$\tilde{O}(\sqrt{T})$ Regret and Polylogarithmic Constraint Violation for COCO

We study constrained online convex optimization with adversarial convex losses and constraints ($\mathsf{COCO}$). At each round \(t\in[T]\), a learner selects \(x_t\) from a \(d\)-dimensional convex decision set \(\mathcal X\), after which an adaptive adversary reveals a convex cost function…