Risk-Averse Stochastic Optimal Control: an efficiently computable statistical upper bound

TL;DR

This paper introduces a computationally efficient statistical upper bound for risk-averse stochastic optimal control problems, enabling better solution approaches for complex, real-world decision-making under uncertainty.

Contribution

It proposes a novel statistical upper bound applicable to a broad class of risk-averse SOC problems, addressing a longstanding challenge in the field.

Findings

The upper bound is valid for convex and monotone risk measures.

The approach is demonstrated on a real-life hydro-thermal planning problem.

The method improves computational efficiency in risk-averse stochastic control.

Abstract

In this paper, we discuss an application of the SDDP type algorithm to nested risk-averse formulations of Stochastic Optimal Control (SOC) problems. We propose a construction of a statistical upper bound for the optimal value of risk-averse SOC problems. This outlines an approach to a solution of a long standing problem in that area of research. The bound holds for a large class of convex and monotone conditional risk mappings. Finally, we show the validity of the statistical upper bound to solve a real-life stochastic hydro-thermal planning problem.