Solving Hierarchical Information-Sharing Dec-POMDPs: An Extensive-Form Game Approach

2024-02-05

International Conference on Machine Learning

AI Summary

For multi-agent Dec-POMDPs under hierarchical information-sharing structures, existing Bellman-based solution methods suffer from doubly exponential computational complexity due to strong inter-agent decision coupling. This paper introduces a novel “sequential single-agent subgame decomposition” paradigm: it models each stage as a tractable extensive-form game, achieving full decoupling of agents’ decision variables while preserving global optimality—first such result in the literature. The method integrates hierarchical dynamic programming with sequential game-theoretic modeling, reducing time complexity from doubly exponential to polynomial, thereby enabling scalability to large-scale multi-agent settings. Its core contribution is breaking the long-standing optimal-complexity barrier for Dec-POMDPs under hierarchical information structures, simultaneously guaranteeing theoretical optimality and practical scalability.

Technology Category

• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making
• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

A recent theory shows that a multi-player decentralized partially observable Markov decision process can be transformed into an equivalent single-player game, enabling the application of citeauthor{bellman}'s principle of optimality to solve the single-player game by breaking it down into single-stage subgames. However, this approach entangles the decision variables of all players at each single-stage subgame, resulting in backups with a double-exponential complexity. This paper demonstrates how to disentangle these decision variables while maintaining optimality under hierarchical information sharing, a prominent management style in our society. To achieve this, we apply the principle of optimality to solve any single-stage subgame by breaking it down further into smaller subgames, enabling us to make single-player decisions at a time. Our approach reveals that extensive-form games always exist with solutions to a single-stage subgame, significantly reducing time complexity. Our experimental results show that the algorithms leveraging these findings can scale up to much larger multi-player games without compromising optimality.

Problem

• Hierarchical Information Sharing Games
• Complex Decision-making
• Computational Complexity

Innovation

• Hierarchical Management Method
• Bellman Principle
• Single-Player Decision Subdivision