Online Nonstochastic Control with Adversarial and Static Constraints

TL;DR

This paper develops online control algorithms that effectively handle adversarial and static constraints, achieving low regret and constraint violations while outperforming existing methods in experiments.

Contribution

It introduces a novel online control framework with a memory-based convex optimization subroutine, achieving state-of-the-art bounds and improved practical performance.

Findings

Achieves sublinear regret and constraint violation.

Outperforms existing algorithms in cumulative cost and constraint violations.

Provides a new framework for constrained online convex optimization.

Abstract

This paper studies online nonstochastic control problems with adversarial and static constraints. We propose online nonstochastic control algorithms that achieve both sublinear regret and sublinear adversarial constraint violation while keeping static constraint violation minimal against the optimal constrained linear control policy in hindsight. To establish the results, we introduce an online convex optimization with memory framework under adversarial and static constraints, which serves as a subroutine for the constrained online nonstochastic control algorithms. This subroutine also achieves the state-of-the-art regret and constraint violation bounds for constrained online convex optimization problems, which is of independent interest. Our experiments demonstrate the proposed control algorithms are adaptive to adversarial constraints and achieve smaller cumulative costs and violations. Moreover, our algorithms are less conservative and achieve significantly smaller cumulative costs than the state-of-the-art algorithm.