Quantum spatial best-arm identification via quantum walks

2025-09-06

AI Summary

This paper addresses the best-arm identification (BAI) problem in multi-armed bandits under graph-structured constraints. We propose the Quantum Spatial Best-Arm Identification (QSBAI) algorithm—the first to integrate the Szegedy quantum walk framework into graph-bandit settings. QSBAI constructs a superposition over the action space via quantum walks and employs amplitude amplification for efficient exploration. Rigorous analysis establishes tight bounds on the maximum success probability and time complexity of BAI on complete and bipartite graphs, demonstrating a provable quadratic speedup over classical counterparts. Our key contributions are: (1) establishing a theoretical bridge between Grover search and structured reinforcement learning; (2) extending the applicability of quantum algorithms to sequential decision-making tasks with spatial (graph-theoretic) constraints; and (3) introducing a novel paradigm for quantum-enhanced graph-structured learning.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Quantum reinforcement learning has emerged as a framework combining quantum computation with sequential decision-making, and applications to the multi-armed bandit (MAB) problem have been reported. The graph bandit problem extends the MAB setting by introducing spatial constraints, yet quantum approaches remain limited. We propose a quantum algorithm for best-arm identification in graph bandits, termed Quantum Spatial Best-Arm Identification (QSBAI). The method employs quantum walks to encode superpositions over graph-constrained actions, extending amplitude amplification and generalizing the Quantum BAI algorithm via Szegedy's walk framework. This establishes a link between Grover-type search and reinforcement learning tasks with structural restrictions. We analyze complete and bipartite graphs, deriving the maximal success probability of identifying the best arm and the time step at which it is achieved. Our results highlight the potential of quantum walks to accelerate exploration in constrained environments and extend the applicability of quantum algorithms for decision-making.

Problem

• Quantum algorithm for best-arm identification in graph bandits
• Extends quantum reinforcement learning to spatial constraints
• Analyzes quantum walks for accelerated exploration in constrained environments

Innovation

• Quantum walks encode superpositions over graph-constrained actions
• Amplitude amplification generalizes via Szegedy's walk framework
• Links Grover-type search to reinforcement learning with restrictions