Stochastic Learning in Kolkata Paise Restaurant Problem: Classical \& Quantum Strategies

TL;DR

This paper reviews stochastic learning strategies, both classical and quantum, for resource allocation in the Kolkata Paise Restaurant Problem, highlighting analytical results, phase transition behavior, and diverse applications.

Contribution

It provides a comprehensive review of classical and quantum stochastic learning strategies and their phase transition phenomena in the context of the Kolkata Paise Restaurant Problem.

Findings

Classical strategies exhibit phase transition behavior.

Quantum strategies analyzed through one-shot methods.

Applications span computer science, transport, and operations research.

Abstract

We will review the results for stochastic learning strategies, both classical (one-shot and iterative) and quantum (one-shot only), for optimizing the available many-choice resources among a large number of competing agents, developed over the last decade in the context of the Kolkata Paise Restaurant Problem. Apart from a few rigorous and approximate analytical results, both for classical and quantum strategies, most of the interesting results on the phase transition behavior (obtained so far for the classical model) using classical Monte Carlo simulations. All these, including the applications to computer science (job or resource allotments in Internet-of-Things), transport engineering (on-line vehicle hire problems), operation research (optimizing efforts for delegated search problem, efficient solution of Travelling Salesman problem), etc will be discussed.