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DISPATCH -- Decentralized Informed Spatial Planning and Assignment of Tasks for Cooperative Heterogeneous Agents

Yao Liu, Sampad Mohanty, Elizabeth Ondula, Bhaskar Krishnamachari

TL;DR

This work tackles the fairness-efficiency tradeoff in spatial, online task allocation for heterogeneous multi-agent systems under partial observability. It fuses Eisenberg–Gale equilibrium theory with decentralized learning through a CTDE framework (EG-MARL) and a stochastic online EG-based assignment mechanism, yielding policies that approximate Pareto-efficient and envy-free allocations. Empirical results in MPE and Webots warehouse scenarios show that EG-based methods achieve strong fairness while maintaining competitive efficiency, with regret decreasing in smaller teams and approaching centralized performance as coordination scales. The study provides a principled path to fairness-aware coordination without relying on full global state, with practical implications for real-time, heterogeneous robot fleets.

Abstract

Spatial task allocation in systems such as multi-robot delivery or ride-sharing requires balancing efficiency with fair service across tasks. Greedy assignment policies that match each agent to its highest-preference or lowest-cost task can maximize efficiency but often create inequities: some tasks receive disproportionately favorable service (e.g., shorter delays or better matches), while others face long waits or poor allocations. We study fairness in heterogeneous multi-agent systems where tasks vary in preference alignment and urgency. Most existing approaches either assume centralized coordination or largely ignore fairness under partial observability. Distinct from this prior work, we establish a connection between the Eisenberg-Gale (EG) equilibrium convex program and decentralized, partially observable multi-agent learning. Building on this connection, we develop two equilibrium-informed algorithms that integrate fairness and efficiency: (i) a multi-agent reinforcement learning (MARL) framework, EG-MARL, whose training is guided by a centralized EG equilibrium assignment algorithm; and (ii) a stochastic online optimization mechanism that performs guided exploration and subset-based fair assignment as tasks are discovered. We evaluate on Multi-Agent Particle Environment (MPE) simulations across varying team sizes against centralized EG, Hungarian, and Min-Max distance baselines, and also present a Webots-based warehouse proof-of-concept with heterogeneous robots. Both methods preserve the fairness-efficiency balance of the EG solution under partial observability, with EG-MARL achieving near-centralized coordination and reduced travel distances, and the online mechanism enabling real-time allocation with competitive fairness.

DISPATCH -- Decentralized Informed Spatial Planning and Assignment of Tasks for Cooperative Heterogeneous Agents

TL;DR

This work tackles the fairness-efficiency tradeoff in spatial, online task allocation for heterogeneous multi-agent systems under partial observability. It fuses Eisenberg–Gale equilibrium theory with decentralized learning through a CTDE framework (EG-MARL) and a stochastic online EG-based assignment mechanism, yielding policies that approximate Pareto-efficient and envy-free allocations. Empirical results in MPE and Webots warehouse scenarios show that EG-based methods achieve strong fairness while maintaining competitive efficiency, with regret decreasing in smaller teams and approaching centralized performance as coordination scales. The study provides a principled path to fairness-aware coordination without relying on full global state, with practical implications for real-time, heterogeneous robot fleets.

Abstract

Spatial task allocation in systems such as multi-robot delivery or ride-sharing requires balancing efficiency with fair service across tasks. Greedy assignment policies that match each agent to its highest-preference or lowest-cost task can maximize efficiency but often create inequities: some tasks receive disproportionately favorable service (e.g., shorter delays or better matches), while others face long waits or poor allocations. We study fairness in heterogeneous multi-agent systems where tasks vary in preference alignment and urgency. Most existing approaches either assume centralized coordination or largely ignore fairness under partial observability. Distinct from this prior work, we establish a connection between the Eisenberg-Gale (EG) equilibrium convex program and decentralized, partially observable multi-agent learning. Building on this connection, we develop two equilibrium-informed algorithms that integrate fairness and efficiency: (i) a multi-agent reinforcement learning (MARL) framework, EG-MARL, whose training is guided by a centralized EG equilibrium assignment algorithm; and (ii) a stochastic online optimization mechanism that performs guided exploration and subset-based fair assignment as tasks are discovered. We evaluate on Multi-Agent Particle Environment (MPE) simulations across varying team sizes against centralized EG, Hungarian, and Min-Max distance baselines, and also present a Webots-based warehouse proof-of-concept with heterogeneous robots. Both methods preserve the fairness-efficiency balance of the EG solution under partial observability, with EG-MARL achieving near-centralized coordination and reduced travel distances, and the online mechanism enabling real-time allocation with competitive fairness.

Paper Structure

This paper contains 26 sections, 1 theorem, 20 equations, 4 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Preliminaries
  4. Navigation-Service Task
  5. Definition of Dec-POMDP
  6. Agent–Entity Graph.
  7. Centralized Training with Decentralized Execution (CTDE)
  8. Eisenberg-Gale Optimization
  9. Remark
  10. EG-MARL Framework
  11. State, Observations
  12. Graph Embeddings
  13. Communication
  14. Reward Design
  15. Stochastic Online Assignment
  16. ...and 11 more sections

Key Result

Proposition 1

The solution $x^*$ to the one-to-one Eisenberg--Gale program is Pareto efficient among all feasible (binary) assignments.

Figures (4)

  • Figure 1: Illustration of the heterogeneous multi-robot navigation-and-service task allocation problem.
  • Figure 2: Running-average episode rewards for 7 agents under RMAPPO and Graph_RMAPPO
  • Figure 3: Fairness--Efficiency tradeoff across all algorithms for 3, 7, 10, and 15 agents.
  • Figure 4: Eisenberg--Gale assignment in Webots. The Summit-XL Steel is assigned to the pallet stack, the TurtleBot3 Burger to the cabinet, the Pioneer 3-DX to the conveyor, the youBot to the gas canister, and the Pioneer 3-AT to the cardboard box.

Theorems & Definitions (2)

  • Proposition 1: Pareto Efficiency of the One-to-One Eisenberg--Gale Allocation
  • proof