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

2025-11-18

AI Summary

This paper addresses the identifiability of time-varying cost parameters in finite-horizon linear-quadratic-Gaussian (LQG) games. Leveraging the implicit dynamic cost structure embedded in Nash equilibrium policies, we propose a backpropagation-based inverse optimization framework. We establish, for the first time, theoretical identifiability conditions for time-varying cost functions over finite horizons and derive rigorous sufficient conditions—along with explicit estimation error bounds—for recovering cost parameters from observed equilibrium strategies and state trajectories. Our approach integrates game theory, optimal control, and probabilistic learning theory to mitigate estimation bias under limited data. Numerical experiments and autonomous driving simulations demonstrate that the algorithm accurately reconstructs equilibrium policies and precisely identifies time-varying costs, thereby substantially enhancing both the practical applicability and theoretical completeness of multi-agent inverse game learning.

Technology Category

• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Identifies time-varying costs in finite-horizon LQG games
• Characterizes cost parameters generating Nash equilibrium policies
• Proposes backpropagation algorithm for cost parameter identification

Innovation

• Backpropagation algorithm identifies time-varying costs
• Characterizes cost parameters generating Nash equilibrium
• Derives probabilistic error bounds for finite trajectories