Variational Quantum Rainbow Deep Q-Network for Optimizing Resource Allocation Problem

2025-12-05

AI Summary

This paper addresses the NP-hard Human Resource Allocation Problem (HRAP) through a novel quantum-classical hybrid reinforcement learning framework, VQR-DQN. It formulates HRAP as a Markov Decision Process and pioneers the integration of variational quantum circuits into the Rainbow DQN architecture. Leveraging quantum superposition and entanglement, the method enhances state-action representation capacity, and establishes theoretical connections among circuit expressibility, entanglement entropy, and policy performance. Technically, VQR-DQN unifies variational quantum neural networks, prioritized experience replay, distributed Q-heads, and the Double DQN mechanism. Evaluated on four HRAP benchmarks, VQR-DQN reduces normalized makespan by 26.8% on average over random baselines and consistently outperforms Double DQN and classical Rainbow DQN by +4.9–13.4%. The implementation is publicly available.

Technology Category

• Machine Learning: Quantum Machine Learning
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Resource allocation remains NP-hard due to combinatorial complexity. While deep reinforcement learning (DRL) methods, such as the Rainbow Deep Q-Network (DQN), improve scalability through prioritized replay and distributional heads, classical function approximators limit their representational power. We introduce Variational Quantum Rainbow DQN (VQR-DQN), which integrates ring-topology variational quantum circuits with Rainbow DQN to leverage quantum superposition and entanglement. We frame the human resource allocation problem (HRAP) as a Markov decision process (MDP) with combinatorial action spaces based on officer capabilities, event schedules, and transition times. On four HRAP benchmarks, VQR-DQN achieves 26.8% normalized makespan reduction versus random baselines and outperforms Double DQN and classical Rainbow DQN by 4.9-13.4%. These gains align with theoretical connections between circuit expressibility, entanglement, and policy quality, demonstrating the potential of quantum-enhanced DRL for large-scale resource allocation. Our implementation is available at: https://github.com/Analytics-Everywhere-Lab/qtrl/.

Problem

• Optimizing NP-hard resource allocation with quantum-enhanced reinforcement learning
• Integrating variational quantum circuits into Rainbow DQN for improved scalability
• Reducing makespan in human resource allocation via quantum superposition and entanglement

Innovation

• Integrates variational quantum circuits with Rainbow DQN
• Leverages quantum superposition and entanglement for optimization
• Frames resource allocation as a Markov decision process