On the Convergence Rate of Off-Policy Policy Optimization Methods with Density-Ratio Correction
Abstract
In this paper, we study the convergence properties of off-policy policy optimization algorithms with state-action density ratio correction under function approximation setting, where the objective function is formulated as a max-max-min problem. We first clearly characterize the bias of the learning objective, and then present two strategies with finite-time convergence guarantees. In our first strategy, we propose an algorithm called P-SREDA with convergence rate $O(\epsilon^{-3})$, whose dependency on $\epsilon$ is optimal. Besides, in our second strategy, we design a new off-policy actor-critic style algorithm named O-SPIM. We prove that O-SPIM converges to a stationary point with total complexity $O(\epsilon^{-4})$, which matches the convergence rate of some recent actor-critic algorithms in the on-policy setting.
BibTeX
@InProceedings{pmlr-v151-huang22a,
title = { On the Convergence Rate of Off-Policy Policy Optimization Methods with Density-Ratio Correction },
author = {Huang, Jiawei and Jiang, Nan},
booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
pages = {2658--2705},
year = {2022},
editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
volume = {151},
series = {Proceedings of Machine Learning Research},
month = {28--30 Mar},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v151/huang22a/huang22a.pdf},
url = {https://proceedings.mlr.press/v151/huang22a.html},
abstract = { In this paper, we study the convergence properties of off-policy policy optimization algorithms with state-action density ratio correction under function approximation setting, where the objective function is formulated as a max-max-min problem. We first clearly characterize the bias of the learning objective, and then present two strategies with finite-time convergence guarantees. In our first strategy, we propose an algorithm called P-SREDA with convergence rate $O(\epsilon^{-3})$, whose dependency on $\epsilon$ is optimal. Besides, in our second strategy, we design a new off-policy actor-critic style algorithm named O-SPIM. We prove that O-SPIM converges to a stationary point with total complexity $O(\epsilon^{-4})$, which matches the convergence rate of some recent actor-critic algorithms in the on-policy setting. }
}