# Reinforcement Learning under Model Mismatch

arXiv: https://arxiv.org/abs/1706.04711 · HTML: https://mlsanity.com/paper/1706.04711/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2017.

## Built on by (most cited first, 30 of 52)

- [RAMBO-RL: Robust Adversarial Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2204.12581/) (2022)
- [Online Robust Reinforcement Learning with Model Uncertainty](https://mlsanity.com/paper/2109.14523/) (2021)
- [Robust Reinforcement Learning using Offline Data](https://mlsanity.com/paper/2208.05129/) (2022)
- [Distributionally Robust Model-Based Offline Reinforcement Learning with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2208.05767/) (2022)
- [RORL: Robust Offline Reinforcement Learning via Conservative Smoothing](https://mlsanity.com/paper/2206.02829/) (2022)
- [Sample Complexity of Robust Reinforcement Learning with a Generative Model](https://mlsanity.com/paper/2112.01506/) (2021)
- [Policy Gradient Method For Robust Reinforcement Learning](https://mlsanity.com/paper/2205.07344/) (2022)
- [The Curious Price of Distributional Robustness in Reinforcement Learning with a Generative Model](https://mlsanity.com/paper/2305.16589/) (2023)
- [Twice regularized MDPs and the equivalence between robustness and regularization](https://mlsanity.com/paper/2110.06267/) (2021)
- [Improved Sample Complexity Bounds for Distributionally Robust Reinforcement Learning](https://mlsanity.com/paper/2303.02783/) (2023)
- [Policy Gradient in Robust MDPs with Global Convergence Guarantee](https://mlsanity.com/paper/2212.10439/) (2022)
- [Natural Actor-Critic for Robust Reinforcement Learning with Function Approximation](https://mlsanity.com/paper/2307.08875/) (2023)
- [First-order Policy Optimization for Robust Markov Decision Process](https://mlsanity.com/paper/2209.10579/) (2022)
- [Policy Gradient for Rectangular Robust Markov Decision Processes](https://mlsanity.com/paper/2301.13589/) (2023)
- [Robust Average-Reward Markov Decision Processes](https://mlsanity.com/paper/2301.00858/) (2023)
- [Model-Free Robust Average-Reward Reinforcement Learning](https://mlsanity.com/paper/2305.10504/) (2023)
- [Robust Policy Learning over Multiple Uncertainty Sets](https://mlsanity.com/paper/2202.07013/) (2022)
- [Minimax Optimal and Computationally Efficient Algorithms for Distributionally Robust Offline Reinforcement Learning](https://mlsanity.com/paper/2403.09621/) (2024)
- [Soft Robust MDPs and Risk-Sensitive MDPs: Equivalence, Policy Gradient, and Sample Complexity](https://mlsanity.com/paper/2306.11626/) (2023)
- [Distributionally Robust Model-based Reinforcement Learning with Large State Spaces](https://mlsanity.com/paper/2309.02236/) (2023)
- [Single-Trajectory Distributionally Robust Reinforcement Learning](https://mlsanity.com/paper/2301.11721/) (2023)
- [Robust Constrained Reinforcement Learning](https://mlsanity.com/paper/2209.06866/) (2022)
- [Bridging Distributionally Robust Learning and Offline RL: An Approach to Mitigate Distribution Shift and Partial Data Coverage](https://mlsanity.com/paper/2310.18434/) (2023)
- [Towards Robust Model-Based Reinforcement Learning Against Adversarial Corruption](https://mlsanity.com/paper/2402.08991/) (2024)
- [Robust Imitation Learning from Corrupted Demonstrations](https://mlsanity.com/paper/2201.12594/) (2022)
- [Solving Long-run Average Reward Robust MDPs via Stochastic Games](https://mlsanity.com/paper/2312.13912/) (2023)
- [Constrained Reinforcement Learning Under Model Mismatch](https://mlsanity.com/paper/2405.01327/) (2024)
- [Robust Reinforcement Learning in Continuous Control Tasks with Uncertainty Set Regularization](https://mlsanity.com/paper/2207.02016/) (2022)
- [First-order Policy Optimization for Robust Policy Evaluation](https://mlsanity.com/paper/2307.15890/) (2023)
- [Confounding Robust Deep Reinforcement Learning: A Causal Approach](https://mlsanity.com/paper/2510.21110/) (2025)

## Abstract (arXiv)

We study reinforcement learning under model misspecification, where we do not have access to the true environment but only to a reasonably close approximation to it. We address this problem by extending the framework of robust MDPs to the model-free Reinforcement Learning setting, where we do not have access to the model parameters, but can only sample states from it. We define robust versions of Q-learning, SARSA, and TD-learning and prove convergence to an approximately optimal robust policy and approximate value function respectively. We scale up the robust algorithms to large MDPs via function approximation and prove convergence under two different settings. We prove convergence of robust approximate policy iteration and robust approximate value iteration for linear architectures (under mild assumptions). We also define a robust loss function, the mean squared robust projected Bellman error and give stochastic gradient descent algorithms that are guaranteed to converge to a local minimum.