Budget-Constrained Causal Bandits: Bridging Uplift Modeling and Sequential Decision-Making

[2604.26169] Budget-Constrained Causal Bandits: Bridging Uplift Modeling and Sequential Decision-Making Skip to main content Search Submit Donate Log in Computer Science > Machine Learning arXiv:2604.26169 (cs) [Submitted on 28 Apr 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Budget-Constrained Causal Bandits: Bridging Uplift Modeling and Sequential Decision-Making Authors: Abhirami Pillai View PDF HTML (experimental) Abstract: Treatment allocation under budget constraints is a central challenge in digital advertising. The standard approach trains an offline uplift model on historical data, then solves a constrained optimization to allocate budget. This fails in cold-start settings where little historical data exists. We propose Budget-Constrained Causal Bandits (BCCB), an online framework that learns which users respond to ads while simultaneously spending the budget. BCCB unifies three components: learning individual-level treatment effects, exploring users whose response is uncertain, and pacing the budget over time. We derive the per-arrival decision rule as the KKT condition of a Lagrangian relaxation of the budgeted causal-allocation objective, providing a principled foundation for the algorithm. We evaluate on the Criteo Uplift dataset using 20 random seeds with paired statistical tests. Our central finding is a data-efficiency crossover at n = 7,500 historical observations (paired one-sided t-test, p = 0.043): below this threshold, offline pipelines either fail or produce unreliable allocations, while BCCB operates from the first user. BCCB exhibits 2-4x lower run-to-run variance than offline methods and outperforms all four online baselines (Thompson Sampling, budgeted Thompson Sampling, HTE Greedy, and Uplifting Bandits) at every budget level tested (p < 0.001). These results give practitioners a concrete decision rule for choosing between offline and online paradigms. Comments: 17 pages, 5 tables. v2: Expanded to 20 random seeds with paired statistical tests; formal crossover test at n=7,500 (p=0.043); added Uplifting Bandits (Hsieh et al., NeurIPS 2022) as fifth baseline; Lagrangian derivation of decision rule with Proposition 1; hyperparameter sensitivity analysis; corrected mathematical claims Subjects: Machine Learning (cs.LG) ; Econometrics (econ.EM); Machine Learning (stat.ML) ACM classes: I.2.6; G.3 Cite as: arXiv:2604.26169 [cs.LG] (or arXiv:2604.26169v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2604.26169 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Abhirami Pillai [ view email ] [v1] Tue, 28 Apr 2026 23:24:26 UTC (487 KB) [v2] Fri, 28 Aug 2026 02:56:12 UTC (28 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2026-04 Change to browse by: cs econ econ.EM stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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