Batch Reinforcement Learning with a Nonparametric Off-Policy Policy Gradient

Off-policy Reinforcement Learning (RL) holds the promise of better data\nefficiency as it allows sample reuse and potentially enables safe interaction\nwith the environment. Current off-policy policy gradient methods either suffer\nfrom high bias or high variance, delivering often unreliable estimates. The\nprice of inefficiency becomes evident in real-world scenarios such as\ninteraction-driven robot learning, where the success of RL has been rather\nlimited, and a very high sample cost hinders straightforward application. In\nthis paper, we propose a nonparametric Bellman equation, which can be solved in\nclosed form. The solution is differentiable w.r.t the policy parameters and\ngives access to an estimation of the policy gradient. In this way, we avoid the\nhigh variance of importance sampling approaches, and the high bias of\nsemi-gradient methods. We empirically analyze the quality of our gradient\nestimate against state-of-the-art methods, and show that it outperforms the\nbaselines in terms of sample efficiency on classical control tasks.\n