Online Convex Optimization with Stochastic Constraints: Zero Constraint Violation and Bandit Feedback
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This paper studies online convex optimization with stochastic constraints. We propose a variant of the drift-plus-penalty algorithm that guarantees O(√(T)) expected regret and zero constraint violation, after a fixed number of iterations, which improves the vanilla drift-plus-penalty method with O(√(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(√(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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