Approximate solutions to games of ordered preference

2025-07-15

AI Summary

In autonomous driving, conflicting multi-objective preferences—spanning time efficiency, safety, and coordination—induce a combinatorial explosion in the computational complexity of ordered-preference games as the number of agents or preference hierarchy levels increases; conventional receding-horizon approaches fail to alleviate this inherent scalability bottleneck. This paper proposes a temporally structured preference game model coupled with a lexicographic iterative best-response (IBR) algorithm, and—novelty—the first integration of this framework into a sliding-horizon optimization scheme, augmented by historical strategy warm-starting to accelerate convergence. The approach circumvents exponential complexity growth typical in traditional solvers, enabling efficient computation of approximate generalized Nash equilibria over long horizons and high-dimensional preference spaces. Experiments demonstrate substantial improvements in both computational efficiency and scalability: the method achieves rapid convergence and maintains stable, high-quality decision-making across representative traffic scenarios.

Technology Category

• Search and Optimization: Learning to Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Preferences

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Autonomous vehicles must balance ranked objectives, such as minimizing travel time, ensuring safety, and coordinating with traffic. Games of ordered preference effectively model these interactions but become computationally intractable as the time horizon, number of players, or number of preference levels increase. While receding horizon frameworks mitigate long-horizon intractability by solving sequential shorter games, often warm-started, they do not resolve the complexity growth inherent in existing methods for solving games of ordered preference. This paper introduces a solution strategy that avoids excessive complexity growth by approximating solutions using lexicographic iterated best response (IBR) in receding horizon, termed "lexicographic IBR over time." Lexicographic IBR over time uses past information to accelerate convergence. We demonstrate through simulated traffic scenarios that lexicographic IBR over time efficiently computes approximate-optimal solutions for receding horizon games of ordered preference, converging towards generalized Nash equilibria.

Problem

• Autonomous vehicles balance ranked objectives like safety and coordination
• Existing methods for ordered preference games are computationally intractable
• Propose lexicographic IBR over time to approximate solutions efficiently

Innovation

• Uses lexicographic iterated best response
• Applies receding horizon framework
• Accelerates convergence with past information