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This arXiv paper is a theoretical machine learning result on contextual bandits with stage-wise cost constraints, where only the chosen action's reward and cost are observed. Its main claim is that the proposed CS-UCCB algorithm achieves feasibility at every round and roughly √T regret without the eluder-dimension term that prior bounds rely on, under polylogarithmic covering-entropy assumptions. For practitioners, the key question is whether those assumptions hold in their setting, and the extension to infinite action sets depends on an explicit reward-design condition that deserves scrutiny.
Eluder-Dimension-Free Regret for Stage-Wise Constrained Contextual Bandits via Offline Regression
arXiv:2505.07101v4 Announce Type: replace-cross Abstract: Contextual bandits with stage-wise constraints model decisions that must control risk while learning from their outcomes. We study this problem when only the selected action's reward and cost are observed, with a general reward class and a convex class of nonlinear cost functions. We propose CS-UCCB, which combines offline regression, cost confidence sets, and upper counterfactual confidence bounds. Each regression fit defines a valid cost confidence set, while a geometry derived from covering entropy controls cumulative cost uncertainty along the sampled decisions. Under polylogarithmic covering entropy for both classes and polylogarithmic offline estimation error, the finite-action algorithm guarantees, with high probability, feasibility at every round and $\widetilde{\mathcal O}(\sqrt T)$ regret without an eluder-dimension term. We also extend the analysis to infinite actions under an explicit reward-design condition and compare our bound with existing eluder-dimension bounds.
Abstract:Contextual bandits with stage-wise constraints model decisions that must control risk while learning from their outcomes. We study this problem when only the selected action's reward and cost are observed, with a general reward class and a convex class of nonlinear cost functions. We propose CS-UCCB, which combines offline regression, cost confidence sets, and upper counterfactual confidence bounds. Each regression fit defines a valid cost confidence set, while a geometry derived from covering entropy controls cumulative cost uncertainty along the sampled decisions. Under polylogarithmic covering entropy for both classes and polylogarithmic offline estimation error, the finite-action algorithm guarantees, with high probability, feasibility at every round and $\widetilde{\mathcal O}(\sqrt T)$ regret without an eluder-dimension term. We also extend the analysis to infinite actions under an explicit reward-design condition and compare our bound with existing eluder-dimension bounds.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2505.07101 [stat.ML]
(or arXiv:2505.07101v4 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2505.07101 Focus to learn more arXiv-issued DOI via DataCite
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