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

Abstract

We 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 (KPR) Problem. Apart from 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) uses classical Monte Carlo simulations. All these including the applications to computer science [job or resource allotments in Internet-of-Things (IoT)], transport engineering (online vehicle hire problems), operation research (optimizing efforts for delegated search problem, efficient solution of Traveling Salesman problem) will be discussed.

Keywords: KPR problem; collective learning; critical slowing down; decoherence; minority game; quantum entanglement; three-player quantum KPR.