Data-driven satisficing measure and ranking

Abstract

We propose a computational framework for real-time risk assessment and prioritising for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a single index for risk comparison. Since SM is a dual representation for a family of risk measures, we consider problems constrained by general convex risk measures and specifically by conditional value-at-risk. Starting from offline optimisation, we apply sample average approximation technique and argue the convergence rate and validation of optimal solutions. In online stochastic optimisation case, we develop primal-dual stochastic approximation algorithms respectively for general risk constrained problems, and derive their regret bounds. For both offline and online cases, we illustrate the relationship between risk ranking accuracy with sample size (or iterations).