An Efficient Direct Search Method for Simulation Optimization With Conditional-Expectation-Based Objectives

In order to generalize the applicability of Conditional Value at Risk, one of the most widely used measurements used in financial risk management, we develop a solution methodology for the conditional expectation (CE)-based simulation optimization problems. To optimize CE-based objective functions in a highly generalized context, we propose a gradient-free, direct search optimization method, called SNM-CE, which inherits the search framework of Stochastic Nelder-Mead (SNM) Simplex Method but further incorporates effective mechanisms designed for handling problems with CE-based objective functions. As we assume the underlying problem is complicated enough that no closed-form expression can represent the objective function, stochastic simulation is applied to estimate CE. We apply Importance Sampling (IS) as a variance reduction technique, which, combined with a newly-developed methodology, called SOCBA-mn, ensures that simulation resources are used with great efficiency. We show that SNM-CE can converge to the true global optimum with probability one (w.p.1) like SNM. An extensive numerical study and a communication system-based empirical study are both conducted to demonstrate the effectiveness, efficiency and viability of this research in both theoretical and practical settings.