# Doubly Robust Off-Policy Value and Gradient Estimation for Deterministic Policies

arXiv: https://arxiv.org/abs/2006.03900 · HTML: https://mlsanity.com/paper/2006.03900/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Offline RL algorithms, one of 13 directions in Offline RL and imitation learning from data.
- First posted on arXiv 6 Jun 2020.

## Placed in

- Offline RL and imitation learning from data / [Offline RL algorithms](https://mlsanity.com/offlinerl/offline-rl-algorithms/)

## Built on by (most cited first, 10 of 10)

- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [A Review of Off-Policy Evaluation in Reinforcement Learning](https://mlsanity.com/paper/2212.06355/) (2022)
- [A Causal Framework for Evaluating Deferring Systems](https://mlsanity.com/paper/2405.18902/) (2024)
- [Treatment Effect Estimation for Optimal Decision-Making](https://mlsanity.com/paper/2505.13092/) (2025)
- [Doubly Robust Proximal Causal Learning for Continuous Treatments](https://mlsanity.com/paper/2309.12819/) (2023)
- [STEEL: Singularity-aware Reinforcement Learning](https://mlsanity.com/paper/2301.13152/) (2023)
- [Explaining Off-Policy Actor-Critic From A Bias-Variance Perspective](https://mlsanity.com/paper/2110.02421/) (2021)
- [Breaking Determinism: Stochastic Modeling for Reliable Off-Policy Evaluation in Ad Auctions](https://mlsanity.com/paper/2512.03354/) (2025)
- [Improving Sample Efficiency in Evolutionary RL Using Off-Policy Ranking](https://mlsanity.com/paper/2208.10583/) (2022)
- [Learning Deployable Causal Action Geometry under Temporal Non-Stationarity](https://mlsanity.com/paper/2610.16644/) (2026)

## Abstract (arXiv)

Offline reinforcement learning, wherein one uses off-policy data logged by a fixed behavior policy to evaluate and learn new policies, is crucial in applications where experimentation is limited such as medicine. We study the estimation of policy value and gradient of a deterministic policy from off-policy data when actions are continuous. Targeting deterministic policies, for which action is a deterministic function of state, is crucial since optimal policies are always deterministic (up to ties). In this setting, standard importance sampling and doubly robust estimators for policy value and gradient fail because the density ratio does not exist. To circumvent this issue, we propose several new doubly robust estimators based on different kernelization approaches. We analyze the asymptotic mean-squared error of each of these under mild rate conditions for nuisance estimators. Specifically, we demonstrate how to obtain a rate that is independent of the horizon length.