Data-driven satisficing measure and ranking

TL;DR

This paper introduces a real-time risk assessment framework using satisficing measures that compare risks without prior probability knowledge, applicable to offline and online scenarios with theoretical convergence and regret guarantees.

Contribution

It develops a novel computational framework based on satisficing measures for risk ranking, including algorithms and convergence analysis for both offline and online settings.

Findings

Convergence rate of the sample average approximation method.

Regret bounds for primal-dual stochastic algorithms.

Relationship between sample size and risk ranking accuracy.

Abstract

We propose an computational framework for real-time risk assessment and prioritizing 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 optimization, we apply sample average approximation technique and argue the convergence rate and validation of optimal solutions. In online stochastic optimization 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).