Online Nonstochastic Control with Adversarial and Static Constraints
This addresses control problems with constraints for applications requiring robust performance, though it appears incremental as it builds on existing online nonstochastic control frameworks.
The paper tackles online nonstochastic control problems with adversarial and static constraints by proposing algorithms that achieve sublinear regret and constraint violations against an optimal constrained policy. Experimental results show the algorithms are adaptive, less conservative, and achieve significantly smaller cumulative costs than state-of-the-art methods.
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.