# Learning-Based Stochastic Optimal Control with Infinite-Horizon Probabilistic Constraints

arXiv: https://arxiv.org/abs/2608.01151 · HTML: https://mlsanity.com/paper/2608.01151/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 2 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Constrained Reinforcement Learning Has Zero Duality Gap](https://mlsanity.com/paper/1910.13393/) (2019)
- [Safe Policies for Reinforcement Learning via Primal-Dual Methods](https://mlsanity.com/paper/1911.09101/) (2019)
- [Probabilistic Constraint for Safety-Critical Reinforcement Learning](https://mlsanity.com/paper/2306.17279/) (2023)
- [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)
- [Probabilistically safe and efficient model-based reinforcement learning](https://mlsanity.com/paper/2504.00626/) (2025)
- [Scenario-based Nonlinear Model Predictive Control for Building Heating Systems](https://mlsanity.com/paper/2012.02011/) (2020)
- [Approximate Dynamic Programming for Constrained Linear Systems: A Piecewise Quadratic Approximation Approach](https://mlsanity.com/paper/2205.10065/) (2022)
- [Solving Mission-Wide Chance-Constrained Optimal Control Using Dynamic Programming](https://mlsanity.com/paper/2209.05979/) (2022)
- [A Unifying Perspective for Safety of Stochastic Systems: From Barrier Functions to Finite Abstractions](https://mlsanity.com/paper/2310.01802/) (2023)
- [Approximate Dynamic Programming for Constrained Piecewise Affine Systems with Stability and Safety Guarantees](https://mlsanity.com/paper/2306.15723/) (2023)
- [Scenario Reduction with Guarantees for Stochastic Optimal Control of Linear Systems](https://mlsanity.com/paper/2404.07746/) (2024)
- [Temporal Logic Control of Nonlinear Stochastic Systems with Online Performance Optimization](https://mlsanity.com/paper/2604.01372/) (2026)

## Abstract (arXiv)

In this paper, we consider stochastic optimal control problems with infinite-horizon joint chance constraints. By means of an appropriate state augmentation, we reformulate the original problem as a constrained Markov decision process, in which both the cost and the constraint function exhibit an additive structure. We then prove that this formulation enjoys strong duality, thereby enabling us to reformulate the problem as an equivalent unconstrained one in the Lagrange dual framework. We propose a dual-ascent algorithm to solve the resulting problem and show that it converges to a deterministic Markov policy defined over the augmented state space that is both optimal and feasible. To accommodate continuous state-input spaces, we propose a dedicated learning algorithm to approximate the value function in an offline training setting, thereby significantly reducing the computational complexity of the online control phase. We then test our approach on a numerical example and demonstrate its effectiveness compared to online predictive control methods in terms of performance and computational complexity.