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**Reducing Sampling Error in Batch Temporal Difference Learning**.

Brahma Pavse,
Ishan Durugkar, Josiah Hanna,
and Peter Stone.

In *Proceedings of the 37th International Conference
on Machine Learning (ICML)*, July 2020.

The paper and talk is available from the ICML
2020 virtual conference page.

[PDF]738.4kB [slides.pdf]5.2MB

Temporal difference (TD) learning is one of the main foundations of modern reinforcement learning. This paper studies the
use of TD(0), a canonical TD algorithm, to estimate the value function of a given policy from a batch of data. In this batch
setting, we show that TD(0) may converge to an inaccurate value function because the update following an action is weighted
according to the number of times that action occurred in the batch -- not the true probability of the action under the given
policy. To address this limitation, we introduce *policy sampling error corrected*-TD(0) (PSEC-TD(0)). PSEC-TD(0) first
estimates the empirical distribution of actions in each state in the batch and then uses importance sampling to correct for
the mismatch between the empirical weighting and the correct weighting for updates following each action. We refine the concept
of a certainty-equivalence estimate and argue that PSEC-TD(0) is a more data efficient estimator than TD(0) for a fixed batch
of data. Finally, we conduct an empirical evaluation of PSEC-TD(0) on three batch value function learning tasks, with a hyperparameter
sensitivity analysis, and show that PSEC-TD(0) produces value function estimates with lower mean squared error than TD(0).

@InProceedings{ICML2020-Pavse, author={Brahma Pavse and Ishan Durugkar and Josiah Hanna and Peter Stone}, title={Reducing Sampling Error in Batch Temporal Difference Learning}, booktitle={Proceedings of the 37th International Conference on Machine Learning (ICML)}, month={July}, year={2020}, location={Vienna, Austria (Virtual Conference)}, abstract={ Temporal difference (TD) learning is one of the main foundations of modern reinforcement learning. This paper studies the use of TD(0), a canonical TD algorithm, to estimate the value function of a given policy from a batch of data. In this batch setting, we show that TD(0) may converge to an inaccurate value function because the update following an action is weighted according to the number of times that action occurred in the batch -- not the true probability of the action under the given policy. To address this limitation, we introduce \textit{policy sampling error corrected}-TD(0) (PSEC-TD(0)). PSEC-TD(0) first estimates the empirical distribution of actions in each state in the batch and then uses importance sampling to correct for the mismatch between the empirical weighting and the correct weighting for updates following each action. We refine the concept of a certainty-equivalence estimate and argue that PSEC-TD(0) is a more data efficient estimator than TD(0) for a fixed batch of data. Finally, we conduct an empirical evaluation of PSEC-TD(0) on three batch value function learning tasks, with a hyperparameter sensitivity analysis, and show that PSEC-TD(0) produces value function estimates with lower mean squared error than TD(0). }, wwwnote={The paper and talk is available from the <a href="https://icml.cc/virtual/2020/poster/6626">ICML 2020 virtual conference page</a>.}, }

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