Exit Time Risk-Sensitive Control for Systems of Cooperative Agents

TL;DR

This paper investigates the limiting behavior of risk-sensitive exit time control problems for large systems of cooperative agents, showing convergence to a deterministic control problem under certain assumptions.

Contribution

It introduces a fully characterizing assumption linking risk-sensitive problems to risk-neutral ones and proves convergence of value functions for large agent systems.

Findings

Sequence of value functions converges to a deterministic control problem

Risk-sensitive problems reduce to risk-neutral problems under specific assumptions

Framework enables design of nearly optimal controls for large agent systems

Abstract

We study sequences, parametrized by the number of agents, of many agent exit time stochastic control problems with risk-sensitive cost structure. We identify a fully characterizing assumption, under which each of such control problem corresponds to a risk-neutral stochastic control problem with additive cost, and sequentially to a risk-neutral stochastic control problem on the simplex, where the specific information about the state of each agent can be discarded. We also prove that, under some additional assumptions, the sequence of value functions converges to the value function of a deterministic control problem, which can be used for the design of nearly optimal controls for the original problem, when the number of agents is sufficiently large.