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Stochastic Learning in Kolkata Paise Restaurant Problem: Classical and Quantum Strategies.

Bikas K Chakrabarti1,2,3, Atanu Rajak4, Antika Sinha5

  • 1Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Kolkata, India.

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Summary

This review covers stochastic learning strategies for resource optimization in the Kolkata Paise Restaurant problem. It highlights classical and quantum approaches, their analytical results, and Monte Carlo simulations for phase transitions.

Keywords:
KPR problemcollective learningcritical slowing downdecoherenceminority gamequantum entanglementthree-player quantum KPR

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Area of Science:

  • Optimization strategies
  • Stochastic learning
  • Resource allocation

Background:

  • The Kolkata Paise Restaurant (KPR) Problem involves optimizing resource allocation among competing agents.
  • Stochastic learning strategies, both classical and quantum, have been developed over the past decade to address this problem.

Approach:

  • This review analyzes classical (one-shot, iterative) and quantum (one-shot) stochastic learning strategies.
  • It discusses analytical results and Monte Carlo simulations used to study phase transition behaviors in classical models.

Key Points:

  • The KPR Problem serves as a model for various real-world applications.
  • Classical Monte Carlo simulations are crucial for understanding phase transitions in classical models.
  • Quantum strategies offer a new paradigm for resource optimization.

Conclusions:

  • The review synthesizes findings on stochastic learning for resource optimization.
  • It emphasizes the applicability of these strategies to diverse fields like computer science, transport engineering, and operations research.