# Entropy Regularization Improves Policy Robustness in Continuous-Time Reinforcement Learning

arXiv: https://arxiv.org/abs/2607.03168 · HTML: https://mlsanity.com/paper/2607.03168/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 42 of its 62 references that are in the map.
- First posted on arXiv 3 Jul 2026.

## 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, 30 of 42)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Sim-to-Real Transfer of Robotic Control with Dynamics Randomization](https://mlsanity.com/paper/1710.06537/) (2017)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (2019)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [Action Robust Reinforcement Learning and Applications in Continuous Control](https://mlsanity.com/paper/1901.09184/) (2019)
- [Policy Mirror Descent for Reinforcement Learning: Linear Convergence, New Sampling Complexity, and Generalized Problem Classes](https://mlsanity.com/paper/2102.00135/) (2021)
- [Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithms](https://mlsanity.com/paper/2111.11232/) (2021)
- [q-Learning in Continuous Time](https://mlsanity.com/paper/2207.00713/) (2022)
- [Policy Evaluation and Temporal-Difference Learning in Continuous Time and Space: A Martingale Approach](https://mlsanity.com/paper/2108.06655/) (2021)
- [Entropy Regularization for Mean Field Games with Learning](https://mlsanity.com/paper/2010.00145/) (2020)
- [Twice regularized MDPs and the equivalence between robustness and regularization](https://mlsanity.com/paper/2110.06267/) (2021)
- [Efficient Adversarial Training without Attacking: Worst-Case-Aware Robust Reinforcement Learning](https://mlsanity.com/paper/2210.05927/) (2022)
- [Queueing Network Controls via Deep Reinforcement Learning](https://mlsanity.com/paper/2008.01644/) (2020)
- [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)
- [Regularized Policies are Reward Robust](https://mlsanity.com/paper/2101.07012/) (2021)
- [Policy Gradient for Rectangular Robust Markov Decision Processes](https://mlsanity.com/paper/2301.13589/) (2023)
- [Policy Optimization for Continuous Reinforcement Learning](https://mlsanity.com/paper/2305.18901/) (2023)
- [Scalable First-Order Methods for Robust MDPs](https://mlsanity.com/paper/2005.05434/) (2020)
- [Convergence of policy gradient methods for finite-horizon exploratory linear-quadratic control problems](https://mlsanity.com/paper/2211.00617/) (2022)
- [Robust Multi-Agent Reinforcement Learning via Adversarial Regularization: Theoretical Foundation and Stable Algorithms](https://mlsanity.com/paper/2310.10810/) (2023)
- [The Reality Gap in Robotics: Challenges, Solutions, and Best Practices](https://mlsanity.com/paper/2510.20808/) (2025)
- [A Fisher-Rao gradient flow for entropy-regularised Markov decision processes in Polish spaces](https://mlsanity.com/paper/2310.02951/) (2023)
- [Actor-Critic learning for mean-field control in continuous time](https://mlsanity.com/paper/2303.06993/) (2023)
- [Continuous-time q-learning for mean-field control problems](https://mlsanity.com/paper/2306.16208/) (2023)
- [Your Policy Regularizer is Secretly an Adversary](https://mlsanity.com/paper/2203.12592/) (2022)

## Abstract (arXiv)

Entropy regularization is widely used in continuous-time reinforcement learning (RL) to reduce sensitivity to environmental perturbations, yet its robustness benefits lack a rigorous theoretical foundation. This paper establishes the first robustness guarantees for entropy-regularized continuous-time Markov decision processes. We show that maximizing an entropy-regularized objective yields a lower bound on a worst-case robust RL problem with joint reward and transition perturbations. We analytically characterize the induced robust sets and prove that they expand monotonically with the regularization strength, justifying the empirical observation that stronger entropy improves robustness. In contrast to prior discrete-time analyses, our results remove the intractable state-distribution entropy term and provide guarantees invariant to action frequency. Experiments on queueing network control and market making confirm our theory, showing that entropy-regularized policies outperform greedy and ε-greedy baselines under dynamics perturbations.