Online Convex Optimization with Stochastic Constraints: Zero Constraint Violation and Bandit Feedback

• URL: http://arxiv.org/abs/2301.11267v2
• Date: Thu, 13 Jul 2023 23:40:26 GMT
• Title: Online Convex Optimization with Stochastic Constraints: Zero Constraint Violation and Bandit Feedback
• Authors: Yeongjong Kim, Dabeen Lee
• Abstract summary: We propose a variant of the drift-plus-penalty algorithm that guarantees $O(sqrtT)$ expected regret and zero constraint violation. Our algorithm is oblivious to the length of the time horizon $T$, in contrast to the vanilla drift-plus-penalty method.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper studies online convex optimization with stochastic constraints. We propose a variant of the drift-plus-penalty algorithm that guarantees $O(\sqrt{T})$ expected regret and zero constraint violation, after a fixed number of iterations, which improves the vanilla drift-plus-penalty method with $O(\sqrt{T})$ constraint violation. Our algorithm is oblivious to the length of the time horizon $T$, in contrast to the vanilla drift-plus-penalty method. This is based on our novel drift lemma that provides time-varying bounds on the virtual queue drift and, as a result, leads to time-varying bounds on the expected virtual queue length. Moreover, we extend our framework to stochastic-constrained online convex optimization under two-point bandit feedback. We show that by adapting our algorithmic framework to the bandit feedback setting, we may still achieve $O(\sqrt{T})$ expected regret and zero constraint violation, improving upon the previous work for the case of identical constraint functions. Numerical results demonstrate our theoretical results.

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