Toward a Scalable Upper Bound for a CVaR-LQ Problem

TL;DR

This paper develops a scalable dynamic programming approach for a CVaR-based linear-quadratic control problem with distributional ambiguity, introducing a new risk-averse policy and comparing it to existing methods.

Contribution

It proposes a novel, scalable dynamic programming method to upper-bound the CVaR-LQ problem and introduces a tunable risk-averse control policy.

Findings

The new approach provides a scalable upper bound for the CVaR-LQ problem.

The proposed control policy is tunable and risk-averse.

Comparative analysis shows advantages over existing methods.

Abstract

We study a linear-quadratic, optimal control problem on a discrete, finite time horizon with distributional ambiguity, in which the cost is assessed via Conditional Value-at-Risk (CVaR). We take steps toward deriving a scalable dynamic programming approach to upper-bound the optimal value function for this problem. This dynamic program yields a novel, tunable risk-averse control policy, which we compare to existing state-of-the-art methods.