Finite-time Analysis of Approximate Policy Iteration for the Linear Quadratic Regulator

Abstract

We study the sample complexity of approximate policy iteration (PI) for the Linear Quadratic Regulator (LQR), building on a recent line of work using LQR as a testbed to understand the limits of reinforcement learning (RL) algorithms on continuous control tasks. Our analysis quantifies the tension between policy improvement and policy evaluation, and suggests that policy evaluation is the dominant factor in terms of sample complexity. Specifically, we show that to obtain a controller that is within $\epsilon$ of the optimal LQR controller, each step of policy evaluation requires at most $(n+d{)}^3/{\epsilon }^2$ samples, where $n$ is the dimension of the state vector and $d$ is the dimension of the input vector. On the other hand, only $\log (1/\epsilon )$ policy improvement steps suffice, resulting in an overall sample complexity of $(n+d{)}^3{\epsilon }^{-2}\log (1/\epsilon )$. We furthermore build on our analysis and construct a simple adaptive procedure based on $\epsilon$-greedy exploration which relies on approximate PI as a sub-routine and obtains $T^{2/3}$ regret, improving upon a recent result of Abbasi-Yadkori et al.

References in corpus (9)

• Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator
• An Analysis of Reinforcement Learning with Function Approximation
• Simple random search provides a competitive approach to reinforcement learning
• On the Sample Complexity of the Linear Quadratic Regulator
• Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systems
• Near optimal finite time identification of arbitrary linear dynamical systems
• Model-Free Linear Quadratic Control via Reduction to Expert Prediction
• Online Least Squares Estimation with Self-Normalized Processes: An Application to Bandit Problems
• Learning Linear-Quadratic Regulators Efficiently with only $\sqrt{T}$ Regret

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