A Nonparametric Offpolicy Policy Gradient

A Nonparametric Off-Policy Policy GradientSamuele Tosatto 1 Jo ao Carvalho 1 Hany Abdulsamad 1 Jan Peters 1,2 1 Technische Universit at Darmstadt 2 Max Planck Institute for Intelligent Systems Abstract Reinforcement learning (RL) algorithms still suffer from high sample complexity despite outstanding recent successes. The need for intensive interactions with the environment is especially observed in many widely popular policy gradient algorithms that perform updates using on-policy samples. The price of such inefficiency becomes evident in real world scenarios such as interaction-driven robot learning, where the success of RL has been rather limited. We address this issue by building on the general sample efficiency of off-policy algorithms. With nonparametric regression and density estimation methods we construct a nonparametric Bellman equation in a principled manner, which allows us to obtain closed-form estimates of the value function, and to analytically express the full policy gradient. We provide a theoretical analysis of our estimate to show that it is consistent under mild smoothness assumptions and empirically show that our approach has better sample efficiency than state-of-the-art policy gradient methods. 1 Introduction Reinforcement learning has made overwhelming progress in recent years (Mnih et al., 2015; Haarnoja et al., 2018; Schulman et al., 2015). However, the vast majority of reinforcement learning approaches are on-policy algorithms with limited applicability to real world scenarios, due to high sample complexity. In contrast, off-policy techniques are theoretically more sample efficient, because they decouple the proceduresPreliminary work. TG NOPG-D DPG TG NOPG-S PWIS Figure 1: Example showing the bias of offline-DPG (left) and the variance of PWIS-G(PO)MDP (right) in the policy-parameter space of a 2d-LQR setting. Both algorithms diverge while they move away from the "on-policy" region.