# q-exponential family for policy optimization

arXiv: https://arxiv.org/abs/2408.07245 · HTML: https://mlsanity.com/paper/2408.07245/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 26 of its 55 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 26 of 26)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [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)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [A Lyapunov-based Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/1805.07708/) (2018)
- [On the Global Convergence Rates of Softmax Policy Gradient Methods](https://mlsanity.com/paper/2005.06392/) (2020)
- [A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural Networks](https://mlsanity.com/paper/1901.06053/) (2019)
- [Understanding the impact of entropy on policy optimization](https://mlsanity.com/paper/1811.11214/) (2018)
- [Fast Global Convergence of Natural Policy Gradient Methods with Entropy Regularization](https://mlsanity.com/paper/2007.06558/) (2020)
- [Sparse Sequence-to-Sequence Models](https://mlsanity.com/paper/1905.05702/) (2019)
- [Continuous Deep Q-Learning with Model-based Acceleration](https://mlsanity.com/paper/1603.00748/) (2016)
- [Extreme Q-Learning: MaxEnt RL without Entropy](https://mlsanity.com/paper/2301.02328/) (2023)
- [Offline RL with No OOD Actions: In-Sample Learning via Implicit Value Regularization](https://mlsanity.com/paper/2303.15810/) (2023)
- [A Policy-Guided Imitation Approach for Offline Reinforcement Learning](https://mlsanity.com/paper/2210.08323/) (2022)
- [Sparse Markov Decision Processes with Causal Sparse Tsallis Entropy Regularization for Reinforcement Learning](https://mlsanity.com/paper/1709.06293/) (2017)
- [Leverage the Average: an Analysis of KL Regularization in RL](https://mlsanity.com/paper/2003.14089/) (2020)
- [The In-Sample Softmax for Offline Reinforcement Learning](https://mlsanity.com/paper/2302.14372/) (2023)
- [Path Consistency Learning in Tsallis Entropy Regularized MDPs](https://mlsanity.com/paper/1802.03501/) (2018)
- [Entropic Regularization of Markov Decision Processes](https://mlsanity.com/paper/1907.04214/) (2019)
- [Two-temperature logistic regression based on the Tsallis divergence](https://mlsanity.com/paper/1705.07210/) (2017)
- [Sparse Continuous Distributions and Fenchel-Young Losses](https://mlsanity.com/paper/2108.01988/) (2021)
- [Greedy Actor-Critic: A New Conditional Cross-Entropy Method for Policy Improvement](https://mlsanity.com/paper/1810.09103/) (2018)
- [On the Sample Complexity and Metastability of Heavy-tailed Policy Search in Continuous Control](https://mlsanity.com/paper/2106.08414/) (2021)
- [Quasi-optimal Reinforcement Learning with Continuous Actions](https://mlsanity.com/paper/2301.08940/) (2023)

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

- [Fat-to-Thin Policy Optimization: Offline RL with Sparse Policies](https://mlsanity.com/paper/2501.14373/) (2025)
- [Distributions as Actions: A Unified Framework for Diverse Action Spaces](https://mlsanity.com/paper/2506.16608/) (2025)

## Abstract (arXiv)

Policy optimization methods benefit from a simple and tractable policy parametrization, usually the Gaussian for continuous action spaces. In this paper, we consider a broader policy family that remains tractable: the q-exponential family. This family of policies is flexible, allowing the specification of both heavy-tailed policies (q>1) and light-tailed policies (q<1). This paper examines the interplay between q-exponential policies for several actor-critic algorithms conducted on both online and offline problems. We find that heavy-tailed policies are more effective in general and can consistently improve on Gaussian. In particular, we find the Student's t-distribution to be more stable than the Gaussian across settings and that a heavy-tailed q-Gaussian for Tsallis Advantage Weighted Actor-Critic consistently performs well in offline benchmark problems. Our code is available at urlhttps://github.com/lingweizhu/qexp.