# Batch Reinforcement Learning with a Nonparametric Off-Policy Policy Gradient

arXiv: https://arxiv.org/abs/2010.14771 · HTML: https://mlsanity.com/paper/2010.14771/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2020.

## Built on by (most cited first, 3 of 3)

- [Doubly Robust Off-Policy Actor-Critic: Convergence and Optimality](https://mlsanity.com/paper/2102.11866/) (2021)
- [Model-free Policy Learning with Reward Gradients](https://mlsanity.com/paper/2103.05147/) (2021)
- [Enhancing PPO with Trajectory-Aware Hybrid Policies](https://mlsanity.com/paper/2502.15968/) (2025)

## Abstract (arXiv)

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