Dyna-Style Planning with Linear Function Approximation and Prioritized Sweeping

TL;DR

This paper extends the Dyna architecture to linear function approximation, providing convergence guarantees and demonstrating improved planning efficiency through prioritized sweeping in large state spaces.

Contribution

It introduces a linear Dyna-style planning method with proven convergence and extends prioritized sweeping to linear function approximation, supported by empirical results.

Findings

Linear Dyna converges to a unique solution regardless of the distribution.

In the policy evaluation setting, the solution aligns with the LSTD method.

Empirical tests show improved performance on Mountain Car and Boyan Chain problems.

Abstract

We consider the problem of efficiently learning optimal control policies and value functions over large state spaces in an online setting in which estimates must be available after each interaction with the world. This paper develops an explicitly model-based approach extending the Dyna architecture to linear function approximation. Dynastyle planning proceeds by generating imaginary experience from the world model and then applying model-free reinforcement learning algorithms to the imagined state transitions. Our main results are to prove that linear Dyna-style planning converges to a unique solution independent of the generating distribution, under natural conditions. In the policy evaluation setting, we prove that the limit point is the least-squares (LSTD) solution. An implication of our results is that prioritized-sweeping can be soundly extended to the linear approximation case, backing up to preceding features rather than to preceding states. We introduce two versions of prioritized sweeping with linear Dyna and briefly illustrate their performance empirically on the Mountain Car and Boyan Chain problems.