Risk Sensitive Path Integral Control

TL;DR

This paper extends path integral methods for stochastic optimal control to incorporate risk sensitivity, allowing for risk seeking or averse behaviors by exponentially weighting the cost-to-go, demonstrated on complex control problems.

Contribution

It introduces a generalization of path integral control to risk sensitive settings, enabling control design with risk preferences beyond linear-quadratic models.

Findings

Method effectively incorporates risk sensitivity into path integral control.

Demonstrates control of multi-modal behaviors under risk preferences.

Applicable to complex, non-linear stochastic control problems.

Abstract

Recently path integral methods have been developed for stochastic optimal control for a wide class of models with non-linear dynamics in continuous space-time. Path integral methods find the control that minimizes the expected cost-to-go. In this paper we show that under the same assumptions, path integral methods generalize directly to risk sensitive stochastic optimal control. Here the method minimizes in expectation an exponentially weighted cost-to-go. Depending on the exponential weight, risk seeking or risk averse behaviour is obtained. We demonstrate the approach on risk sensitive stochastic optimal control problems beyond the linear-quadratic case, showing the intricate interaction of multi-modal control with risk sensitivity.