A Kernel Mean Embedding Approach to Reducing Conservativeness in Stochastic Programming and Control

2020/01/28 by Zhu, Jia-Jie, Diehl, Moritz, Schölkopf, Bernhard
#FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2001.10398

Abstract

We apply kernel mean embedding methods to sample-based stochastic optimization and control. Specifically, we use the reduced-set expansion method as a way to discard sampled scenarios. The effect of such constraint removal is improved optimality and decreased conservativeness. This is achieved by solving a distributional-distance-regularized optimization problem. We demonstrated this optimization formulation is well-motivated in theory, computationally tractable and effective in numerical algorithms.

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