An overview of optimal control optimization problems driven by non-convexity measures

TL;DR

This paper reviews recent developments in dynamic programming optimal control problems that involve non-convex measures, highlighting the mathematical challenges and the broadening of risk-sensitive performance evaluation methods.

Contribution

It provides an overview of recent research on non-convexity in dynamic control problems, including risk measures like prospect theory and conditional variance at risk.

Findings

Highlights mathematical intricacies of non-convex measures

Summarizes recent advances in dynamic programming with non-convex risk measures

Discusses implications for risk-sensitive control optimization

Abstract

Recently, literature on dynamic coherent risk measures has broadened the choices for risk-sensitive performance evaluation. A running example includes Cumulative prospect theory and Conditional variance at risk. Most of them can be can be interpreted in general as a non-linear transformation of a given random variable. Non-convexity property has implied a lot of mathematical intricacies and challenges. The paper gives overview on the recent development of dynamic programming optimal control optimization problems driven by non-convex measures.