Online Convex Optimization with Stochastic Constraints

TL;DR

This paper introduces a new algorithm for online convex optimization with stochastic constraints, achieving sublinear regret and constraint violations, applicable to various constrained decision-making problems.

Contribution

It proposes a novel algorithm for OCO with stochastic constraints, providing theoretical guarantees and practical validation in data center scheduling.

Findings

Achieves $O( oot{T})$ expected regret and constraint violations.

Attains $O( oot{T}\log(T))$ high probability bounds.

Demonstrates effectiveness on real-world data center scheduling.

Abstract

This paper considers online convex optimization (OCO) with stochastic constraints, which generalizes Zinkevich's OCO over a known simple fixed set by introducing multiple stochastic functional constraints that are i.i.d. generated at each round and are disclosed to the decision maker only after the decision is made. This formulation arises naturally when decisions are restricted by stochastic environments or deterministic environments with noisy observations. It also includes many important problems as special cases, such as OCO with long term constraints, stochastic constrained convex optimization, and deterministic constrained convex optimization. To solve this problem, this paper proposes a new algorithm that achieves $O(\sqrt{T})$ expected regret and constraint violations and $O(\sqrt{T}\log(T))$ high probability regret and constraint violations. Experiments on a real-world data center scheduling problem further verify the performance of the new algorithm.