From Importance Sampling to Doubly Robust Policy Gradient
Abstract
We show that on-policy policy gradient (PG) and its variance reduction variants can be derived by taking finite-difference of function evaluations supplied by estimators from the importance sampling (IS) family for off-policy evaluation (OPE). Starting from the doubly robust (DR) estimator (Jiang & Li, 2016), we provide a simple derivation of a very general and flexible form of PG, which subsumes the state-of-the-art variance reduction technique (Cheng et al., 2019) as its special case and immediately hints at further variance reduction opportunities overlooked by existing literature. We analyze the variance of the new DR-PG estimator, compare it to existing methods as well as the Cramer-Rao lower bound of policy gradient, and empirically show its effectiveness.
BibTeX
@InProceedings{pmlr-v119-huang20b,
title = {From Importance Sampling to Doubly Robust Policy Gradient},
author = {Huang, Jiawei and Jiang, Nan},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {4434--4443},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/huang20b/huang20b.pdf},
url = {https://proceedings.mlr.press/v119/huang20b.html},
abstract = {We show that on-policy policy gradient (PG) and its variance reduction variants can be derived by taking finite-difference of function evaluations supplied by estimators from the importance sampling (IS) family for off-policy evaluation (OPE). Starting from the doubly robust (DR) estimator (Jiang & Li, 2016), we provide a simple derivation of a very general and flexible form of PG, which subsumes the state-of-the-art variance reduction technique (Cheng et al., 2019) as its special case and immediately hints at further variance reduction opportunities overlooked by existing literature. We analyze the variance of the new DR-PG estimator, compare it to existing methods as well as the Cramer-Rao lower bound of policy gradient, and empirically show its effectiveness.}
}