CISE Seminar: Abhishek Sinha, School of Technology and Computer Science at the Tata Institute of Fundamental Research

Date: June 17th, 2025
Time: 2:00pm – 3:00pm
Location: 665 Commonwealth Ave., CDS 1101

Abhishek Sinha
School of Technology and Computer Science
Tata Institute of Fundamental Research

Optimal Algorithms for Online Convex Optimization with Adversarial Constraints

A well-studied generalization of the standard online convex optimization (OCO) is constrained online convex optimization (COCO). In COCO, on every round, a convex cost function and a convex constraint function are revealed to the learner after the action for that round is chosen. The objective is to design an online policy that simultaneously achieves a small regret while ensuring a small cumulative constraint violation (CCV) against an adaptive adversary interacting over a horizon of length $T$. A long-standing open question in COCO is whether an online policy can simultaneously achieve $O(\sqrt{T})$ regret and $O(\sqrt{T})$ CCV without any restrictive assumptions. For the first time, we answer this in the affirmative and show that an online policy can simultaneously achieve $O(\sqrt{T})$ regret and $\tilde{O}(\sqrt{T})$ CCV. Furthermore, in the case of strongly convex cost and convex constraint functions, the regret guarantee can be improved to $O(\log T)$ while keeping the CCV bound the same as above. We establish these results by effectively combining the adaptive regret bound of the AdaGrad algorithm with Lyapunov optimization – a classic tool from control theory. Surprisingly, the analysis is short and elegant.