Using Stochastic AI Techniques to Achieve Unbounded Resolution in Finite Player Goore Games and its Applications

Abstract

Abstract-The Goore Game (GG) introduced by M. L. Tsetlin in 1973 has the fascinating property that it can be resolved in a completely distributed manner with no intercommunication between the players. The game has recently found applications in many domains, including the field of sensor networks and Quality-of-Service (QoS) routing. In actual implementations of the solution, the players are typically replaced by Learning Automata (LA). The problem with the existing reported approaches is that the accuracy of the solution achieved is intricately related to the number of players participating in the game -which, in turn, determines the resolution. In other words, an arbitrary accuracy can be obtained only if the game has an infinite number of players. In this paper, we show how we can attain an unbounded accuracy for the GG by utilizing no more than three stochastic learning machines, and by recursively pruning the solution space to guarantee that the retained domain contains the solution to the game with a probability as close to unity as desired. The paper also conjectures on how the solution can be applied to some of the application domains.

The design of absorbing Bayesian pursuit algorithms and the formal analyses of their ε-optimality

“…This proof is not repeated here, but can be included if requested by the Referees. 7 In the interest of simplicity, at this juncture we have assumed thatd j are independent of each other. We believe that this assumption can be easily relaxed by considering only the individual d j 's as in Eq.…”

“…LA have found applications in a variety of fields, including game playing [7], parameter optimization [8], channel selecting for secondary users in cognitive radio networks [9,10], solving knapsack problems [11], optimizing the web polling problem [12,13], stochastically optimally allocating limited resources [11,14,15], service selection in stochastic environments [16], vehicle path control [17], and assigning capacities in prioritized networks [18]. LA have also been used in natural language processing, string taxonomy [19], graph patitioning [20], and map learning [21].…”

Discretized Bayesian Pursuit – A New Scheme for Reinforcement Learning

“…They have been used in game playing [6,7], parameter optimization [8,9], vehicle path control [10], channel selection in cognitive radio networks [11], assigning capacities in prioritized networks [12], and resource allocation [13]. LA have also been used in natural language processing, string taxonomy [14], graph patitioning [15], and map learning [16].…”

On incorporating the paradigms of discretization and Bayesian estimation to create a new family of pursuit learning automata

“…They have been used in game playing [4][5][6][7][8][9][10], parameter optimization [11,12], channel selection in cognitive radio networks [13], assigning capacities in prioritized networks [14], solving knapsack problems [15], optimizing the web polling problem [16,17], stochastically optimally allocating limited resources [15,18,19], service selection in stochastic environments [20], numerical optimization [21], web crawling [22], microassembly path planning [23], multiagent learning [24], and in batch sequencing and sizing in just-intime manufacturing systems [25]. An asynchronous actionreward learning has been used for nonstationary serial supply chain inventory control [26].…”