## Revisiting Peng's Q(λ) for modern reinforcement learning

##### Abstract

Off-policy multi-step reinforcement learning algorithms consist of conservative and non-conservative algorithms: the former actively cut traces, whereas the latter do not. Recently, Munos et al. (2016) proved the convergence of conservative algorithms to an optimal Q-value function. On the other, non-conservative algorithms are thought to be unsafe and have a limited or no theoretical guarantee. Nonetheless, recent studies have shown that non-conservative algorithms empirically outperform conservative ones. To fill this gap, we carry out theoretical analyses of Peng's Q($\lambda$), an instance of non-conservative algorithms, and prove that it also converges to an optimal policy provided that the behavior policy slowly tracks a greedy policy in a way similar to conservative policy iteration. Such a result is conjectured to be true for a long time but has not been proven. We also experiment with Peng's Q($\lambda$) in complex continuous control tasks, confirming that Peng's Q($\lambda$) often outperforms conservative algorithms despite its simplicity. These results indicate that Peng's Q($\lambda$), which is thought to be unsafe, is indeed a theoretically-sound and better-performing algorithm.

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