Risk Sensitive Stochastic Shortest Path and LogSumExp: From Theory to Practice

Abstract

Stochastic Shortest Path (SSP) is the most popular framework to model sequential decision-making problems under stochasticity. However, decisions for real problems should consider risk sensitivity to provide robust decisions taking into account bad scenarios. SSPs that deal with risk are called Risk-Sensitive SSPs (RSSSPs), and an interesting framework from a theoretical perspective considers Expected Utility Theory under an exponential utility function. However, from a practical perspective, exponential utility function causes overflow or underflow in computer implementation even in small state spaces. In this paper, we make use of LogSumExp technique to solve RSSSPs under exponential utility in practice within Value Iteration, Policy Iteration, and Linear Programming algorithms. Experiments were performed on a toy problem to show scalability of the proposed algorithms.