# Pessimism Meets Risk: Risk-Sensitive Offline Reinforcement Learning

arXiv: https://arxiv.org/abs/2407.07631 · HTML: https://mlsanity.com/paper/2407.07631/

## Key facts

- Cited by 6 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.
- Builds on 61 of its 91 references that are in the map.
- First posted on arXiv 10 Jul 2024.

## Placed in

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

## Builds on (most cited first, 30 of 61)

- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1604.00923/) (2016)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [FLAMBE: Structural Complexity and Representation Learning of Low Rank MDPs](https://mlsanity.com/paper/2006.10814/) (2020)
- [Provably Efficient Exploration in Policy Optimization](https://mlsanity.com/paper/1912.05830/) (2019)
- [Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processes](https://mlsanity.com/paper/2012.08507/) (2020)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [Policy Finetuning: Bridging Sample-Efficient Offline and Online Reinforcement Learning](https://mlsanity.com/paper/2106.04895/) (2021)
- [What are the Statistical Limits of Offline RL with Linear Function Approximation?](https://mlsanity.com/paper/2010.11895/) (2020)
- [Risk-sensitive Reinforcement Learning](https://mlsanity.com/paper/1311.2097/) (2013)
- [Representation Learning for Online and Offline RL in Low-rank MDPs](https://mlsanity.com/paper/2110.04652/) (2021)
- [Minimax-Optimal Off-Policy Evaluation with Linear Function Approximation](https://mlsanity.com/paper/2002.09516/) (2020)
- [Provable Benefits of Actor-Critic Methods for Offline Reinforcement Learning](https://mlsanity.com/paper/2108.08812/) (2021)
- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [Provably Efficient Reinforcement Learning for Discounted MDPs with Feature Mapping](https://mlsanity.com/paper/2006.13165/) (2020)
- [PC-PG: Policy Cover Directed Exploration for Provable Policy Gradient Learning](https://mlsanity.com/paper/2007.08459/) (2020)
- [On Reward-Free Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2006.11274/) (2020)
- [Pessimistic Q-Learning for Offline Reinforcement Learning: Towards Optimal Sample Complexity](https://mlsanity.com/paper/2202.13890/) (2022)
- [Settling the Sample Complexity of Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2204.05275/) (2022)
- [Model-free Representation Learning and Exploration in Low-rank MDPs](https://mlsanity.com/paper/2102.07035/) (2021)
- [Logarithmic Regret for Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2011.11566/) (2020)
- [Conservative Offline Distributional Reinforcement Learning](https://mlsanity.com/paper/2107.06106/) (2021)
- [Towards Instance-Optimal Offline Reinforcement Learning with Pessimism](https://mlsanity.com/paper/2110.08695/) (2021)
- [Risk-Averse Offline Reinforcement Learning](https://mlsanity.com/paper/2102.05371/) (2021)
- [Near-optimal Offline Reinforcement Learning with Linear Representation: Leveraging Variance Information with Pessimism](https://mlsanity.com/paper/2203.05804/) (2022)
- [Risk-Sensitive Reinforcement Learning: Near-Optimal Risk-Sample Tradeoff in Regret](https://mlsanity.com/paper/2006.13827/) (2020)
- [Nearly Minimax Optimal Offline Reinforcement Learning with Linear Function Approximation: Single-Agent MDP and Markov Game](https://mlsanity.com/paper/2205.15512/) (2022)

## Built on by (most cited first, 6 of 6)

- [Dual-Robust Cross-Domain Offline Reinforcement Learning Against Dynamics Shifts](https://mlsanity.com/paper/2512.02486/) (2025)
- [Efficient Cross-Domain Offline Reinforcement Learning with Dynamics- and Value-Aligned Data Filtering](https://mlsanity.com/paper/2512.02435/) (2025)
- [Mildly Conservative Regularized Evaluation for Offline Reinforcement Learning](https://mlsanity.com/paper/2508.05960/) (2025)
- [Pessimistic Risk-Aware Policy Learning in Contextual Bandits](https://mlsanity.com/paper/2605.15620/) (2026)
- [Long-Term Sequential Decision Making under Risk](https://mlsanity.com/paper/2607.19914/) (2026)
- [Fast Rates for Offline Q-Learning with KL Regularization](https://mlsanity.com/paper/2610.18839/) (2026)

## Abstract (arXiv)

We study risk-sensitive reinforcement learning (RL), a crucial field due to its ability to enhance decision-making in scenarios where it is essential to manage uncertainty and minimize potential adverse outcomes. Particularly, our work focuses on applying the entropic risk measure to RL problems. While existing literature primarily investigates the online setting, there remains a large gap in understanding how to efficiently derive a near-optimal policy based on this risk measure using only a pre-collected dataset. We center on the linear Markov Decision Process (MDP) setting, a well-regarded theoretical framework that has yet to be examined from a risk-sensitive standpoint. In response, we introduce two provably sample-efficient algorithms. We begin by presenting a risk-sensitive pessimistic value iteration algorithm, offering a tight analysis by leveraging the structure of the risk-sensitive performance measure. To further improve the obtained bounds, we propose another pessimistic algorithm that utilizes variance information and reference-advantage decomposition, effectively improving both the dependence on the space dimension d and the risk-sensitivity factor. To the best of our knowledge, we obtain the first provably efficient risk-sensitive offline RL algorithms.