# Exchange Policy Optimization Algorithm for Semi-Infinite Safe Reinforcement Learning

arXiv: https://arxiv.org/abs/2511.04147 · HTML: https://mlsanity.com/paper/2511.04147/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Safe and constrained RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 22 of its 53 references that are in the map.
- First posted on arXiv 6 Nov 2025.

## Placed in

- Deep reinforcement learning methods / [Safe and constrained RL](https://mlsanity.com/deeprl/safe-and-constrained-rl/)

## Builds on (most cited first, 22 of 22)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2002.00444/) (2020)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [Projection-Based Constrained Policy Optimization](https://mlsanity.com/paper/2010.03152/) (2020)
- [Constrained Reinforcement Learning Has Zero Duality Gap](https://mlsanity.com/paper/1910.13393/) (2019)
- [Exploration-Exploitation in Constrained MDPs](https://mlsanity.com/paper/2003.02189/) (2020)
- [CRPO: A New Approach for Safe Reinforcement Learning with Convergence Guarantee](https://mlsanity.com/paper/2011.05869/) (2020)
- [IPO: Interior-point Policy Optimization under Constraints](https://mlsanity.com/paper/1910.09615/) (2019)
- [Benchmarking Batch Deep Reinforcement Learning Algorithms](https://mlsanity.com/paper/1910.01708/) (2019)
- [Saute RL: Almost Surely Safe Reinforcement Learning Using State Augmentation](https://mlsanity.com/paper/2202.06558/) (2022)
- [Penalized Proximal Policy Optimization for Safe Reinforcement Learning](https://mlsanity.com/paper/2205.11814/) (2022)
- [Convergent Policy Optimization for Safe Reinforcement Learning](https://mlsanity.com/paper/1910.12156/) (2019)
- [Safe Reinforcement Learning Using Advantage-Based Intervention](https://mlsanity.com/paper/2106.09110/) (2021)
- [Constrained Upper Confidence Reinforcement Learning](https://mlsanity.com/paper/2001.09377/) (2020)
- [CUP: A Conservative Update Policy Algorithm for Safe Reinforcement Learning](https://mlsanity.com/paper/2202.07565/) (2022)
- [Safe Learning and Optimization Techniques: Towards a Survey of the State of the Art](https://mlsanity.com/paper/2101.09505/) (2021)
- [An Inexact Primal-Dual Algorithm for Semi-Infinite Programming](https://mlsanity.com/paper/1803.10898/) (2018)
- [An adaptive discretization method solving semi-infinite optimization problems with quadratic rate of convergence](https://mlsanity.com/paper/1910.13798/) (2019)

## Built on by (most cited first, 1 of 1)

- [MoSSP: A Momentum-Based Single-Loop Stochastic Penalty Method for Nonconvex Constrained DC-Regularized Optimization](https://mlsanity.com/paper/2605.29635/) (2026)

## Abstract (arXiv)

Safe reinforcement learning (RL) aims to optimize long-term performance while adhering to safety requirements. However, many practical applications involve an infinite number of constraints, forming semi-infinite safe RL (SI-safe RL). Such scenarios typically appear when safety conditions must be enforced across an entire continuous parameter space, such as ensuring adequate resource distribution at every spatial location. Existing approaches typically tackle these continuous constraints through naive spatial discretization or stochastic sampling. Such methods inherently suffer from residual violations or provide only probabilistic safety guarantees. Therefore, no current framework can handle infinitely many constraints to provide reliable safety certificates. In this paper, we propose exchange policy optimization (EPO), an algorithmic framework that achieves optimal policy performance with provably bounded safety guarantees. EPO operates by iteratively solving safe RL subproblems restricted to a finite constraint set, adaptively adjusting the active set through constraint expansion and deletion. Specifically, at each iteration, constraints violating a predefined tolerance are added to refine the policy, while those with zero Lagrange multipliers are removed after the policy update. This exchange rule limits the subproblem complexity to ensure computational tractability while driving policy convergence. Theoretically, we establish that, under mild assumptions, EPO achieves finite convergence to a policy that both ensures the optimal reward performance and keeps the global constraint violation within the prescribed tolerance. Furthermore, we derive an upper bound on the required number of iterations and quantify the gap between the obtained policy and the true optimum.