Identifying Time-varying Costs in Finite-horizon Linear Quadratic Gaussian Games

TL;DR

This paper introduces a method to identify time-varying costs in finite-horizon LQG games by characterizing cost parameters, proposing a backpropagation algorithm, and providing error bounds, validated through simulations.

Contribution

It presents a novel backpropagation-based algorithm for identifying time-varying costs in finite-horizon LQG games, along with theoretical error bounds and empirical validation.

Findings

The algorithm accurately recovers cost parameters from observed policies.

The method provides probabilistic bounds on identification errors.

Validated effectiveness in numerical and driving simulations.

Abstract

We address cost identification in a finite-horizon linear quadratic Gaussian game. We characterize the set of cost parameters that generate a given Nash equilibrium policy. We propose a backpropagation algorithm to identify the time-varying cost parameters. We derive a probabilistic error bound when the cost parameters are identified from finite trajectories. We test our method in numerical and driving simulations. Our algorithm identifies the cost parameters that can reproduce the Nash equilibrium policy and trajectory observations.