Generalized differentiation in Wasserstein space and application to multiagent control problem

TL;DR

This paper introduces a new concept of admissible variation in Wasserstein space, enabling the derivation of a comparison principle for viscosity solutions in multiagent optimal control problems.

Contribution

It proposes a unified framework for generalized differentiation in Wasserstein space and applies it to Hamilton-Jacobi-Bellman equations in multiagent control.

Findings

Unified admissible variation concept for Wasserstein space

Comparison principle for viscosity solutions established

Application to multiagent control problems demonstrated

Abstract

Several concepts of generalized differentiation in Wasserstein space have been proposed in order to deal with the intrinsic nonsmoothness arising in the context of optimization problems in Wasserstein spaces. In this paper we introduce a concept of admissible variation encompassing some of the most popular definitions as special cases, and using it to derive a comparison principle for viscosity solutions of an Hamilton Jacobi Bellman equation following from an optimal control of a multiagent systems.