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Importance Sampling in Reinforcement Learning with an Estimated Behavior Policy.
Josiah
P. Hanna, Scott Niekum, and Peter
Stone.
Machine Learning (MLJ), 110:1267–1317, May 2021.
In reinforcement learning, importance sampling is a widely used method for evaluating an expectation under the distribution of data of one policy when the data has in fact been generated by a different policy. Importance sampling requires computing the likelihood ratio between the action probabilities of a target policy and those of the data-producing behavior policy. In this article, we study importance sampling where the behavior policy action probabilities are replaced by their maximum likelihood estimate of these probabilities under the observed data. We show this general technique reduces variance due to sampling error in Monte Carlo style estimators. We introduce two novel estimators that use this technique to estimate expected values that arise in the RL literature. We find that these general estimators reduce the variance of Monte Carlo sampling methods, leading to faster learning for policy gradient algorithms and more accurate off-policy policy evaluation. We also provide theoretical analysis showing that our new estimators are consistent and have asymptotically lower variance than Monte Carlo estimators.
@article{MLJ21-Hanna,
author = {Josiah P. Hanna and Scott Niekum and Peter Stone},
title = {Importance Sampling in Reinforcement Learning with an Estimated Behavior Policy},
journal = {Machine Learning (MLJ)},
year = {2021},
volume ={110},
issue={6},
month={May},
pages={1267--1317},
abstract = {
In reinforcement learning, importance sampling is a
widely used method for evaluating an expectation under
the distribution of data of one policy when the data has
in fact been generated by a different policy.
Importance sampling requires computing the likelihood
ratio between the action probabilities of a target
policy and those of the data-producing behavior
policy. In this article, we study importance sampling
where the behavior policy action probabilities are
replaced by their maximum likelihood estimate of these
probabilities under the observed data. We show this
general technique reduces variance due to sampling error
in Monte Carlo style estimators. We introduce two novel
estimators that use this technique to estimate expected
values that arise in the RL literature. We find that
these general estimators reduce the variance of Monte
Carlo sampling methods, leading to faster learning for
policy gradient algorithms and more accurate off-policy
policy evaluation. We also provide theoretical analysis
showing that our new estimators are consistent and have
asymptotically lower variance than Monte Carlo
estimators.
},
}
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