Despite the empirical success of the actor-critic algorithm, its theoretical understanding lags behind. In a broader context, actor-critic can be viewed as an online alternating update algorithm for bilevel optimization, whose convergence is known to be fragile. To understand the instability of actor-critic, we focus on its application to linear quadratic regulators, a simple yet fundamental setting of reinforcement learning. We establish a nonasymptotic convergence analysis of actor-critic in this setting. In particular, we prove that actor-critic finds a globally optimal pair of actor (policy) and critic (action-value function) at a linear rate of convergence. Our analysis may serve as a preliminary step towards a complete theoretical understanding of bilevel optimization with nonconvex subproblems, which is NP-hard in the worst case and is often solved using heuristics.
|Original language||English (US)|
|Journal||Advances in Neural Information Processing Systems|
|State||Published - 2019|
|Event||33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019 - Vancouver, Canada|
Duration: Dec 8 2019 → Dec 14 2019
Bibliographical notePublisher Copyright:
© 2019 Neural information processing systems foundation. All rights reserved.