Inverse Linear-Quadratic Gaussian Differential Games

TL;DR

This paper introduces a novel method for inverse analysis in finite-horizon LQG differential games, estimating players' cost functions and noise parameters from observed trajectories.

Contribution

It combines strategy estimation, Riccati equation reformulation, and maximum likelihood to accurately recover game parameters from data.

Findings

The method successfully recovers cost function parameters.

Trajectories generated match observed data closely.

The approach effectively estimates noise scaling parameters.

Abstract

This paper presents a method for solving the Inverse Stochastic Differential Game (ISDG) problem in finite-horizon linear-quadratic Gaussian (LQG) differential games. The objective is to recover cost function parameters of all players, as well as noise scaling parameters of the stochastic system, consistent with observed trajectories. The proposed framework combines (i) estimation of the feedback strategies, (ii) identification of the cost function parameters via a novel reformulation of the coupled Riccati differential equations, and (iii) maximum likelihood estimation of the noise scaling parameters. Simulation results demonstrate that the approach recovers parameters, yielding trajectories that closely match the observed trajectories.