# Robust Reinforcement Learning in Finance: Modeling Market Impact with Elliptic Uncertainty Sets

arXiv: https://arxiv.org/abs/2510.19950 · HTML: https://mlsanity.com/paper/2510.19950/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Adversarial robustness and RL in finance, one of 15 directions in Deep reinforcement learning methods.
- Builds on 43 of its 91 references that are in the map.
- First posted on arXiv 22 Oct 2025.

## Placed in

- Deep reinforcement learning methods / [Adversarial robustness and RL in finance](https://mlsanity.com/deeprl/adversarial-robustness-and-rl-in-finance/)

## Builds on (most cited first, 30 of 43)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Reinforcement learning](https://mlsanity.com/paper/2405.10369/) (2024)
- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithms](https://mlsanity.com/paper/2111.11232/) (2021)
- [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)
- [Deep Reinforcement Learning for Trading](https://mlsanity.com/paper/1911.10107/) (2019)
- [Wasserstein Robust Reinforcement Learning](https://mlsanity.com/paper/1907.13196/) (2019)
- [Double Pessimism is Provably Efficient for Distributionally Robust Offline Reinforcement Learning: Generic Algorithm and Robust Partial Coverage](https://mlsanity.com/paper/2305.09659/) (2023)
- [Distributionally Robust Reinforcement Learning](https://mlsanity.com/paper/1902.08708/) (2019)
- [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)
- [Sample Complexity of Variance-reduced Distributionally Robust Q-learning](https://mlsanity.com/paper/2305.18420/) (2023)
- [MarS: a Financial Market Simulation Engine Powered by Generative Foundation Model](https://mlsanity.com/paper/2409.07486/) (2024)
- [Distributionally Robust Reinforcement Learning with Interactive Data Collection: Fundamental Hardness and Near-Optimal Algorithms](https://mlsanity.com/paper/2404.03578/) (2024)
- [Distributionally Robust Off-Dynamics Reinforcement Learning: Provable Efficiency with Linear Function Approximation](https://mlsanity.com/paper/2402.15399/) (2024)
- [Simulating Financial Market via Large Language Model based Agents](https://mlsanity.com/paper/2406.19966/) (2024)
- [Model-based Deep Reinforcement Learning for Dynamic Portfolio Optimization](https://mlsanity.com/paper/1901.08740/) (2019)
- [Robust Risk-Aware Reinforcement Learning](https://mlsanity.com/paper/2108.10403/) (2021)
- [Learning Robust Policy against Disturbance in Transition Dynamics via State-Conservative Policy Optimization](https://mlsanity.com/paper/2112.10513/) (2021)
- [Plan To Predict: Learning an Uncertainty-Foreseeing Model for Model-Based Reinforcement Learning](https://mlsanity.com/paper/2301.08502/) (2023)
- [Soft Robust MDPs and Risk-Sensitive MDPs: Equivalence, Policy Gradient, and Sample Complexity](https://mlsanity.com/paper/2306.11626/) (2023)
- [Robust Gymnasium: A Unified Modular Benchmark for Robust Reinforcement Learning](https://mlsanity.com/paper/2502.19652/) (2025)
- [Reinforcement Learning for Portfolio Management](https://mlsanity.com/paper/1909.09571/) (2019)

## Abstract (arXiv)

In financial applications, reinforcement learning (RL) agents are commonly trained on historical data, where their actions do not influence prices. However, during deployment, these agents trade in live markets where their own transactions can shift asset prices, a phenomenon known as market impact. This mismatch between training and deployment environments can significantly degrade performance. Traditional robust RL approaches address this model misspecification by optimizing the worst-case performance over a set of uncertainties, but typically rely on symmetric structures that fail to capture the directional nature of market impact. To address this issue, we develop a novel class of elliptic uncertainty sets. We establish both implicit and explicit closed-form solutions for the worst-case uncertainty under these sets, enabling efficient and tractable robust policy evaluation. Experiments on single-asset and multi-asset trading tasks demonstrate that our method achieves superior Sharpe ratio and remains robust under increasing trade volumes, offering a more faithful and scalable approach to RL in financial markets.