Controlling Unknown Linear Dynamics with Bounded Multiplicative Regret

TL;DR

This paper introduces a control strategy for unknown linear systems that guarantees near-optimal performance within a constant factor for a fixed time horizon, focusing on bounded multiplicative regret.

Contribution

It presents a novel control approach that achieves near-optimality with bounded multiplicative regret for unknown linear dynamics over a fixed horizon.

Findings

Achieves near-optimal control performance within a constant factor.

Provides a strategy effective for fixed time horizons.

Demonstrates bounded multiplicative regret in control of unknown systems.

Abstract

We consider a simple control problem in which the underlying dynamics depend on a parameter that is unknown and must be learned. We exhibit a control strategy which is optimal to within a multiplicative constant. While most authors find strategies which are successful as the time horizon tends to infinity, our strategy achieves lowest expected cost up to a constant factor for a fixed time horizon.