Leverage the Average: an Analysis of KL Regularization in Reinforcement Learning

Part of Advances in Neural Information Processing Systems 33 pre-proceedings (NeurIPS 2020)

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Nino Vieillard, Tadashi Kozuno, Bruno Scherrer, Olivier Pietquin, Remi Munos, Matthieu Geist


<p>Recent Reinforcement Learning (RL) algorithms making use of Kullback-Leibler (KL) regularization as a core component have shown outstanding performance. Yet, only little is understood theoretically about why KL regularization helps, so far. We study KL regularization within an approximate value iteration scheme and show that it implicitly averages q-values. Leveraging this insight, we provide a very strong performance bound, the very first to combine two desirable aspects: a linear dependency to the horizon (instead of quadratic) and an error propagation term involving an averaging effect of the estimation errors (instead of an accumulation effect). We also study the more general case of an additional entropy regularizer. The resulting abstract scheme encompasses many existing RL algorithms. Some of our assumptions do not hold with neural networks, so we complement this theoretical analysis with an extensive empirical study.</p>