Optimizing Conditional Value-at-Risk via gradient-based adaptive stochastic search

Abstract

Optimizing risk measures such as Conditional Value-at-Risk (CVaR) is often a difficult problem, because 1) the loss function might lack structural properties such as convexity or differentiability, since it is usually generated via black-box simulation of a stochastic system; 2) evaluation of CVaR usually requires rare-event simulation, which is computationally expensive. In this paper, we study the extension of the recently proposed gradient-based adaptive stochastic search (GASS) method to the optimization of CVaR. Instead of optimizing CVaR at the risk level of interest directly, we propose to initialize the algorithm at a small risk level, and then increase the risk level at each iteration adaptively until the target risk level is achieved, while the algorithm converges to an optimal solution of the original problem. It enables us to adaptively reduce the number of samples needed to estimate the CVaR at each iteration, and improves the overall efficiency of the algorithm.