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CH-MARL: Constrained Hierarchical Multiagent Reinforcement Learning for Sustainable Maritime Logistics

Saad Alqithami

TL;DR

CH-MARL introduces a constrained hierarchical multi-agent reinforcement learning framework to tackle sustainable maritime logistics under global emission caps and fairness constraints. By combining a primal-dual constraint enforcement layer with fairness-aware reward shaping and a two-tier architecture (high-level strategic decisions and low-level operational actions), the approach achieves emissions reductions while maintaining throughput and equity. Theoretical foundations for CMDP-based hierarchical convergence and fairness guarantees are paired with a maritime digital-twin validation, demonstrating practical reductions in emissions and improvements in efficiency and fairness. The work highlights a scalable, generalizable blueprint for constrained, multi-agent coordination in dynamic industrial environments with regulatory and equity considerations. This framework has potential implications beyond maritime logistics, enabling safer, cleaner, and more equitable operations in other constrained multi-agent systems.

Abstract

Addressing global challenges such as greenhouse gas emissions and resource inequity demands advanced AI-driven coordination among autonomous agents. We propose CH-MARL (Constrained Hierarchical Multiagent Reinforcement Learning), a novel framework that integrates hierarchical decision-making with dynamic constraint enforcement and fairness-aware reward shaping. CH-MARL employs a real-time constraint-enforcement layer to ensure adherence to global emission caps, while incorporating fairness metrics that promote equitable resource distribution among agents. Experiments conducted in a simulated maritime logistics environment demonstrate considerable reductions in emissions, along with improvements in fairness and operational efficiency. Beyond this domain-specific success, CH-MARL provides a scalable, generalizable solution to multi-agent coordination challenges in constrained, dynamic settings, thus advancing the state of the art in reinforcement learning.

CH-MARL: Constrained Hierarchical Multiagent Reinforcement Learning for Sustainable Maritime Logistics

TL;DR

CH-MARL introduces a constrained hierarchical multi-agent reinforcement learning framework to tackle sustainable maritime logistics under global emission caps and fairness constraints. By combining a primal-dual constraint enforcement layer with fairness-aware reward shaping and a two-tier architecture (high-level strategic decisions and low-level operational actions), the approach achieves emissions reductions while maintaining throughput and equity. Theoretical foundations for CMDP-based hierarchical convergence and fairness guarantees are paired with a maritime digital-twin validation, demonstrating practical reductions in emissions and improvements in efficiency and fairness. The work highlights a scalable, generalizable blueprint for constrained, multi-agent coordination in dynamic industrial environments with regulatory and equity considerations. This framework has potential implications beyond maritime logistics, enabling safer, cleaner, and more equitable operations in other constrained multi-agent systems.

Abstract

Addressing global challenges such as greenhouse gas emissions and resource inequity demands advanced AI-driven coordination among autonomous agents. We propose CH-MARL (Constrained Hierarchical Multiagent Reinforcement Learning), a novel framework that integrates hierarchical decision-making with dynamic constraint enforcement and fairness-aware reward shaping. CH-MARL employs a real-time constraint-enforcement layer to ensure adherence to global emission caps, while incorporating fairness metrics that promote equitable resource distribution among agents. Experiments conducted in a simulated maritime logistics environment demonstrate considerable reductions in emissions, along with improvements in fairness and operational efficiency. Beyond this domain-specific success, CH-MARL provides a scalable, generalizable solution to multi-agent coordination challenges in constrained, dynamic settings, thus advancing the state of the art in reinforcement learning.

Paper Structure

This paper contains 56 sections, 4 theorems, 4 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation
  3. Problem Statement
  4. Contributions
  5. Paper Organization
  6. Background and Related Work
  7. Multiagent Reinforcement Learning
  8. Constrained Reinforcement Learning
  9. MARL for Maritime & Logistics
  10. Fairness in Multiagent Systems
  11. Problem Formulation
  12. System Description
  13. Agents and Hierarchical Roles
  14. High-Level Agents (Strategic Layer).
  15. Low-Level Agents (Operational Layer).
  16. ...and 41 more sections

Key Result

Proposition 4.1

If $\mathcal{L}(\pi,\lambda)$ is continuously differentiable and $\mathbb{E}[C]$ is convex w.r.t. $\pi$, then a gradient-based optimization over $(\pi,\lambda)$ converges to a policy $\pi^*$ such that $\mathbb{E}[C]\le \kappa$.

Figures (3)

  • Figure 1: Conceptual overview of CH-MARL, highlighting the division between high-level (strategic) and low-level (operational) agents, along with the primal-dual and fairness modules that modulate rewards.
  • Figure 2: Reward curves (mean $\pm$ std over three seeds) for each run. Emission caps and fairness both tend to decrease the max reward--additional constraints on vessel behaviors.
  • Figure 3: Emissions curves (mean $\pm$ std) across training. Runs with active caps (Run B, Run D) converge to lower fuel usage, while storms and fairness can introduce variability.

Theorems & Definitions (12)

  • Proposition 4.1: Convergence to a Constraint-Satisfying Policy
  • proof
  • Proposition 4.2: Bounded Constraint Violations
  • proof
  • Definition 4.1: Constrained Markov Decision Process (CMDP)
  • Proposition 4.3: Hierarchical Policy Convergence
  • proof
  • Proposition 4.4: Fairness Metric Guarantees
  • proof
  • proof
  • ...and 2 more