Shape-Constrained Distributional Optimization via Importance-Weighted Sample Average Approximation

Understand

Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years.

• In the DRO literature, these problems are usually solved via reduction into moment-constrained problems using the Choquet representation.
• While powerful, such an approach could face tractability challenges arising from the geometries and the compatibility between the shape and the objective function and moment constraints.
• In this paper, we propose an alternative methodology to solve shape-constrained optimization problems by integrating sample average approximation with importance sampling, the latter used to convert the distributional optimization into an optimization problem over the likelihood ratio with respect to a sampling distribution.