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Single-Agent Planning in a Multi-Agent System: A Unified Framework for Type-Based Planners

Fengming Zhu, Fangzhen Lin

TL;DR

This work addresses single-agent planning in multi-agent environments with unknown opponents by proposing a unified, tree-search–based framework that spans exact to scalable approximate planners. It models the problem as a Contextual MDP/POMDP over opponent types and derives three core formulations: Exact Dynamic Programming, Belief-Induced MDP, and Belief-mixed MDP (QMDP). The authors instantiate 13 planners within this framework and validate them on a challenging multi-agent route-planning benchmark (MARP) with up to 50 agents, finding that safe-agents offer robust, scalable performance, while deeper online search improves accuracy where computation allows. The framework provides practical guidance for selecting planners across scales and suggests directions for future work, including incorporating domain knowledge, modeling inter-agent dependencies, and extending to broader domains such as mechanism design and negotiation.

Abstract

We consider a general problem where an agent is in a multi-agent environment and must plan for herself without any prior information about her opponents. At each moment, this pivotal agent is faced with a trade-off between exploiting her currently accumulated information about the other agents and exploring further to improve future (re-)planning. We propose a theoretic framework that unifies a spectrum of planners for the pivotal agent to address this trade-off. The planner at one end of this spectrum aims to find exact solutions, while those towards the other end yield approximate solutions as the problem scales up. Beyond theoretical analysis, we also implement \textbf{13} planners and conduct experiments in a specific domain called \textit{multi-agent route planning} with the number of agents \textbf{up to~50}, to compare their performaces in various scenarios. One interesting observation comes from a class of planners that we call \textit{safe-agents} and their enhanced variants by incorporating domain-specific knowledge, which is a simple special case under the proposed general framework, but performs sufficiently well in most cases. Our unified framework, as well as those induced planners, provides new insights on multi-agent decision-making, with potential applications to related areas such as mechanism design.

Single-Agent Planning in a Multi-Agent System: A Unified Framework for Type-Based Planners

TL;DR

This work addresses single-agent planning in multi-agent environments with unknown opponents by proposing a unified, tree-search–based framework that spans exact to scalable approximate planners. It models the problem as a Contextual MDP/POMDP over opponent types and derives three core formulations: Exact Dynamic Programming, Belief-Induced MDP, and Belief-mixed MDP (QMDP). The authors instantiate 13 planners within this framework and validate them on a challenging multi-agent route-planning benchmark (MARP) with up to 50 agents, finding that safe-agents offer robust, scalable performance, while deeper online search improves accuracy where computation allows. The framework provides practical guidance for selecting planners across scales and suggests directions for future work, including incorporating domain knowledge, modeling inter-agent dependencies, and extending to broader domains such as mechanism design and negotiation.

Abstract

We consider a general problem where an agent is in a multi-agent environment and must plan for herself without any prior information about her opponents. At each moment, this pivotal agent is faced with a trade-off between exploiting her currently accumulated information about the other agents and exploring further to improve future (re-)planning. We propose a theoretic framework that unifies a spectrum of planners for the pivotal agent to address this trade-off. The planner at one end of this spectrum aims to find exact solutions, while those towards the other end yield approximate solutions as the problem scales up. Beyond theoretical analysis, we also implement \textbf{13} planners and conduct experiments in a specific domain called \textit{multi-agent route planning} with the number of agents \textbf{up to~50}, to compare their performaces in various scenarios. One interesting observation comes from a class of planners that we call \textit{safe-agents} and their enhanced variants by incorporating domain-specific knowledge, which is a simple special case under the proposed general framework, but performs sufficiently well in most cases. Our unified framework, as well as those induced planners, provides new insights on multi-agent decision-making, with potential applications to related areas such as mechanism design.

Paper Structure

This paper contains 26 sections, 2 theorems, 9 equations, 12 figures, 6 tables, 7 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Model and Solution Concepts
  4. Stochastic Game
  5. The Modelling Agent's Problem
  6. Potential Solution Formulations
  7. Exact Dynamic Programming
  8. Belief-Induced MDP
  9. Belief-mixed MDP (QMDP)
  10. Unification
  11. Experiments
  12. Benchmark
  13. Multi-Agent Route Planning
  14. Nash Equilibrium
  15. A Special Case: Safe Agents
  16. ...and 11 more sections

Key Result

theorem 1

The backup operator $\Gamma$ in Section sec:unification.(eq:van_bellman) is a $\gamma$-contraction. Mathematically, for $u,v \in \mathcal{V}$, we have

Figures (12)

  • Figure 1: The convergence dynamics.
  • Figure 2: The exact optimal plan (a), a potential approximated online plan with repeated replanning by layered tree search (b), and a closer look at the tree diagram for one depth of the lookahead search (c).
  • Figure 3: Statistics of the RL training samples.
  • Figure 4: Detailed experiments for "Small2a" configurations.
  • Figure 5: Detailed experiments for "Square2a" configurations.
  • ...and 7 more figures

Theorems & Definitions (2)

  • theorem 1
  • theorem 2