A Kernel Mean Embedding Approach to Reducing Conservativeness in Stochastic Programming and Control
; Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:915-923, 2020.
In this paper, 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.