Exact Asymptotics for Linear Quadratic Adaptive Control

by   Feicheng Wang, et al.

Recent progress in reinforcement learning has led to remarkable performance in a range of applications, but its deployment in high-stakes settings remains quite rare. One reason is a limited understanding of the behavior of reinforcement algorithms, both in terms of their regret and their ability to learn the underlying system dynamics—existing work is focused almost exclusively on characterizing rates, with little attention paid to the constants multiplying those rates that can be critically important in practice. To start to address this challenge, we study perhaps the simplest non-bandit reinforcement learning problem: linear quadratic adaptive control (LQAC). By carefully combining recent finite-sample performance bounds for the LQAC problem with a particular (less-recent) martingale central limit theorem, we are able to derive asymptotically-exact expressions for the regret, estimation error, and prediction error of a rate-optimal stepwise-updating LQAC algorithm. In simulations on both stable and unstable systems, we find that our asymptotic theory also describes the algorithm's finite-sample behavior remarkably well.


page 1

page 2

page 3

page 4


Thompson Sampling for Linear-Quadratic Control Problems

We consider the exploration-exploitation tradeoff in linear quadratic (L...

Finite-sample Analysis of Greedy-GQ with Linear Function Approximation under Markovian Noise

Greedy-GQ is an off-policy two timescale algorithm for optimal control i...

Finite Time Analysis of Optimal Adaptive Policies for Linear-Quadratic Systems

We consider the classical problem of control of linear systems with quad...

Learning Linearized Models from Nonlinear Systems with Finite Data

Identifying a linear system model from data has wide applications in con...

Thompson Sampling Achieves Õ(√(T)) Regret in Linear Quadratic Control

Thompson Sampling (TS) is an efficient method for decision-making under ...

Finite-Sample Analyses for Fully Decentralized Multi-Agent Reinforcement Learning

Despite the increasing interest in multi-agent reinforcement learning (M...

A Tour of Reinforcement Learning: The View from Continuous Control

This manuscript surveys reinforcement learning from the perspective of o...

Please sign up or login with your details

Forgot password? Click here to reset