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Fair-GNE : Generalized Nash Equilibrium-Seeking Fairness in Multiagent Healthcare Automation

Promise Ekpo, Saesha Agarwal, Felix Grimm, Lekan Molu, Angelique Taylor

TL;DR

The paper tackles fairness in workload distribution among collaborating agents in healthcare automation by modeling MARL as a constrained generalized Nash equilibrium (GNE) problem. It introduces Fair-GNE, a primal--dual algorithm that embeds a Jain fairness index constraint into the learning process via a dual ascent multiplier, enabling self-enforceable fairness during runtime. Theoretical guarantees tie the method to KKT conditions and stationary Markov GNE in finite policy spaces, while practical deep-RL instantiations apply shaped rewards with adaptive penalties. Empirically, Fair-GNE achieves substantially higher workload balance (e.g., Jain index up to $0.89$) with comparable task success (around $0.86$) to baselines, validated in a hospital CPR-inspired MARL environment and accompanied by robust statistical significance. This work offers a principled framework for fairness-aware multi-agent coordination in safety-critical healthcare automation with broad potential applicability.

Abstract

Enforcing a fair workload allocation among multiple agents tasked to achieve an objective in learning enabled demand side healthcare worker settings is crucial for consistent and reliable performance at runtime. Existing multi-agent reinforcement learning (MARL) approaches steer fairness by shaping reward through post hoc orchestrations, leaving no certifiable self-enforceable fairness that is immutable by individual agents at runtime. Contextualized within a setting where each agent shares resources with others, we address this shortcoming with a learning enabled optimization scheme among self-interested decision makers whose individual actions affect those of other agents. This extends the problem to a generalized Nash equilibrium (GNE) game-theoretic framework where we steer group policy to a safe and locally efficient equilibrium, so that no agent can improve its utility function by unilaterally changing its decisions. Fair-GNE models MARL as a constrained generalized Nash equilibrium-seeking (GNE) game, prescribing an ideal equitable collective equilibrium within the problem's natural fabric. Our hypothesis is rigorously evaluated in our custom-designed high-fidelity resuscitation simulator. Across all our numerical experiments, Fair-GNE achieves significant improvement in workload balance over fixed-penalty baselines (0.89 vs.\ 0.33 JFI, $p < 0.01$) while maintaining 86\% task success, demonstrating statistically significant fairness gains through adaptive constraint enforcement. Our results communicate our formulations, evaluation metrics, and equilibrium-seeking innovations in large multi-agent learning-based healthcare systems with clarity and principled fairness enforcement.

Fair-GNE : Generalized Nash Equilibrium-Seeking Fairness in Multiagent Healthcare Automation

TL;DR

The paper tackles fairness in workload distribution among collaborating agents in healthcare automation by modeling MARL as a constrained generalized Nash equilibrium (GNE) problem. It introduces Fair-GNE, a primal--dual algorithm that embeds a Jain fairness index constraint into the learning process via a dual ascent multiplier, enabling self-enforceable fairness during runtime. Theoretical guarantees tie the method to KKT conditions and stationary Markov GNE in finite policy spaces, while practical deep-RL instantiations apply shaped rewards with adaptive penalties. Empirically, Fair-GNE achieves substantially higher workload balance (e.g., Jain index up to ) with comparable task success (around ) to baselines, validated in a hospital CPR-inspired MARL environment and accompanied by robust statistical significance. This work offers a principled framework for fairness-aware multi-agent coordination in safety-critical healthcare automation with broad potential applicability.

Abstract

Enforcing a fair workload allocation among multiple agents tasked to achieve an objective in learning enabled demand side healthcare worker settings is crucial for consistent and reliable performance at runtime. Existing multi-agent reinforcement learning (MARL) approaches steer fairness by shaping reward through post hoc orchestrations, leaving no certifiable self-enforceable fairness that is immutable by individual agents at runtime. Contextualized within a setting where each agent shares resources with others, we address this shortcoming with a learning enabled optimization scheme among self-interested decision makers whose individual actions affect those of other agents. This extends the problem to a generalized Nash equilibrium (GNE) game-theoretic framework where we steer group policy to a safe and locally efficient equilibrium, so that no agent can improve its utility function by unilaterally changing its decisions. Fair-GNE models MARL as a constrained generalized Nash equilibrium-seeking (GNE) game, prescribing an ideal equitable collective equilibrium within the problem's natural fabric. Our hypothesis is rigorously evaluated in our custom-designed high-fidelity resuscitation simulator. Across all our numerical experiments, Fair-GNE achieves significant improvement in workload balance over fixed-penalty baselines (0.89 vs.\ 0.33 JFI, ) while maintaining 86\% task success, demonstrating statistically significant fairness gains through adaptive constraint enforcement. Our results communicate our formulations, evaluation metrics, and equilibrium-seeking innovations in large multi-agent learning-based healthcare systems with clarity and principled fairness enforcement.

Paper Structure

This paper contains 31 sections, 4 theorems, 12 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Fairness-Constrained MARL as a Stationary Markov GNE
  4. Markov-Constrained Dynamic Games
  5. Problem Formulation
  6. Lagrangian and KKT Conditions
  7. Primal--Dual update rule.
  8. Convergence Analysis for Finite Policy Spaces
  9. Environment Setup: MARLHospital
  10. Experiments
  11. Baselines
  12. Training and Evaluation
  13. Metrics
  14. Results: Fairness–Efficiency Trade-offs with $\lambda$ and $\tau$
  15. Statistical Testing.
  16. ...and 16 more sections

Key Result

Proposition 3.1

If $(\pi^\star,\lambda^\star)$ satisfies eq:kkt, then $\pi^\star$ is an SM--GNE.

Figures (2)

  • Figure 1: The MARLHospital Environment. The environment integrates a PDDL planner with a MARL state layer to model skill-aligned fairness and shared-task coordination among healthcare workers. The goal is to pick the backboard from the crash cart, move to the patient, place it under the patient, compress patient chest multiple times, retrieve the Bag-Valve-Mask (BVM) from the crash cart, give patient rescue breaths multiple times.
  • Figure 2: Task flow diagrams for the check compression (CPR) and rescue breath tasks in MARLHospital. The yellow-shaded subtask supports shared action with energy constraints.

Theorems & Definitions (6)

  • Proposition 3.1: KKT relationship with SM--GNE
  • Lemma C.1: Descent Property of Primal--Dual Fair-GNE
  • proof
  • Theorem C.2: Convergence to Stationary Markov GNE
  • Corollary C.3: Fairness satisfaction
  • Remark C.1