Constrained Online Decision-Making: A Unified Framework
Haichen Hu, David Simchi-Levi, Navid Azizan

TL;DR
This paper introduces a unified framework for constrained online decision-making that handles various applications and provides algorithms with strong theoretical guarantees, leveraging new complexity measures.
Contribution
It proposes a general algorithmic framework for constrained decision-making, incorporating upper counterfactual confidence bounds and a generalized eluder dimension for complex environments.
Findings
The framework applies to multiple constrained learning problems.
Algorithms achieve strong theoretical guarantees.
Introduces a generalized eluder dimension for complex density classes.
Abstract
Contextual online decision-making problems with constraints appear in a wide range of real-world applications, such as adaptive experimental design under safety constraints, personalized recommendation with resource limits, and dynamic pricing under fairness requirements. In this paper, we investigate a general formulation of sequential decision-making with stage-wise feasibility constraints, where at each round, the learner must select an action based on observed context while ensuring that a problem-specific feasibility criterion is satisfied. We propose a unified algorithmic framework that captures many existing constrained learning problems, including constrained bandits, active learning with label budgets, online hypothesis testing with Type I error control, and model calibration. Central to our approach is the concept of upper counterfactual confidence bounds, which enables the…
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Game Theory and Applications · Gaussian Processes and Bayesian Inference
