Beyond \tilde{O}(\sqrt{T}) Constraint Violation for Online Convex Optimization with Adversarial Constraints

We study Online Convex Optimization with adversarial constraints (COCO). At each round a learner selects an action from a convex decision set and then an adversary reveals a convex cost and a convex constraint function. The goal of the learner is to select a sequence of actions to minimize both regret and the cumulative constraint violation (CCV) over a horizon of length $T$.