Machine learning approach to chance-constrained problems: An algorithm based on the stochastic gradient descent

2019/05/27 by Lukáš Adam, Adam, Lukáš, Martin Branda +1
Computer Science · Decision Sciences · Mathematics · #49M05 #90C15 #90C26 #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Statistical Methods and Inference #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.1905.10986

openalex publication_date 2019/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the decision variable based only on considering a few scenarios. We modify it to handle the non-separable objective. Complexity analysis and a comparison with the standard (batch) gradient descent method is provided. We give three examples with non-convex data and show that our method provides a good solution fast even when the number of scenarios is large.

Citations

• Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization
• Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization
• Robust Convex Optimization
• ImageNet classification with deep convolutional neural networks
• Mechanical and chemical recycling of solid plastic waste
• Theory of Deep Learning III: explaining the non-overfitting puzzle

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