10]–[14], [19]. Our earlier AVA work combined value of information (VoI) and AoI to decide whether to update raw service status for subsequent task forwarding [17]. The present work changes this control boundary in three coupled respects. It learns a compact dynamics-aware status abstraction instead of transmitting the full raw state. It gives the SN a paired send/no-send and next-decision-interval action. It also extends EN control to three-way task handling under overload through local execution, offloading, or active rejection. To this end, CoSMO coordinates status abstraction, update timing, overload-aware task acceptance, and execution routing through realized downstream task utility. C. Semantic-Aware Edge Offloading Semantic and task-oriented methods are increasingly applied to edge computing and offloading. Surveys summarize semantic edge computing and its role in prospective 6G networks [20]. On the control side, deep reinforcement learning (DRL) is widely used for computation offloading and resource allocation. Lyapunov-guided DRL stabilizes online offloading under stochastic arrivals [21]. Other DRL-based schemes allocate resources for task-oriented semantic communication [22] and semantic-aware networks with task offloading [23]. Multiobjective RL jointly optimizes semantic extraction and task scheduling in vehicular edge computing [24]. QoE-driven MAPPO jointly optimizes semantic extraction and multi-task offloading for multiple users connected to a single access point and a single edge server [25]. Utility-loss minimization schedules semantic status generation and satellite transmission to balance state-estimation mismatch and energy consumption [26]. These approaches typically optimize offloading or resource allocation for an available state and emphasize throughput or latency. In contrast, we couple offloading with the upstream decision of when to update its remote state. The policy can also decline tasks when the available capacity cannot support timely completion. In summary, prior work provides the individual foundations for compute-aware offloading, goal-oriented updating, semantic representation, and learning-based edge control. CoSMO differs by composing them into one asynchronous decision process. Particularly, a recurrent semi-Markov updater controls both transmission and revisit time, while a task-terminal value learner uses the resulting cached semantic for overloadaware accept/reject decisions and route selection. This scope differs from freshness optimization with a fixed downstream controller and from offloading optimization that treats the available remote state as given. III. D ECISION -O RIENTED C LOSED -L OOP S YSTEM M ODEL AND P ROBLEM F ORMULATION A. System Model In this section, we specify the three-tier MEC architecture, task and mobility models, node service states, agent observa-

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tions, event-driven decisions, and optimization objective. 1) Network Architecture We consider a three-tier MEC system consisting of multiple UEs, an EN, and an SN. The UEs submit tasks to the EN over wireless uplinks. The EN acts as the task controller and, for each arriving task, either processes it locally, offloads it to the SN for execution, or rejects it. The EN and SN are connected by a backhaul link used for task upload, result return, and SN status updates. As shown in Fig. 1, the system contains two flows: An information flow, in which the SN sends its state information to the EN, and a task flow, which carries task arrivals, offloaded tasks, and returned results. The SN status updates are delivered intermittently to the EN and stored with their timestamps in an EN-side cache. At a task arrival, the EN observes local EN-side information and uses the latest cached SN status, which may differ from the instantaneous SN service state. After receiving and caching a status update, the EN can notify the SN through an acknowledgment (ACK) mechanism. A rejected task terminates at the EN and is not forwarded to either of the execution queues. The UE mobility changes the wireless access condition and connection persistence, which are represented by the accessstate variables defined below. 2) Task Model and Delay Cost We assume that tasks from the UEs arrive at the EN according to a stochastic process. The k-th task is characterized by the following five-tuple Jk = (tk , ik , bk , ck , Dk ),

(1)

where tk ∈ R≥0 is the arrival time, and ik ∈ {1, 2, . . . , N } identifies the source UE among the N UEs. The variables bk , ck , Dk ∈ R>0 denote the input data size, compute demand, and delay constraint, respectively. For delay accounting, the EN-side route indicator ak applies only to the accepted tasks: ak = 0 denotes local execution at the EN, and ak = 1 denotes offloading to the SN. The complete EN action space and the SN update action are specified below. A locally executed task enters the EN queue, whereas an offloaded task is executed at the SN and incurs EN–SN upload and return delays. At either node, the accepted tasks enter service, based on the first-come first-served (FCFS) ordering. For an accepted task (ak ∈ {0, 1}), the end-to-end completion delay is
Tk = Tkul + ak Tkup + Tkdn + Tkwait + Tkcomp , (2) where Tkul is the wireless uplink delay from UE ik to the EN, Tkup is the EN-to-SN task upload delay, Tkdn is the SN-toEN result download delay, Tkwait is the queueing delay at the selected node, and Tkcomp is its computation delay. We do not embed an explicit queueing model in the optimization problem. Instead, Tkwait and Tkcomp are realized delays generated by the execution process and enter Tk directly. An accepted task succeeds if and only if Tk ≤ Dk . The node service states represent the corresponding queue and workload conditions. An actively rejected task terminates immediately without consuming compute or transmission resources and

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is scored through the rejection outcomes in the task-utility definition. 3) Mobility and Access State In the considered single-EN setting, mobility affects task performance primarily through the wireless access process. UE motion relative to the EN changes link quality, taskupload delay, and link sustainability, thus affecting the EN’s offloading choice [1], [27]. Following mobility-aware vehicular edge computing (VEC) offloading models [28], we use a compact access-state representation rather than the complete UE trajectory. For task Jk from UE ik arriving at time tk , the corresponding mobility state is
mk = Riulk (tk ), sik ,k , τik ,k , (3) where Riulk (tk ) is the estimated effective uplink throughput observed at arrival, sik ,k is the access-state trend, and τik ,k is the residual connection time. These three quantities characterize the current access capability, short-term direction of change, and connection sustainability, respectively. The uplink-throughput feature is derived from measured task-upload delay. For a task with data size bk and measured UE–EN uplink delay Tkul , the measured uplink-throughput sample is bk (4) R̂iulk (tk ) = ul . Tk To reduce measurement noise, the observation uses an exponentially weighted moving average (EWMA). This recursive estimator is also used for network-delay estimation, including TCP’s smoothed-RTT estimator [29]: Riulk (tk ) = αR R̂iulk (tk ) + (1 − αR )Riulk (tk− ),

(5)

where αR ∈ [0, 1] is the smoothing coefficient, and tk− denotes the previous task-arrival time of the same UE. The trend feature is then given as sik ,k = Riulk (tk ) − Riulk (tk− ).

(6)

The residual connection time τik ,k is computed from the relative positions and velocitys of UE ik and the EN. It represents the remaining time before the UE leaves the configured service radius. 4) Node Service State To support local decisions, each execution node r ∈ {EN, SN} maintains a service state:
xrt = Ntr , Wtr , Btr , Mtr , r ∈ {EN, SN}. (7) Here, Ntr is the idle compute resource, Wtr is the head-ofline waiting time in the waiting queue, and Btr is the total residual compute demand of outstanding tasks. The variable Mtr denotes the available storage. The workload component is then given by X X Btr = cj + crem r ∈ {EN, SN}, (8) j (t), j∈Qwait,r t

j∈Qrun,r t

where Qwait,r and Qrun,r are the waiting and running task t t sets at node r, respectively; cj is the total compute demand of task j; and crem j (t) is its residual demand at time t.

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B. Decision-Oriented Status and Observations We next define the SN status abstraction transmitted to the EN, the observations available to each agent, and the cached remote status used by the EN. 1) SN Status Abstraction The EN relies on delayed SN information, while frequent raw-state transmission incurs communication overhead and may retain details unnecessary for task decisions. We encode the information-flow payload as a compact SN status semantic
, fθ : R4 → R2 , zt = fθ xSN (9) t where fθ (·) is a parameterized status-abstraction mapping, and zt ∈ R2 is the resulting status semantic. The SN transmits this semantic to the EN, which caches it for subsequent task decisions. Section IV specifies fθ (·). 2) Asymmetric EN/SN-Side Observations The system operates under partial observability and information asymmetry. During online execution, the SN and EN only use their locally available observations. SN observation at decision epoch un : Let un denote the n-th SN decision epoch, and σn ∈ {0, 1} indicate whether the SN transmits a semantic update at that epoch. The SN information set at un is defined as  InSN = zun , zcνn , Aun , Hncomp , ℓSN (10) un , 2 where zun = fθ (xSN un ) ∈ R is the status semantic of the SN current service state xun ∈ R4 . Let νn ≤ un be the source timestamp of the status semantic most recently acknowledged by the EN before decision epoch un . Then zcνn is that cached copy and Aun = un − νn is its AoI. This definition remains valid when one or more preceding SN decisions choose nosend. Here Hncomp is the history of offloaded tasks completed by un . The variable ℓSN un is a local statistic of the SN-to-EN update link, such as its mean rate, rate standard deviation, and short-term rate trend. Task outcomes, including success and final delay, become observable to the SN only after completion. Hence, Hncomp contains only tasks offloaded before un whose outcomes are known:  Hncomp ⊆ (Ji , ai , Ti ) : ti < un , ai = 1, ti + Ti ≤ un . (11) EN observation at task-arrival epoch tk : The EN information set at the arrival time of the k-th task is defined as  c EN , (12) IkEN = mk , xEN tk , Jk , zun(k) , Atk , ℓtk

where mk is the source UE’s mobility state, xEN tk is the local EN service state, and Jk contains the current task features. The variable zcun(k) is the SN status semantic cached at the EN, and Atk = tk − un(k) is its age. Here, un(k) is the source timestamp of the latest SN update cached before tk . Finally, ℓEN tk is a local statistic of the EN-to-SN link, such as its mean rate, rate standard deviation, and short-term rate trend.

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C. Closed-Loop Event-Driven Decision Process

D. Problem Formulation

The closed-loop decision process evolves in continuous time through two event streams. Task arrivals {tk } trigger EN task decisions, whereas SN decision epochs {un } trigger semantic-update decisions. Because task interarrival times and SN decision intervals are generally nonuniform, we model the control problem as an asynchronous event-driven semi-Markov decision process (semi-MDP). The two event-triggered decisions are defined below. Task-offloading decision: At each arrival time tk , the EN observes the local information set IkEN and chooses a task action from the three-way action space

The objective is to jointly design the SN semantic-update policy π SN and the EN task-offloading policy π EN to maximize the long-term average net system utility while balancing task utility against semantic-update cost. Suppose that the k-th task arrive at tk , and let the n-th SN decision epoch occur at un . The objective is written as   X 1  X E max lim Uk − λs Cn  , (20) π SN , π EN T →∞ T

AEN = {0, 1, 2},

ak ∈ AEN ,

where the action indices are defined by   0, local execution at the EN, ak = 1, offloading to the SN,   2, active rejection. Equivalently, the EN policy is written as
ak = π EN IkEN ,

(13)

(14)

(15)

where σn ∈ {0, 1} is the transmit indicator for zun , and gn ∈ G ⊆ [gmin , gmax ] is the waiting time before the next decision epoch. The next epoch is therefore written as (17)

If σn = 1, the EN cache is updated to zun with timestamp un once the EN receives it. If σn = 0, the SN skips the current transmission opportunity and revisits the update decision after gn time units at un+1 ; during this interval, the EN keeps the previous cached semantic and timestamp. The two decisions therefore operate on distinct event streams. The EN acts at each task arrival, whereas the SN selects semantic transmission and the next interval at each SN decision epoch. Define the number of EN task decisions in the n-th SN interval [un , un+1 ) as Nn = |{k : un ≤ tk < un+1 }| ,

where Uk is the task utility defined below, Cn is the update communication cost at SN decision epoch un , and λs > 0 is the update-cost coefficient. To specify Cn , let σn ∈ {0, 1} indicate whether the SN transmits the current status semantic at un , let cs be the per-dimension communication cost, and dz be the semantic dimension. Then, Cn = σn cs dz .

where ak ∈ AEN follows the action semantics in (14). State-update decision: At the nth SN decision epoch un , the SN controls the information flow by jointly deciding whether to transmit the current status semantic and when to make the next decision:
(σn , gn ) = π SN InSN , (16)

un+1 = un + gn .

n:un ≤T

k:tk ≤T

(18)

whose mean satisfies ḡ (19) N̄ = E[Nn ] ≈ ¯ , ∆ ¯ = where ḡ = E[gn ] is the mean SN decision interval and ∆ E[tk+1 − tk ] the mean task inter-arrival time. The formulation ¯ When ḡ ≫ ∆, ¯ the system behaves as does not require ḡ ≫ ∆. a two-timescale process, and one update typically affects many ¯ Nn may be tasks. When ḡ is comparable to or smaller than ∆, small, but the model and training pipeline remain unchanged. A transmitted update can therefore affect EN task decisions throughout the subsequent interval.

(21)

Thus, a no-send decision (σn = 0) incurs zero update cost, while a send decision (σn = 1) is charged only for transmitting the current status semantic. For each task, the decision-oriented utility Uk measures the contribution of the EN decision after its outcome is known. It combines an outcome-dependent value with the task-side execution cost, i.e., Φk = λT Tk + λc 1{ak =1} bk ,

(22)

where Tk is the realized end-to-end delay; bk is the task input size; and λT and λc ≥ 0 are the delay and EN– SN transmission coefficients, respectively. The scaling weight ηc ≥ 0 controls how strongly this execution cost enters the decision-oriented reward. Let χk denote the resulting closedloop decision outcome: True positive (TP): The EN chooses local execution or offloading, the task is accepted, and it completes by its deadline. • False positive (FP): The EN chooses local execution or offloading, but the selected node cannot accept the task or the accepted task misses its deadline. • True negative (TN): The EN actively rejects the task and no deadline-feasible execution route exists under the current estimated system state. • False negative (FN): The EN actively rejects the task even though at least one deadline-feasible execution route exists.   χk = TP; wTP V − ηc Φk ,    −wFP V − ηc Φk , χk = FP;   •

Uk =

w V,  TN    −wFN V,    0,

χk = TN;

χk = FN;

no EN decision for task k. (23) The scalar V > 0 sets the base task value, and the positive coefficients wχ , one for each χ ∈ {TP, FP, TN, FN}, weight the

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corresponding decision outcomes. Thus, Uk rewards successful acceptance and correct rejection, and penalizes accepted failures and erroneous rejection. The optimization is subject to the following constraints. C1. Resource constraints: For each node r ∈ {EN, SN} and all time t, 0 ≤ Ntr ≤ Nrmax ; 0 ≤ Mtr ≤ Mrmax ;

(24)

|Qrt | ≤ Qmax , r with the SN provisioned more strongly than the EN: max max NSN > NEN ; max max MSN > MEN .

(25)

C2. Task-outcome mechanism constraint: Let ρ(0) = EN and ρ(1) = SN. Before inserting task k, the feasibility of accepting it on route a ∈ {0, 1} is

ρ(a) ρ(a) (26) Fka = Mtk ≥ bk ∧ |Qtk | < Qmax ρ(a) . For rejection evaluation, let Tbka be the estimated completion delay of route a before insertion, and define
Rak = Fka ∧ Tbka ≤ Dk , a ∈ {0, 1}. (27) The closed-loop task outcome is then  ak  TP, ak ∈ {0, 1}, Fk , Tk ≤ Dk ;    FP, ak ∈ {0, 1}, ¬F ak ∨ (F ak ∧ Tk > Dk )
; k k χk =
0 1  TN, ak = 2, ¬ Rk ∨ Rk ;     FN, a = 2, R0 ∨ R1 . k k k (28) These constraints define resource feasibility and taskoutcome labels for the long-term net-utility objective. The labels distinguish correct from erroneous rejections: Rejecting a task is a true negative if no route can complete it by its deadline and a false negative otherwise. Accepting a task that cannot enter a queue or complete on time is a false positive. The labels therefore penalize both blind acceptance under overload and unnecessary rejection. The objective (20) couples the two event-triggered decisions. The EN acts at task arrivals and generates Uk , whereas the SN selects (σn , gn ) at its decision epochs and incurs Cn only when σn = 1. Because one semantic update may affect multiple subsequent tasks, the update and task-decision subproblems are not independent. We optimize their long-term time average jointly, accounting for task utility, state staleness, and update cost. Problem (20) defines the system-level objective, but the implementation does not combine both event streams in one centralized Bellman recursion. Instead, CoSMO derives agentspecific returns from the same realized utility stream. The EN estimates the terminal utility of each task action, whereas the SN estimates a semi-Markov return over consecutive update intervals. This decomposition matches the times at which each agent’s consequences become observable while retaining reinforcement learning at both agents.

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IV. C O SMO: C OOPERATIVE S EMANTIC -AWARE U PDATING AND O FFLOADING A. Architecture Overview To solve the coupled update-and-offloading problem, we design C O SMO, a two-agent event-driven RL framework. The upper branch of Fig. 2 implements the information flow at the SN. The frozen encoder fθ (·) maps the raw SN state into a compact status semantic. This semantic, its cached copy, AoI, and link/task statistics form the SN observation. A temporal feature adapter then feeds the observation to the temporal semantic decision network, which produces update action values for each paired action (σn , gn ). The lower branch implements the task flow through dualbranch state encoding. The remote-context encoder processes the cached SN observation, while the local-context encoder processes the EN local observation. This separation encodes remote-semantic and local-task features with different dimensions, timescales, and statistical meanings before fusion. The feature fusion module combines both outputs and passes them to the hierarchical forwarding decision network. Its gate and route dueling heads produce the final forward actions: Rejection, local execution, or offloading. The utility-guided learning branch coordinates the agents without a centralized execution policy. Its reward mapping coordinator maps the common task utility stream Uk to EN per-task rewards and SN interval rewards. The agents retain separate replay streams and update through the EN loss branch and SN loss branch, while the encoder remains frozen. B. Raw-State Semantic Encoder We implement the encoder fθ (·) in (9) as a lightweight multilayer perceptron (MLP). The four-dimensional SN raw is first rescaled by a fixed per-dimension normalizer state xSN t and then encoded by
(1) ht = ReLU W1 xSN (29) t + b1 ;   (2) (1) ht = ReLU W2 ht + b2 ; (30) (2)

zt = W3 ht + b3 ,

(31)

with parameters θ = {W1 , b1 , W2 , b2 , W3 , b3 }. The output zt serves two purposes. It is the remote status semantic sent to and cached at the EN, and it forms part of the SN scheduler input. We use a lightweight MLP to map the multidimensional, physically interpretable raw state into a compact unified representation at low inference cost. Before utility-coordinated two-agent RL training, we pretrain fθ (·) independently with an interval-conditioned forwarddynamics prediction loss. The selected update interval gn conditions the predicted service-state evolution. A lightweight prediction head on zun computes   gn c , (32) ∆xun = gψ zun , gmax where gn is the selected SN decision interval, gmax is the c u is the predicted maximum candidate interval, and ∆x n

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Value Head Advantage Head

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Local-context Encoder FC-ReLU-FC-ReLU

Mobility

𝑄 (𝒉! , 𝑎$ )

SN Agent

𝑟-./ = > 𝑈0 − 𝜆1 𝐶-

Gate Dueling Head

FC-ReLU-FC-ReLU

ℝ#,

25 ms

Hierarchical Forwarding Decision Network

…

EN (Local) Observations

𝐴(𝒉$ , 𝑎)

20 ms

Semantic

Remote-context Encoder

Downlink Network Statistics

FC-ReLU-FC

Advantage Head

𝑄 (𝒉! , 𝑎" ) 𝑄 (𝒉! , 𝑎# )

𝑡

Dual-Branch State Encoding Semantic

𝑉(𝒉$ )

FC-ReLU-FC

Task

Cached SN Observations

Update Action Values

Value Head

𝑄 (𝒉$ , 𝑎) GRU

ReLU ReLU ReLU

Uplink Network Statistics

AoI

Temporal Dependency Encoder

…

SN State 𝒙"

7

− +

∑

Utility-Guided EN Policy Update

𝑄(Local)

+

∑

𝑟$%& = 𝑈$

𝑄(Of1load)

+ 𝑄&'() Accept = 𝑚𝑎𝑥(𝑄 Local , 𝑄(Of;load))

EN Agent

Fig. 2. Overview of the C O SMO architecture and information flow. SN information flows from Historical SN Observations through the Semantic State Encoder, which compresses service states into status semantics, to the Temporal Semantic Decision Network. Its Temporal Feature Adapter projects observation features, and its Temporal Dependency Encoder models temporal dependencies; the Value Head estimates state value and the Advantage Head estimates action advantages to select the next update interval. EN information flows from local EN observations and cached SN observations through Dual-Branch State Encoding, which separately encodes local task/service context and remote semantic/link context. Feature Fusion combines the two representations, and the Hierarchical Forwarding Decision Network first determines acceptance through its gate and then selects local execution or SN offloading through its route head. The Utility-Guided EN Policy Update and Utility-Guided SN Policy Update coordinate both agents through the shared task utility.

normalized state increment. The interval-conditioned forwarddynamics loss is ! N xSN − xSN 1 X u u n+1 n cu , SmoothL1 ∆x , Lpre (θ, ψ) = n N n=1 s (33) where s is the per-dimension normalization scale of the raw SN state. This loss governs the state change associated with the current service state and selected interval. It avoids contrastive negative samples, which can be ambiguous when service states repeat. The learned status semantic supports downstream control rather than raw-state reconstruction. The prediction loss Lpre therefore shapes zt to capture dynamics without reconstructing xSN t . After pretraining, the encoder is frozen and provides a fixed control semantic while only the SN update scheduler and EN offloading agent are updated. Service Node State 𝒙! Compute Resources

Workload Condition

Queueing Status

Storage Resources

Pretraining

Action-conditioned forward-dynamics head

Semantic 𝒛! Concat [𝒛! ; ∆t] Update Interval ∆t

Encoder 𝑓!

Semantic 𝒛!

Transition Head 𝑔"

Predicted Increment & ∆𝒙

Forwarddynamics loss ℒ#$%

Ground-truth Increment ∆𝒙

Fig. 3. Semantic encoder pretraining. The normalized SN raw state is mapped by fθ to the control semantic. Together with the normalized update interval, this semantic is fed to gψ to predict the normalized state increment for training with Lpre .

Fig. 3 illustrates the encoder workflow. The encoder fθ maps the normalized SN raw state to the control semantic zt . At

runtime, the SN transmits zt as the cached status and also supplies it to the update scheduler. The interval-conditioned head gψ reads zt and the selected decision interval only during the independent pretraining stage in (33). Then, this auxiliary head is discarded and the encoder is frozen, yielding a fixed representation shared by the updating and offloading policies. C. Temporal Semantic Decision Network The SN invokes its update scheduler at decision epoch un . The scheduler chooses whether to transmit the current semantic and how long to wait before the next decision. The candidate interval set is  G = g (1) , g (2) , . . . , g (L) , (34) with gmin ≤ g (1) < g (2) < · · · < g (L) ≤ gmax .

(35)

With the no-send option enabled, the discrete SN action set is  ASN = (σ, g (ℓ) ) : σ ∈ {0, 1}, ℓ = 1, . . . , L , (36) where σ = 1 denotes sending the current semantic and σ = 0 denotes skipping the current transmission. If nosend is disabled, ASN reduces to the always-send subset {(1, g (ℓ) ) : ℓ = 1, . . . , L}. From InSN in (10), we form the SN observation vector as
SN SN oSN In n =Γ 
eu , ψH Hcomp , (37) = zun , zcνn , A n n
 SN SN ψℓ ℓun , where ΓSN (·) is the feature construction, zun = fθ (xSN un ) is the current raw state’s semantic, and zcνn is the semantic eu cached at the EN before the new SN action. The term A n comp is the normalized age of the cached semantic. ψH (Hn ) comprises normalized statistics over offloaded tasks completed

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within the most recent window, including completion delay and success/failure rates. ψℓSN (ℓSN un ) comprises the short-term mean rate, rate standard deviation, and rate trend of the SN-toEN update link. Correspondingly, ψℓEN (ℓEN tk ) below uses the same kind of statistics for the EN-to-SN link. An SN update affects the objective through tasks served during the subsequent interval rather than immediately. We therefore project each SN observation into a feature vector and feed the resulting sequence into the GRU. Let
SN SN eSN (38) n = ϕωp on denote the projected SN feature, and let hSN n be the hidden state for the n-th decision:
SN SN (39) hSN n = GRUωg en , hn−1 , with projection parameters ωp and GRU parameters ωg . We apply a dueling Double DQN to hSN n , using a state-value branch and an advantage branch:

SN VωSN hSN , ASN a ∈ ASN , (40) n ωa hn , a , v and combine them into the SN action-value function


SN SN SN SN QSN + ASN ω hn , a =Vωv hn ωa hn , a X
1 SN ASN − SN ωa hn , ã , |A | SN

a∈ASN

To align the SN action values with the overall objective, the return for the nth decision includes all tasks arriving in its selected interval: (43)

The base interval reward is X

Uk − λs Cn ,

with target parameters ω − , discount base γSN ∈ (0, 1), and reference interval g0 = g (1) (the shortest candidate in G). The exponent gn /g0 measures the elapsed interval in units of g0 . The SN training loss is h
i SN SN SN , (47) LSN (ω) = E SmoothL1 QSN ω (hn , an ), yn where SmoothL1(·, ·) is the Huber loss (β = 1). It is less sensitive than squared error to the heavier-tailed SN targets induced by interval-level returns and sequence bootstrap. The replay buffer samples contiguous SN transition sequences, and the GRU is unrolled over each sequence during the update. During utility-coordinated training, the encoder fθ (·) is frozen. Thus, zun = fθ (xSN un ) is recomputed only to construct the current SN observation, while zcνn is taken directly from the cached EN copy stored in replay and bypasses re-encoding. D. EN Selective-Offloading Agent

with ω = {ωp , ωg , ωv , ωa }. The network takes oSN n and the SN SN previous hidden state hSN . It outputs [Q (h , a)] a∈ASN ∈ ω n n−1 R18 over the SN action set, yielding the decision
SN SN aSN aSN n = arg max Qω hn , a , n = (σn , gn ). (42)

SN rn,0 = βSN

heterogeneous intervals gn , a semi-Markov discount assigns greater discounts to longer waits. The implementation uses SN the normalized reward renSN = rnSN /sSN takes the r , where sr base task value V by default. With terminal indicator dn , the SN target value is
gn /g0 SN ⋆ ynSN = renSN + (1 − dn )γSN Qω− h̄SN (46) n+1 , an+1 ,

(41)

ã∈A

Kn = {k : un ≤ tk < un+1 }.

8

(44)

k∈Kn

This reward sums the task utilities over the following interval, optionally scaled by βSN for ablations, and subtracts the explicit semantic-update cost. In the main objective, βSN = 1. Since Cn = σn cs dz , the update cost is charged only for σn = 1. When no task arrives in the interval, the taskutility sum is zero. The trainer also supports an optional APvalue stale-loss shaping term in ablations; when its configured weight is zero, the reward used by the SN replay is exactly SN rnSN = rn,0 . Double DQN separates next-action selection and evaluation across two networks to reduce Q-value overestimation. The online network computes the next hidden state hSN n+1 and selects the greedy action:
′ a⋆n+1 = arg max QSN hSN (45) ω n+1 , a , a′ ∈ASN

The target network computes h̄SN n+1 and evaluates the selected action. Because consecutive SN decisions are separated by

At each task arrival, the EN selective-offloading agent selects one action from AEN = {0, 1, 2}: Local execution, offloading to the SN, or active rejection. As shown in the lower branch of Fig. 2, the agent encodes the directly observed local context separately from the cached remote SN context. A hierarchical gate–route network then processes the fused representation. This design reflects the different reliability and timescales of the two information sources. Local task, access, and EN service features are current and directly observed, whereas the remote semantic is compact, delayed, and affected by the update schedule and inter-node link. The gate makes the accept/reject decision under resource and deadline risk. Conditional on acceptance, the route head selects local execution or SN offloading. This structure preserves local feasibility cues, learns how much to trust stale remote semantics, and reduces interference between rejection and route selection. 1) Dual-Branch State Encoding From IkEN in (12), we construct the local and remote inputs: h i EN (48) oEN k,loc = mk , xtk , (bk , ck , Dk ) ; h i
c EN EN oEN ℓtk , (49) k,rem = zun(k) , ψℓ where oEN k,loc collects the directly observed access, task, and EN service state at arrival. The remote observation oEN k,rem contains the cached SN status semantic and inter-node link information. In particular, ψℓEN (ℓEN tk ) comprises the short-term mean rate, rate standard deviation, and rate trend of the EN-to-SN link. Separate two-layer MLPs encode the two inputs:
loc EN hEN (50) k,loc = fφℓ ok,loc ,
EN rem EN hk,rem = fφr ok,rem , (51)

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where φℓ and φr denote the two branch parameter sets. The resulting features are fused into the EN decision representation  EN 
EN hEN (52) k = ReLU Wf hk,loc , hk,rem + bf , where [ ·, · ] denotes concatenation, and Wf andbf are the fusion parameters. 2) Hierarchical Forwarding Decision Network Given the fused representation hEN k , the hierarchical forwarding decision network separates accept/reject from route selection. The gate head scores B = {reject, accept}, whereas the route head scores R = {0, 1}, corresponding to local execution and SN offloading. Each head adopts a dueling value–advantage decomposition:

EN Vφgate hEN , Agate b ∈ B; (53) k φga hk , b , gv

route EN route EN Vφρv hk , Aφρa hk , r , r ∈ R. (54) The corresponding dueling scores are


gate EN Qgate hEN hEN + Agate φ k , b = Vφgv k φga hk , b 1 X gate  EN  Aφga hk , b̃ ; (55) − |B| b̃∈B


route Qroute hEN hEN + Aroute hEN φ k , r = Vφρv k φρa k ,r 1 X route EN
Aφρa hk , r̃ . (56) − |R| r̃∈R

We combine the two heads through a hierarchy-consistent action-value reconstruction. The reject action retains the gate’s reject value. Each accepted action combines the gate’s accept value with its max-normalized route score:
 gate EN Qφ hk , accept   
 route hEN
 + Qφ , a ∈ {0, 1}; k ,a EN EN
Qφ hk , a = route EN  − max Qφ hk , r̃   r̃∈R 
 gate EN Qφ hk , reject , a = 2. (57) Under this reconstruction, the gate head determines the value of the accepted subtree. The route head represents only the relative preference between local execution and offloading within that subtree. Specifically,

gate max QEN hEN hEN (58) φ k , a = Qφ k , accept , a∈{0,1}

and

EN QEN hEN hEN φ k , 0 − Qφ k ,1

route = Qroute hEN hEN φ k , 0 − Qφ k ,1 .

(59)

Equation (58) assigns the gate’s accept value to the best accepted action. Equation (59) preserves the local/offload preference learned by the route head. In this sense, gate governs the top-level comparison, while the route head determines the conditional choice within the accepted branch. We define
qkrej = Qgate hEN (60) φ k , reject ,
acc gate EN qk = Qφ hk , accept . (61)

9

The gate-first decoder selects  2, qkrej ≥ qkacc ,
ak = rej acc arg max Qroute hEN φ k , r , qk < qk .

(62)

r∈R

The first stage makes the accept/reject decision. The second selects an execution route only for the accepted branch. The training-only gate and route auxiliary losses introduced below regularize these conditional decisions but are not used during execution. To align EN learning with the system objective, each tasklevel transition receives the realized net task utility rkEN = Uk .

(63)

The value of Uk may be unavailable at task arrival because it depends on the realized delay Tk and deadline outcome. For active rejection (ak = 2), the utility is immediately determined as a true-negative reward or false-negative penalty, according to (23) and (28), respectively. The false-positive utility is also available before execution if a local or offload attempt fails the selected-node acceptance check. Otherwise, for an accepted task, the EN first stores the transition prefix
EN EN ẽEN (64) k,pre = ok,loc , ok,rem , ak . After the task reaches a terminal outcome, the EN fills in rkEN = Uk and writes the completed transition to the replay buffer. During an EN optimizer update, the stored utility is normalized as ek = Uk , sEN = V. (65) U r sEN r This positive scaling preserves the action ordering while controlling the numerical range of targets across the four outcome classes. The EN learns the expected terminal utility of each hierarchical action from task-level environment feedback rather than minimizing only instantaneous transmission delay. Its value estimate is conditioned on the current access state, local load, cached remote semantic, and task timeliness requirement. Under overload, the learned policy may reject tasks that are unlikely to complete on time, avoiding their transmission, queueing, and compute costs. Each EN replay sample is completed only after the corresponding task outcome is known. We model the finalized task as a terminal EN transition. The general Bellman target therefore reduces to the normalized realized utility because the next-state bootstrap term vanishes: ykEN =

EN rkEN b e + γEN 1 − dEN Q k k+1 = Uk , sEN r

dEN k = 1,

(66) b EN denotes a generic next-state bootstrap value, where Q k+1 which is not evaluated for the EN’s task-terminal transitions. The resulting temporal-difference loss is 
EN
 EN LTD hEN . (67) EN (φ) = E SmoothL1 Qφ k , ak , yk Accordingly, the EN action-value function estimates h i
EN e QEN hEN φ k , ak ≈ E Uk | hk , ak .

(68)

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The EN remains an off-policy, value-based RL agent trained through exploration, environment feedback, and experience replay. Its task-terminal formulation does not require intertask bootstrapping. By contrast, the SN scheduler retains a semi-Markov Double DQN target across consecutive update intervals. The remote semantic in oEN k,rem is the historical copy transmitted by the SN and cached during interaction. The EN replay stores this copy and its remote-context features directly, rather than regenerating them from the instantaneous raw SN state during training. This preserves consistency with decentralized online execution. The EN loss updates only the offloadingagent parameters φ; the encoder parameters θ are pretrained and remain frozen throughout utility-coordinated training. E. Utility-Coordinated Training Algorithm The two trainable agents share an event-driven environment and are coordinated through the realized task-utility stream in Fig. 2. The encoder fθ (·) is pretrained and then frozen. Utility-coordinated training updates only the SN scheduler EN QSN ω (·, ·) and EN selective-offloading agent Qφ (·, ·). The reward coordinator maps each finalized task utility to the EN reward rkEN . It also aggregates the utilities realized over [un , un+1 ) into the SN reward rnSN , together with the optional normalization and shaping terms defined above. The agents use separate observations, replay buffers, and value losses. The EN learns a task-terminal action-value function from finalized outcomes, whereas the SN learns a recurrent semi-Markov action-value function across update intervals. The common task-utility stream coordinates these agents without a centralized critic. Optional oracle-derived gate–route labels regularize EN training but are unavailable during decentralized execution. Algorithm 1 summarizes the complete procedure. Algorithm 1 aligns the training loop with the event-driven execution interface. Line 2 initializes the episode. Line 5 selects SN transmission and the next decision interval, whereas Line 11 handles the EN task decision. A transmitted semantic affects the EN only after delivery to the EN cache. Because the utility of an accepted task is known only at its terminal outcome, Line 14 completes the delayed EN replay entry with the realized utility. Line 17 assigns the interval reward to the SN sequence sample. Line 19 then performs the agent-specific parameter updates. The EN updates follow (66)–(67). Since each completed EN transition is task-terminal, its value target contains no next-state bootstrap term and therefore does not require targetnetwork evaluation. When enabled, the training-only gate– route auxiliary losses are added to the EN loss but are not used during execution. These auxiliary terms are implementationlevel regularizers and are specified with the training hyperparameters in Section V-A2. The SN updates follow (46)–(47). The target parameters ω − are delayed copies of the online parameters ω. They evaluate the next action selected by the online network in the semiMarkov Double DQN target and are synchronized at the configured frequency. The training procedure thereby coordinates

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Algorithm 1 Utility-coordinated training of semantic updating and selective offloading. Require: Shared environment E, frozen pretrained encoder fθ , SN online and target parameters ω and ω − , EN parameters φ, and replay buffers DSN and DEN 1: for each training episode do 2: Reset E and clear the EN cached semantic and SN GRU state 3: while the episode is unfinished do 4: if an SN decision event un occurs then SN SN 5: Encode zun = fθ (xSN un ), build on , select an = (σn , gn ) using (42), transmit zun if σn = 1, and schedule the next decision at un+1 = un + gn 6: end if 7: if a transmitted SN semantic reaches the EN then 8: Update the EN semantic cache with the delivered semantic and its source timestamp 9: end if 10: if a task arrival tk occurs then 11: Build the EN local and cached-remote observations, select ak using (62), and store an EN transition prefix if its utility is not yet known 12: end if 13: if a task outcome is determined then 14: Finalize Uk using (23), assign rkEN = Uk , complete the EN transition, and write it to DEN 15: end if 16: if the update interval [un , un+1 ) ends then SN using (44) and write the corresponding SN 17: Compute rn sequence sample to DSN 18: end if 19: At the configured frequencies, update φ from DEN using the taskterminal EN loss and update ω from DSN using the semi-Markov Double DQN loss, with fθ frozen; synchronize ω − from ω when scheduled 20: end while 21: end for

semantic updating and selective offloading through a common utility objective while retaining agent-specific value-learning mechanisms. During decentralized execution, each agent uses only locally available observations, without real-time global state or training-only oracle information. The SN outputs aSN n = (σn , gn ) from InSN via (37), (39), and (42). The EN outputs ak from IkEN via (48), (49), (52), and (62). Thus, both execution policies are realizable from local information. F. Complexity Analysis tr Let CEN denote the EN network’s per-sample training cost. It includes forward and backward propagation through the local and remote encoders, feature-fusion layer, and hierartr chical gate–route heads. Let CSN denote the SN scheduler’s per-step training cost. It includes the frozen semantic-encoder forward pass, forward and backward propagation through the projection, GRU, and dueling head, and SN target-network evaluation. For one training episode with MEN EN optimizer updates, MSN SN optimizer updates, EN batch size BEN , SN batch size BSN , and sampled SN sequence length τ + 1, the neural training cost is

tr tr O MEN BEN CEN + Caux + MSN BSN (τ + 1)CSN , (69)

where Caux denotes the per-sample cost of generating and applying the training-only oracle-derived gate–route auxiliary

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TABLE I S IMULATION ENVIRONMENT CONFIGURATION . Component

Configuration

UE

4 nodes with straight-line constant-velocity mobility at 1 m/s; initial EN distances 5.2 m, 6.0 m, 6.8 m and 5.2 m; 8 m service radius IEEE 802.11n at 5 GHz with 40 MHz channel bandwidth; effective throughput ∼90–100 Mbps two-hop point-to-point path via one relay; EN→SN 96 Mbps, SN→EN 192 Mbps, 1 ms per hop 2 compute slots × 18 000 cycles/ms; storage 240 000 B; queue capacity 64 tasks 4 compute slots × 27 000 cycles/ms; storage 480 000 B; queue capacity 64 tasks 10 s arrival window; 2 s measurement warm-up; simulation continues until all generated tasks terminate

UE–EN access link

EN–SN backhaul

EN capability SN capability Episode protocol

supervision. With bounded EN and SN queues, this additional cost is constant with respect to the episode length. Replay memory scales as O(|DEN |dEN + |DSN |(τ + 1)dSN ) ,

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The controlled single-EN/single-SN topology holds the network structure, access conditions, and backhaul rates fixed across methods. The evaluation isolates semantic updating, task acceptance, and execution routing from topology and rate adaptation. Tasks arrive during a 10 s window in each episode, after which the simulation continues until every task reaches a terminal state. UE mobility determines the remaining connection time. Packet-transfer time includes serialization, queueing, propagation, and task-dependent transfer delays. The backhaul uses the fixed asymmetric directional rates in Table I. These experiments do not assess adaptation to backhaul-rate variability or short-term rate trends. For each UE–EN link, the payload size and measured upload delay determine the effective uplink-rate estimate, which is then smoothed by an EWMA. 2) Agent Implementation The learned policies are trained and selected using the taskutility parameters in Table II and (23). The training-only oracle described in Section IV provides the auxiliary gate and route labels. Table III reports the core architecture, action spaces, and training parameters.

(70)

where dEN and dSN denote the stored dimensions of one EN transition and one SN transition step, respectively. inf inf Let CEN and CSN denote the corresponding per-decision inference costs. At execution, replay sampling, oracle labeling, target-network evaluation, and backpropagation are removed. Therefore, an episode with NEN task decisions and NSN update decisions incurs
inf inf O NEN CEN + NSN CSN , (71) which is constant time per decision event for fixed network widths and bounded action sets. V. E XPERIMENTS We evaluate the proposed cooperative semantic-update and task-offloading policy when only stale remote-state information is available. The experiments assess whether the learned EN–SN policy can (i) make load-aware accept/reject decisions near and beyond the compute-capacity boundary, (ii) maintain on-time task completion, and (iii) reduce semantic-update overhead relative to freshness-driven policies. All methods use the same simulation environment, workload generation procedure, and measurement protocol. A. Experiment Settings 1) Simulation Environment The simulation is implemented in the ns-3.42 discrete-event network simulator [30] and connected to the Python learning process through the ns3-gym OpenGym bridge [31]. The topology contains four UEs, one EN, one forwarding relay, and one SN. The relay supports only two-hop EN–SN forwarding and provides no compute resources. Table I summarizes the environment parameters.

TABLE II R EWARD AND TRAINING CONFIGURATION . Category Parameter settings Task-utility scale and V = 80; (wTP , wFP , wTN , wFN ) = outcome weights (1.2, 5.0, 1.0, 1.5) Task-cost weights λT = 0.15; λc = 1 × 10−4 ; ηc = 0.20 SN update cost λs = 4.0 Auxiliary losses (wg , wr , wm ) = (1.0, 0.5, 0.2) for gate, route, and gate-margin losses; wb = 0.3 for failure-boundary ranking Exploration ϵ-greedy; linearly decayed from 1.0 to 0.05 over 3000 steps Training duration 80 episodes for each load and arrival-process setting Reported results Aggregated over three independent runs

The outcome weights prioritize accurate task selection. With V = 80, the base utilities before the secondary task-cost term are +96 for TP, −400 for FP, +80 for TN, and −120 for FN. Successful service is therefore preferred to justified rejection (wTP V > wTN V ), which discourages an overly conservative rejection policy. A false positive receives a larger penalty than a false negative (wFP V > wFN V ) because a task that is accepted but misses its deadline consumes limited queue and compute resources without meeting the service objective. The positive TN reward favors rejecting tasks that cannot be served under overload, whereas the FN penalty discourages excessive rejection. The scale V = 80 makes TP/FP/TN/FN outcomes the primary learning signal. The weight ηc = 0.20 keeps the taskcost term secondary when selecting among feasible accepted routes, preventing delay or transfer cost from dominating the accept/reject decision. The auxiliary loss weights prioritize gate prediction, route prediction, and gate-margin separation in decreasing order. The smaller ranking weight wb = 0.3 regularizes failure-boundary ordering without overriding the primary decision losses.

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TABLE III AGENT ARCHITECTURE AND REINFORCEMENT- LEARNING PARAMETERS . Parameter Semantic encoder

EN –

SN 4 → 32 → 16 → 2; pretrained and frozen during joint RL Decision network Local/remote MLPs 32–Projection 32; GRU hidden 32; fusion 64 size 32 Action space {Reject, local, offload} {send, no-send} × {20, 25, 30, 35, 40, 45, 50, 100, 200} ms Encoder pretraining – 20 ns-3 collection episodes; 50 epochs; batch 128; learning rate 5 × 10−4 RL learning rate 3 × 10−4 3 × 10−4 Discount γ Terminal targeta 0.99 (semi-Markov) Batch size 32 16 Replay buffer capac-4096 (uniform) 4096 (uniform) ity a Target-network syn-Inactive Every 200 updates chronization Optimizer update fre-Every 4 transitions Every 2 transitions quency Sequence length – 2 SN decisions Optimization Smooth L1 ; gradient clipSmooth L1 ; gradient clip 1.0 1.0 Note: The EN target-network object is retained for compatibility with the general Double DQN trainer. Because EN targets are task-terminal, the EN discount and target synchronization are inactive; the effective discount and target synchronization listed above apply only to the SN target.

3) Baselines We compare C O SMO with six baselines under identical workloads and the same evaluation protocol: • All local (EN): Accepts every task and executes it at the EN without offloading or adaptive status updates. • All offload (SN): Accepts every task and forwards it to the SN for remote execution. • Local until AP full: Executes tasks locally while ENside capacity is available and otherwise forwards them to the SN. • AoI threshold: Uses an analytically derived continuous AoI threshold to schedule raw-state updates without semantic awareness or RL [7]. • AoV gap: Sends a raw-state update when the normalized gap between the current and cached SN states exceeds a fixed threshold. • AoCI online: Follows the online Age of Changed Information (AoCI) threshold policy [32], which adapts a delay-aware update threshold from observed content changes. We also evaluate a hierarchical-decision ablation, denoted by C O SMO (w/o Gate). This variant replaces the accept/reject gate and the local/offload routing head with a single flat dueling Double DQN head that directly chooses among the same three EN actions. We evaluate the ablation at representative light-load, capacity-boundary, and overload points λ ∈ {120, 220, 320} tasks/s. 4) Datasets The workload is generated synthetically from the taskarrival and attribute distributions in Table IV. We use two arrival processes at the same mean rate λ: Deterministic arrivals with constant interarrival times and Poisson arrivals with exponential interarrival times. Deterministic arrivals provide evenly

TABLE IV DATASET AND WORKLOAD PARAMETERS . Parameter

Value

Arrival process

deterministic (constant interval), Poisson (exponential interval) {120, 160, 200, 220, 240, 280, 320} tasks/s (ρ ∈ [0.54, 1.45]) U (20 000, 50 000) B U (1.0 × 105 , 1.2 × 106 ) cycles e2e_lower_bound: 1.35 · min(local, offload) path delay + U (10, 30) ms, clipped to [60, 220] ms

Mean rate λ Input size Compute demand Deadline

spaced tasks for controlled load variation. Poisson arrivals introduce random bursts and temporary queues. Together, they test the policy under smooth and variable traffic at the same mean load. The seven arrival rates are chosen relative to the aggregate EN+SN compute capacity. Since the EN provides 2×18 000 cycles/ms and the SN provides 4×27 000 cycles/ms, the aggregate compute budget is 144 000 cycles/ms. With mean task demand c̄ = (1.0 × 105 + 1.2 × 106 )/2 = 6.5 × 105 cycles, the reference service rate is µ⋆ =

1000 × 144 000 ≈ 221 tasks/s. 6.5 × 105

(72)

Thus, λ ∈ {120, 160, 200, 220, 240, 280, 320} tasks/s spans ρ = λ/µ⋆ ∈ [0.54, 1.45], covering underload, the capacityboundary region, and overload. Deadlines are generated from the minimum feasible path delay plus limited slack, so overload requires active rejection rather than blind acceptance. 5) Evaluation Metrics All learned-policy evaluations use greedy actions (ϵ = 0). Final metrics for each run are computed from a five-episode ns-3 evaluation. Reported values are means over three runs, and error bars show two-sided 95% confidence intervals. Arrivals before 2000 ms are excluded as warm-up. Requests that do not reach the EN within 5 s after their deadlines receive zero reward and are omitted from the TP/FP/TN/FN decision counts. The primary metrics are: • System success rate: The fraction of measured tasks completed before their deadlines. • Decision accuracy: (TP + TN)/Ndec , where Ndec is the number of tasks for which the EN makes a valid decision. Under overload, a rejection may be forced by limited compute capacity rather than by an incorrect task-selection decision. We therefore define a common capacity-based rejection quota:   max (0, Dmeas − µcyc Wsvc ) q= . (73) c̄ The numerator is the demand that exceeds the compute service available during the service window; dividing by the mean per-task demand converts this excess into an estimated number of tasks. Specifically, Dmeas is the measured compute demand in CPU cycles, c̄ = Dmeas /Ndec is the mean per-task demand, µcyc = 2 × 18 000 + 4 × 27 000 = 144 000 cycles/ms is the aggregate

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2) On-Time Task Completion To compare on-time task completion across load conditions, Fig. 5 reports the system success rate, defined as the fraction of measured tasks completed before their deadlines. 1.0

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1) Capacity-Aware Decision Accuracy Fig. 4 compares capacity-aware decision accuracy across the complete load sweep. At λ ≤ 200 tasks/s (ρ ≤ 0.90), C O SMO achieves 0.990–1.000 under deterministic arrivals and 0.924–0.998 under Poisson arrivals. At the capacity boundary (λ = 220 tasks/s), the corresponding values are 0.954 and 0.880. Under strict overload (λ ∈ {240, 280, 320} tasks/s), its accuracy remains 0.930–0.941 under deterministic arrivals and 0.901–0.931 under Poisson arrivals. For example, at 320 tasks/s under Poisson arrivals, decision accuracy remains 0.901, although the system success rate is 0.620.

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In (74), 1{sendn =1} is an indicator that equals one if the nth decision sends an update and zero otherwise, Ntask is the number of generated tasks, and λ is the arrival rate in tasks/s, so Ntask /λ approximates the workload duration in seconds.

online, which corresponds to a 27.7% relative improvement. At 320 tasks/s, the three Poisson rejection-capable baselines range from 0.813 to 0.832. Overall, C O SMO maintains high capacity-aware decision accuracy from light load to deep overload and consistently outperforms the competing baselines. These results show that its task-selection accuracy is maintained across both arrival processes and the evaluated range of offered loads.

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EN+SN service rate, and Wsvc is the service window. A rejected task is normally a false negative when it could have been served on time. Under overload, however, the system may have to reject tasks because its capacity is insufficient. We therefore count up to q such rejections as load-justified true negatives. The same quota construction is used for every method. • Update-cost rate: For each SN update decision, sending an update incurs cost c0 dupd , while no-send incurs zero cost. We set c0 = 0.5; C O SMO uses dupd = 2 for semantic updates, and raw-state baselines use dupd = 4. Here c0 is the unit update-cost coefficient, dupd denotes the update payload dimension, and the subscript n indexes the n-th SN update decision. The normalized rate is P c0 dupd,n 1{sendn =1} . (74) Rupd = n Ntask /λ

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Fig. 4. Capacity-aware decision accuracy under deterministic and Poisson arrivals.

The rejection-capable baselines achieve lower decision accuracy under overload. Across the three strict-overload points, C O SMO’s relative gain over the best-performing competing method at each load ranges from 10.7% to 25.5% under deterministic arrivals and from 8.3% to 26.7% under Poisson arrivals. Averaged over these points, the corresponding gains are 17.6% and 17.9%. At the Poisson capacity boundary, C O SMO achieves 0.880, compared with 0.690 for AoCI

C O SMO attains the highest success rate at every evaluated load under both arrival processes. Its deterministic success rate decreases from 1.000 at 120 tasks/s to 0.642 at 320 tasks/s; the corresponding Poisson values are 0.998 and 0.620. The aggregate EN+SN compute capacity is approximately µ⋆ = 221 tasks/s. Therefore, at the strict-overload points λ ∈ {240, 280, 320} tasks/s, the capacity-limited upper bound is µ⋆ /λ. C O SMO achieves 93%–94% of this bound under deterministic arrivals and 89%–92% under Poisson arrivals. The lower Poisson ratios are consistent with greater queueing variability from bursty arrivals at the same mean load. The fixed baselines degrade as the load increases because their static rules either rely on a single execution site or cannot reject tasks under overload. Under Poisson arrivals, All offload decreases from 0.987 at 120 tasks/s to 0.168 at 320 tasks/s as the remote path saturates. All local decreases from 0.259 to 0.061 because it can use only EN compute. Local until AP full uses both execution sites but has no rejection control and achieves only 0.405 at the heaviest load. The rejectioncapable heuristics (AoV gap, AoI threshold, and AoCI online) outperform these fixed policies under overload but remain below C O SMO. Across all seven Poisson loads, C O SMO’s relative improvement over the best-performing competing method at each load averages 21.2%. From the capacity boundary through deep overload (λ ≥ 220 tasks/s), the improvement ranges from 24.5% to 28.0%. Its mean across the three strictoverload points is 26.7%. The deterministic sweep yields a mean relative improvement of 18.6%. At 320 tasks/s under Poisson arrivals, C O SMO achieves 0.620, compared with 0.498 for AoV gap, the best-performing competing method. This difference corresponds to a 24.5% improvement.

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C O SMO matches or exceeds every competing method in on-time completion rate at every load under both arrival processes and remains close to the capacity-limited upper bound under overload. Together with the preceding decision-accuracy results, these findings support C O SMO’s intended frameworklevel behavior. Across the evaluated settings, the complete closed-loop design coordinates SN semantic updates with EN task decisions while maintaining accurate task selection and high on-time completion. 3) Status-Update Efficiency To quantify status-update expenditure, we next compare the update-cost rate defined in (74). Methods that never transmit status updates have zero update cost in Fig. 6.

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cost than AoI threshold but achieves higher system success rate and decision accuracy under both arrival processes. It also outperforms the best-performing competitor for each task metric. The additional update effort therefore accompanies better decision quality and on-time completion under deep overload. 4) Training-Reward Stabilization To assess how quickly the training reward stabilizes across load and arrival-process settings, we examine its episode-wise trajectory. Fig. 7 shows five-episode moving averages of the training reward over three runs.

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Under deterministic arrivals, C O SMO’s update-cost rate increases from 5.10 cost units/s at 120 tasks/s to 46.71 cost units/s at 320 tasks/s. Under Poisson arrivals, it increases from 5.16 to 46.96 cost units/s over the same range. AoV gap incurs higher update cost, increasing from 223.45 to 429.53 cost units/s under deterministic arrivals and from 235.06 to 431.40 cost units/s under Poisson arrivals. AoCI online remains within 53.18–56.68 cost units/s and is also more expensive than C O SMO throughout the sweep. At 320 tasks/s, C O SMO reduces update cost relative to AoV gap by 89.1% under either arrival process. Relative to AoCI online, the reductions are 14.1% under deterministic arrivals and 15.5% under Poisson arrivals. Among the policies that transmit status updates, AoI threshold has the lowest mean update-cost rate at the two heaviest loads. From λ = 120 tasks/s to λ = 320 tasks/s, its rate increases from 12.39 to 20.19 cost units/s under deterministic arrivals and from 17.73 to 30.97 cost units/s under Poisson arrivals. At λ = 320 tasks/s, C O SMO’s corresponding rates are 46.71 (deterministic) and 46.96 (Poisson) cost units/s. These rates are 131.3% and 51.6% higher than those of AoI threshold. Across the separately trained load settings, the learned SN policies allocate little update cost at light load and more under overload. The SN controls this expenditure by deciding both whether to send an update and when to make the next update decision, rather than following a fixed update period. Together, the update-cost and task metrics characterize C O SMO’s closed-loop tradeoff. The load-specific learned policies keep update cost low at light load and raise it under overload. At λ = 320 tasks/s, C O SMO incurs higher update

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We use t90 as a descriptive reward-stabilization indicator. For each run, it is the first episode at which the smoothed reward reaches 90% of the change from its initial value to its final-ten-episode mean and remains beyond that level for five episodes. The median t90 is 6–7 episodes for all loads up to 220 tasks/s. Under deterministic overload, the medians are 11, 13, and 13 episodes at λ ∈ {240, 280, 320} tasks/s. Under Poisson arrivals, they are 18, 17, and 20 episodes. Thus, the median t90 does not exceed 20 episodes in any evaluated setting. 5) Hierarchical Decision Ablation To isolate the hierarchical decision structure, we replace the accept/reject gate and local/offload routing head with a single flat dueling Double DQN head that selects the same three actions. The remaining architecture, training budget, data, checkpoint selection, and evaluation protocol are unchanged. We compare this variant, denoted as C O SMO (w/o Gate), with C O SMO using paired runs at λ ∈ {120, 220, 320} tasks/s. Table V summarizes the paired success rate and decisionaccuracy results. At 120 tasks/s, the two policies have nearly identical mean outcomes. At the capacity boundary, C O SMO’s mean success rate and decision accuracy are higher than those of C O SMO (w/o Gate) by 1.0% and 1.3% under deterministic arrivals and by 1.5% and 1.0% under Poisson arrivals. The relative gains are larger in deep overload. At 320 tasks/s, they are 13.4% in success rate and 9.9% in decision accuracy under deterministic arrivals, and 8.8% and 2.6% under Poisson arrivals. As detailed in Table VI, at the same Poisson load, the hierarchical policy achieves 4.7% higher mean accepted-task success rate and 4.0% higher mean route accuracy. It also reduces the mean false-positive rate by 18.9%, from 0.123 to 0.099, while using comparable mean update cost.

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workload fluctuates more drastically around the same mean arrival rate, the hierarchical policy retains its convergence advantage over the flat action head, indicating more stable training behavior under workload variability.

TABLE V H IERARCHICAL GATE – ROUTE ABLATION ( MEAN ± STANDARD DEVIATION ). λ

Success Decision rate accuracy Deterministic arrivals C O SMO 1.000±0.000 1.000±0.000 C O SMO (w/o Gate) 1.000±0.000 1.000±0.000 C O SMO 0.950±0.012 0.954±0.012 C O SMO (w/o Gate) 0.941±0.006 0.943±0.008 C O SMO 0.642±0.039 0.930±0.043 C O SMO (w/o Gate) 0.566±0.021 0.847±0.035 Poisson arrivals C O SMO 0.998±0.001 0.998±0.001 C O SMO (w/o Gate) 0.999±<0.001 0.999±<0.001 C O SMO 0.868±0.010 0.880±0.014 C O SMO (w/o Gate) 0.856±0.004 0.872±0.006 C O SMO 0.620±0.024 0.901±0.027 C O SMO (w/o Gate) 0.570±0.044 0.877±0.049

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TABLE VI H IERARCHICAL GATE – ROUTE ABLATION METRICS UNDER P OISSON ARRIVALS ( MEAN ± STANDARD DEVIATION ). FP ↓ FN ↓ Gate-decision metrics C O SMO 0.002±0.001 0.000±0.000 120 C O SMO (w/o Gate) 0.001±<0.001 0.000±0.000 C O SMO 0.109±0.025 0.011±0.011 220 C O SMO (w/o Gate) 0.111±0.018 0.017±0.011 C O SMO 0.099±0.027 0.000±0.000 320 C O SMO (w/o Gate) 0.123±0.049 0.000±0.000 λ

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Accepted-task Episode Route success rate ↑ accuracy ↑ update cost ↓ Task-routing and update metrics C O SMO 0.998±0.001 0.998±0.001 51±0 120 C O SMO (w/o Gate) 0.999±<0.001 0.999±<0.001 51±0 C O SMO 0.889±0.024 0.911±0.013 101±27 220 C O SMO (w/o Gate) 0.885±0.017 0.917±0.007 105±18 C O SMO 0.862±0.036 0.895±0.025 471±36 320 C O SMO (w/o Gate) 0.823±0.068 0.861±0.059 468±69 λ

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We proposed C O SMO, a cooperative semantic-aware statusupdating and selective-offloading framework for decisions based on stale remote state. Across separately trained deterministic and Poisson load settings, C O SMO maintained high capacity-aware decision accuracy under overload and achieved the highest on-time completion rate. Its learned policies did not minimize update cost at every load. Instead, they used low update cost at light load and more under overload. This tradeoff is accompanied by higher task metrics than AoI threshold and lower update cost than AoV gap. The descriptive ablation trends associate the hierarchical gate–route structure with higher task metrics and earlier reward stabilization under deep overload. End-to-end comparisons support the complete decision-oriented co-design within the evaluated topology. The gate ablation isolates only the hierarchical EN factorization; the remaining gains are reported at the integrated-framework level rather than attributed to any individual module. The evaluation is limited to a controlled single-EN/singleSN topology. Fixed-rate backhaul and a fixed modulation and coding scheme isolate the coupling of status staleness with accept/reject and execution-routing decisions but do not test transfer across topologies. Future work will consider multiple ENs and SNs, time-varying backhaul, interference-coupled access, and policy transfer across topologies. R EFERENCES

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Fig. 8. Training-reward trajectories with and without the hierarchical gate– route factorization.

Fig. 8 shows that the two policies have similar trainingreward trajectories at light load. Under deep overload, the hierarchical policy stabilizes earlier and reaches a higher reward level for both arrival processes. Together with the task-outcome results, the mean trends suggest that the gate– route factorization is the most useful when accept/reject and routing decisions become tightly coupled under overload. In particular, under Poisson arrivals, where the instantaneous

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