# Risk-sensitive Actor-Critic with Static Spectral Risk Measures for Online and Offline Reinforcement Learning

arXiv: https://arxiv.org/abs/2507.03900 · HTML: https://mlsanity.com/paper/2507.03900/

## Key facts

- Cited by 2 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 33 of its 69 references that are in the map.
- First posted on arXiv 5 Jul 2025.

## 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 33)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [On the Global Convergence Rates of Softmax Policy Gradient Methods](https://mlsanity.com/paper/2005.06392/) (2020)
- [A Survey on Offline Reinforcement Learning: Taxonomy, Review, and Open Problems](https://mlsanity.com/paper/2203.01387/) (2022)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Distributed Distributional Deterministic Policy Gradients](https://mlsanity.com/paper/1804.08617/) (2018)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Optimizing the CVaR via Sampling](https://mlsanity.com/paper/1404.3862/) (2014)
- [Conservative Offline Distributional Reinforcement Learning](https://mlsanity.com/paper/2107.06106/) (2021)
- [Risk-Averse Offline Reinforcement Learning](https://mlsanity.com/paper/2102.05371/) (2021)
- [Being Optimistic to Be Conservative: Quickly Learning a CVaR Policy](https://mlsanity.com/paper/1911.01546/) (2019)
- [Efficient Risk-Averse Reinforcement Learning](https://mlsanity.com/paper/2205.05138/) (2022)
- [Mean-Variance Policy Iteration for Risk-Averse Reinforcement Learning](https://mlsanity.com/paper/2004.10888/) (2020)
- [One Risk to Rule Them All: A Risk-Sensitive Perspective on Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2212.00124/) (2022)
- [Reinforcement Learning with Dynamic Convex Risk Measures](https://mlsanity.com/paper/2112.13414/) (2021)
- [An intelligent financial portfolio trading strategy using deep Q-learning](https://mlsanity.com/paper/1907.03665/) (2019)
- [Minimizing Spectral Risk Measures Applied to Markov Decision Processes](https://mlsanity.com/paper/2012.04521/) (2020)
- [Optimizing Return Distributions with Distributional Dynamic Programming](https://mlsanity.com/paper/2501.13028/) (2025)

## Built on by (most cited first, 2 of 2)

- [Decoupling Time and Risk: Risk-Sensitive Reinforcement Learning with General Discounting](https://mlsanity.com/paper/2602.04131/) (2026)
- [Position: Deployed Reinforcement Learning should be Continual](https://mlsanity.com/paper/2606.04029/) (2026)

## Abstract (arXiv)

The development of Distributional Reinforcement Learning (DRL) has introduced a natural way to incorporate risk sensitivity into value-based and actor-critic methods by employing risk measures other than expectation in the value function. While this approach is widely adopted in many online and offline RL algorithms due to its simplicity, the naive integration of risk measures often results in suboptimal policies. This limitation can be particularly harmful in scenarios where the need for effective risk-sensitive policies is critical and worst-case outcomes carry severe consequences. To address this challenge, we propose a novel framework for optimizing static Spectral Risk Measures (SRM), a flexible family of risk measures that generalizes objectives such as CVaR and Mean-CVaR, and enables the tailoring of risk preferences. Our method is applicable to both online and offline RL algorithms. We establish theoretical guarantees by proving convergence in the finite state-action setting. Moreover, through extensive empirical evaluations, we demonstrate that our algorithms consistently outperform existing risk-sensitive methods in both online and offline environments across diverse domains.