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arXiv · 2403.05786

Optimistic Safety for Online Convex Optimization with Unknown Linear Constraints

Spencer Hutchinson·Tianyi Chen·Mahnoosh Alizadeh
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Abstract

We study the problem of online convex optimization (OCO) under unknown linear constraints that are either static, or stochastically time-varying. For this problem, we introduce an algorithm that we term Optimistically Safe OCO (OSOCO) and show that it enjoys $\tilde{O}(\sqrt{T})$ regret and no constraint violation. In the case of static linear constraints, this improves on the previous best known $\tilde{O}(T^{2/3})$ regret under the same assumptions. In the case of stochastic time-varying constraints, our work supplements existing results that show $O(\sqrt{T})$ regret and $O(\sqrt{T})$ cumulative violation under more general convex constraints and a different set of assumptions. In addition to our theoretical guarantees, we also give numerical results that further validate the effectiveness of our approach.

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Spencer Hutchinson, Tianyi Chen, Mahnoosh Alizadeh. 2024-03-09. Optimistic Safety for Online Convex Optimization with Unknown Linear Constraints. https://arxiv.org/abs/2403.05786

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