A Kernel Mean Embedding Approach to Reducing Conservativeness in Stochastic Programming and Control
This work addresses conservativeness in stochastic programming and control, which is an incremental improvement for optimization and control domains.
The paper tackled the problem of conservativeness in sample-based stochastic optimization and control by applying kernel mean embedding methods to discard sampled scenarios, resulting in improved optimality and reduced conservativeness through a distributional-distance-regularized optimization approach.
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.