# Joint Chance Constrained Safe-Optimal Control

arXiv: https://arxiv.org/abs/2606.30829 · HTML: https://mlsanity.com/paper/2606.30829/

## 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 17 of its 38 references that are in the map.
- First posted on arXiv 29 Jun 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, 17 of 17)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [A Survey of Autonomous Driving: Common Practices and Emerging Technologies](https://mlsanity.com/paper/1906.05113/) (2019)
- [Trustworthy Reinforcement Learning Against Intrinsic Vulnerabilities: Robustness, Safety, and Generalizability](https://mlsanity.com/paper/2209.08025/) (2022)
- [Receding-horizon Stochastic Model Predictive Control with Hard Input Constraints and Joint State Chance Constraints](https://mlsanity.com/paper/1506.08471/) (2015)
- [Policy Gradients for Probabilistic Constrained Reinforcement Learning](https://mlsanity.com/paper/2210.00596/) (2022)
- [Operator Splitting for Convex Constrained Markov Decision Processes](https://mlsanity.com/paper/2412.14002/) (2024)
- [Computing Optimal Joint Chance Constrained Control Policies](https://mlsanity.com/paper/2312.10495/) (2023)
- [A learning-based approach to stochastic optimal control under reach-avoid constraint](https://mlsanity.com/paper/2412.16561/) (2024)
- [Probabilistic Control Barrier Functions: Safety in Probability for Discrete-Time Stochastic Systems](https://mlsanity.com/paper/2510.01501/) (2025)
- [Recursive Feasibility of Stochastic Model Predictive Control with Mission-Wide Probabilistic Constraints](https://mlsanity.com/paper/2110.04570/) (2021)
- [Solving Mission-Wide Chance-Constrained Optimal Control Using Dynamic Programming](https://mlsanity.com/paper/2209.05979/) (2022)
- [Robust Model Predictive Control of Irrigation Systems with Active Uncertainty Learning and Data Analytics](https://mlsanity.com/paper/1810.05947/) (2018)
- [Self Punishment and Reward Backfill for Deep Q-Learning](https://mlsanity.com/paper/2004.05002/) (2020)
- [Volume Control of Low-Cost Ventilator with Automatic Set-Point Adaptation](https://mlsanity.com/paper/2009.01530/) (2020)
- [Joint Chance Constrained Optimal Control via Linear Programming](https://mlsanity.com/paper/2402.19360/) (2024)

## Abstract (arXiv)

We consider the finite-time optimal control of stochastic systems subject to a probabilistic constraint on the trajectories' safety. Such formulations are known as joint chance constrained optimal control problems. The common practice is to jointly minimise the expected cost of all trajectories, safe and unsafe. This leads to policies which invite constraint violations to exploit low-cost unsafe trajectories. When constraints represent states of critical failure, such behaviour is undesirable. We demonstrate that this behaviour can be overcome by only minimizing the expected cost of safe trajectories. The underlying rationale follows a practical intuition: In many applications, the cost incurred by unsafe trajectories is irrelevant (e.g., the battery usage of a crashed quadcopter), and one is usually interested in minimizing the cost of trajectories that are safe. We show that this problem can be cast as a constrained Markov Decision Process over an augmented state space. This allows solving it via dynamic programming. We derive bounds on the policies' safety under errors resulting from gridding approximations when the system's state space is continuous. Finally, we empirically compare dynamic programming as well as reinforcement learning solutions on a simulated 2D unicycle system in cluttered reach-avoid environments.