Online Control with Adversarial Disturbances

TL;DR

This paper introduces an efficient online control algorithm for linear systems with adversarial disturbances, achieving near-optimal regret bounds and extending previous models to include adversarial noise and convex costs.

Contribution

It presents a novel algorithm that handles adversarial disturbances in linear control with general convex costs, providing tight regret guarantees.

Findings

Achieves nearly tight regret bounds for adversarial disturbances.

Extends control models to include general convex costs.

Provides an efficient algorithm for online control under adversarial noise.

Abstract

We study the control of a linear dynamical system with adversarial disturbances (as opposed to statistical noise). The objective we consider is one of regret: we desire an online control procedure that can do nearly as well as that of a procedure that has full knowledge of the disturbances in hindsight. Our main result is an efficient algorithm that provides nearly tight regret bounds for this problem. From a technical standpoint, this work generalizes upon previous work in two main aspects: our model allows for adversarial noise in the dynamics, and allows for general convex costs.