Parallelization in Computer Board GamesIan Princivalli

Introduction

“Solved” Game

Ultra-weak

Weak

Strong

Current Efforts

Chess

Shogi

Reversi (Othello)

Go

Computer Go

General Overview

19 x 19 board with intersections

Objective: Have the most territory

Black and white stones surround and capture

Programming Challenges

3N possible board positions where N =

size of board (19 x 19 board has 361)

Evaluating function

Endgame

How Parallel Computation fits in

Most popular design philosophies

Tree searching

Application of Monte Carlo methods

Pattern matching and knowledge based systems

Machine learning

Example: MoGo

MCTS (UCT)

UCT (Upper Conditional bounds for Trees)

Balance out exploration and exploitation

Example: MoGo continued

Utilizes both multicore parallelization for shared memory and cluster parallelization with message passing

Example: MoGo final

In a 2008 Taiwan Go tournament MoGo was able to defeat professional Go player Myungwan Kim (8p) 2 out of 4 matches with a 9 stone handicap.

Professionals gave MoGo an approximate ranking of 2d and Kim himself noted that with more time MoGo would have fared better

Limitations of Improvement via Parallelization

Increased computation seems to have diminishing returns

In a 2009 Computer Olympiad, Zen, a program running on a single four-core machine took first place over second place Fuego, running on ten, eight-core machines and third place MoGo, running on twenty, thirty-two core machines

In general MCTS cannot reliably solve certain situations, e.g. cases involving visual elements or other human sophisticated techniques and therefore parallelization of said MCTS does nothing for these cases

Improvement algorithmically seems to proceed improvement via parallelization

e.g. some later iterations of MCTS (UCT) based Computer Go programs have accommodated expert heuristics when these edge cases arise

Questions?