An online algorithm exploiting the geometry of nested convex constraint sets achieves O(√T) static regret and O(1) cumulative constraint violation for spheres, boxes, and the online constraint satisfaction problem.
Online convex optimization with hard constraints: Towards the best of two worlds and beyond
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$O(\sqrt{T})$ Static Regret and Instance Dependent Constraint Violation for Constrained Online Convex Optimization
An online algorithm exploiting the geometry of nested convex constraint sets achieves O(√T) static regret and O(1) cumulative constraint violation for spheres, boxes, and the online constraint satisfaction problem.