Safety in the Face of Adversity: Achieving Zero Constraint Violation in Online Learning with Slowly Changing Constraints

TL;DR

This paper introduces a primal-dual online learning method that guarantees zero constraint violations over all rounds despite slowly changing constraints, ensuring safety and low regret.

Contribution

It provides the first theoretical framework for zero constraint violation in online convex optimization with dynamic constraints, using a novel dichotomous learning rate.

Findings

Guarantees zero constraint violation across all rounds.

Achieves sublinear regret with safety guarantees.

Handles gradually evolving constraints effectively.

Abstract

We present the first theoretical guarantees for zero constraint violation in Online Convex Optimization (OCO) across all rounds, addressing dynamic constraint changes. Unlike existing approaches in constrained OCO, which allow for occasional safety breaches, we provide the first approach for maintaining strict safety under the assumption of gradually evolving constraints, namely the constraints change at most by a small amount between consecutive rounds. This is achieved through a primal-dual approach and Online Gradient Ascent in the dual space. We show that employing a dichotomous learning rate enables ensuring both safety, via zero constraint violation, and sublinear regret. Our framework marks a departure from previous work by providing the first provable guarantees for maintaining absolute safety in the face of changing constraints in OCO.