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

• URL: http://arxiv.org/abs/2608.01151v1
• Date: Sun, 02 Aug 2026 11:00:41 GMT
• Title: Learning-Based Stochastic Optimal Control with Infinite-Horizon Probabilistic Constraints
• Abstract summary: We consider optimal control problems with infinite-horizon joint chance constraints.<n>We reformulate the original problem as a constrained Markov decision process.<n>We show that it converges to a deterministic Markov policy defined over the augmented state space.
• Score: 9.67618824743514
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• A Single-Loop Bilevel Deep Learning Method for Optimal Control of Obstacle Problems [10.846737757627638]
  We propose a single-loop bilevel deep learning method, which is mesh-free, scalable to high-dimensional and complex domains, and avoids repeated solution of discretized subproblems.<n>The proposed method achieves satisfactory accuracy while reducing computational cost compared to classical numerical methods.
  arXiv  Detail & Related papers  (2026-01-07T17:30:42Z)
• Learning based convex approximation for constrained parametric optimization [11.379408842026981]
  We propose an input neural network (ICNN)-based self-supervised learning framework to solve constrained optimization problems.<n>We provide rigorous convergence analysis, showing that the framework converges to a Karush-Kuhn-Tucker (KKT) approximation point of the original problem.<n>Our approach achieves a superior balance among accuracy, feasibility, and computational efficiency.
  arXiv  Detail & Related papers  (2025-05-07T00:33:14Z)
• Single-loop Algorithms for Stochastic Non-convex Optimization with Weakly-Convex Constraints [49.76332265680669]
  This paper examines a crucial subset of problems where both the objective and constraint functions are weakly convex.<n>Existing methods often face limitations, including slow convergence rates or reliance on double-loop designs.<n>We introduce a novel single-loop penalty-based algorithm to overcome these challenges.
  arXiv  Detail & Related papers  (2025-04-21T17:15:48Z)
• Trust-Region Sequential Quadratic Programming for Stochastic Optimization with Random Models [57.52124921268249]
  We propose a Trust Sequential Quadratic Programming method to find both first and second-order stationary points. To converge to first-order stationary points, our method computes a gradient step in each iteration defined by minimizing a approximation of the objective subject. To converge to second-order stationary points, our method additionally computes an eigen step to explore the negative curvature the reduced Hessian matrix.
  arXiv  Detail & Related papers  (2024-09-24T04:39:47Z)
• A Double Tracking Method for Optimization with Decentralized Generalized Orthogonality Constraints [4.6796315389639815]
  Decentralized optimization problems are unsolvable in the presence of distributed constraints. We introduce a novel algorithm that tracks the gradient of the objective function and the Jacobian of the constraint mapping simultaneously. We present numerical results on both synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2024-09-08T06:57:35Z)
• Double Duality: Variational Primal-Dual Policy Optimization for Constrained Reinforcement Learning [132.7040981721302]
  We study the Constrained Convex Decision Process (MDP), where the goal is to minimize a convex functional of the visitation measure. Design algorithms for a constrained convex MDP faces several challenges, including handling the large state space.
  arXiv  Detail & Related papers  (2024-02-16T16:35:18Z)
• Fully Stochastic Trust-Region Sequential Quadratic Programming for Equality-Constrained Optimization Problems [62.83783246648714]
  We propose a sequential quadratic programming algorithm (TR-StoSQP) to solve nonlinear optimization problems with objectives and deterministic equality constraints. The algorithm adaptively selects the trust-region radius and, compared to the existing line-search StoSQP schemes, allows us to utilize indefinite Hessian matrices.
  arXiv  Detail & Related papers  (2022-11-29T05:52:17Z)
• Learning to Optimize with Stochastic Dominance Constraints [103.26714928625582]
  In this paper, we develop a simple yet efficient approach for the problem of comparing uncertain quantities. We recast inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses apparent intractability. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.
  arXiv  Detail & Related papers  (2022-11-14T21:54:31Z)
• Algorithm for Constrained Markov Decision Process with Linear Convergence [55.41644538483948]
  An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs. A new dual approach is proposed with the integration of two ingredients: entropy regularized policy and Vaidya's dual. The proposed approach is shown to converge (with linear rate) to the global optimum.
  arXiv  Detail & Related papers  (2022-06-03T16:26:38Z)
• Adaptive Discretization for Model-Based Reinforcement Learning [10.21634042036049]
  We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm. Our algorithm is based on optimistic one-step value iteration extended to maintain an adaptive discretization of the space.
  arXiv  Detail & Related papers  (2020-07-01T19:36:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.