Adaptive Gradient Online Control

TL;DR

This paper introduces an adaptive gradient online control method for linear systems with adversarial disturbances, achieving improved regret guarantees that interpolate between known bounds.

Contribution

It generalizes the online Disturbance Response Controller to an adaptive gradient version, providing novel regret bounds that improve upon previous results.

Findings

Achieves intermediate regret rates between √T and log T.

Recovers known regret bounds for convex and strongly convex costs.

Demonstrates improved theoretical guarantees for online control.

Abstract

In this work we consider the online control of a known linear dynamic system with adversarial disturbance and adversarial controller cost. The goal in online control is to minimize the regret, defined as the difference between cumulative cost over a period $T$ and the cumulative cost for the best policy from a comparator class. For the setting we consider, we generalize the previously proposed online Disturbance Response Controller (DRC) to the adaptive gradient online Disturbance Response Controller. Using the modified controller, we present novel regret guarantees that improves the established regret guarantees for the same setting. We show that the proposed online learning controller is able to achieve intermediate intermediate regret rates between $\sqrt{T}$ and $\log{T}$ for intermediate convex conditions, while it recovers the previously established regret results for general convex controller cost and strongly convex controller cost.