# Rectified Robust Policy Optimization for Model-Uncertain Constrained Reinforcement Learning without Strong Duality

arXiv: https://arxiv.org/abs/2508.17448 · HTML: https://mlsanity.com/paper/2508.17448/

## Key facts

- Cited by 4 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 67 of its 96 references that are in the map.
- First posted on arXiv 24 Aug 2025.

## 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 67)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [A Lyapunov-based Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/1805.07708/) (2018)
- [Safe Exploration in Continuous Action Spaces](https://mlsanity.com/paper/1801.08757/) (2018)
- [Projection-Based Constrained Policy Optimization](https://mlsanity.com/paper/2010.03152/) (2020)
- [Neural Policy Gradient Methods: Global Optimality and Rates of Convergence](https://mlsanity.com/paper/1909.01150/) (2019)
- [Constrained Reinforcement Learning Has Zero Duality Gap](https://mlsanity.com/paper/1910.13393/) (2019)
- [A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic](https://mlsanity.com/paper/2007.05170/) (2020)
- [CRPO: A New Approach for Safe Reinforcement Learning with Convergence Guarantee](https://mlsanity.com/paper/2011.05869/) (2020)
- [Safe Reinforcement Learning in Constrained Markov Decision Processes](https://mlsanity.com/paper/2008.06626/) (2020)
- [Online Robust Reinforcement Learning with Model Uncertainty](https://mlsanity.com/paper/2109.14523/) (2021)
- [Is Q-Learning Minimax Optimal? A Tight Sample Complexity Analysis](https://mlsanity.com/paper/2102.06548/) (2021)
- [Sample Complexity of Robust Reinforcement Learning with a Generative Model](https://mlsanity.com/paper/2112.01506/) (2021)
- [Safe Reinforcement Learning with Model Uncertainty Estimates](https://mlsanity.com/paper/1810.08700/) (2018)
- [Policy Gradient Method For Robust Reinforcement Learning](https://mlsanity.com/paper/2205.07344/) (2022)
- [Accelerated Primal-Dual Policy Optimization for Safe Reinforcement Learning](https://mlsanity.com/paper/1802.06480/) (2018)
- [Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environments](https://mlsanity.com/paper/2209.15090/) (2022)
- [Safe Reinforcement Learning via Shielding under Partial Observability](https://mlsanity.com/paper/2204.00755/) (2022)
- [Reinforcement Learning under Model Mismatch](https://mlsanity.com/paper/1706.04711/) (2017)
- [Double Pessimism is Provably Efficient for Distributionally Robust Offline Reinforcement Learning: Generic Algorithm and Robust Partial Coverage](https://mlsanity.com/paper/2305.09659/) (2023)
- [Achieving Zero Constraint Violation for Constrained Reinforcement Learning via Primal-Dual Approach](https://mlsanity.com/paper/2109.06332/) (2021)
- [Twice regularized MDPs and the equivalence between robustness and regularization](https://mlsanity.com/paper/2110.06267/) (2021)
- [Policy Gradient in Robust MDPs with Global Convergence Guarantee](https://mlsanity.com/paper/2212.10439/) (2022)
- [Near-Optimal Sample Complexity Bounds for Constrained MDPs](https://mlsanity.com/paper/2206.06270/) (2022)
- [Natural Actor-Critic for Robust Reinforcement Learning with Function Approximation](https://mlsanity.com/paper/2307.08875/) (2023)

## Built on by (most cited first, 4 of 4)

- [Primal-Only Actor Critic Algorithm for Robust Constrained Average Cost MDPs](https://mlsanity.com/paper/2511.05758/) (2025)
- [Provably Efficient Sample Complexity for Robust CMDP](https://mlsanity.com/paper/2511.07486/) (2025)
- [Robust Reinforcement Learning in Finance: Modeling Market Impact with Elliptic Uncertainty Sets](https://mlsanity.com/paper/2510.19950/) (2025)
- [Optimistic Policy Learning under Pessimistic Adversaries with Regret and Violation Guarantees](https://mlsanity.com/paper/2604.14243/) (2026)

## Abstract (arXiv)

The goal of robust constrained reinforcement learning (RL) is to optimize an agent's performance under the worst-case model uncertainty while satisfying safety or resource constraints. In this paper, we demonstrate that strong duality does not generally hold in robust constrained RL, indicating that traditional primal-dual methods may fail to find optimal feasible policies. To overcome this limitation, we propose a novel primal-only algorithm called Rectified Robust Policy Optimization (RRPO), which operates directly on the primal problem without relying on dual formulations. We provide theoretical convergence guarantees under mild regularity assumptions, showing convergence to an approximately optimal feasible policy with iteration complexity matching the best-known lower bound when the uncertainty set diameter is controlled in a specific level. Empirical results in a grid-world environment validate the effectiveness of our approach, demonstrating that RRPO achieves robust and safe performance under model uncertainties while the non-robust method can violate the worst-case safety constraints.