A hybridisation technique for game playing using the upper confidence for trees algorithm with artificial neural networks

In the domain of strategic game playing, the use of statistical techniques such as the Upper Confidence for Trees (UCT) algorithm, has become the norm as they offer many benefits over classical algorithms. These benefits include requiring no game-specific strategic knowledge and time-scalable performance. UCT does not incorporate any strategic information specific to the game considered, but instead uses repeated sampling to effectively brute-force search through the game tree or search space. The lack of game-specific knowledge in UCT is thus both a benefit but also a strategic disadvantage. Pattern recognition techniques, specifically Neural Networks (NN), were identified as a means of addressing the lack of game-specific knowledge in UCT. Through a novel hybridisation technique which combines UCT and trained NNs for pruning, the UCTNN algorithm was derived. The NN component of UCT-NN was trained using a UCT self-play scheme to generate game-specific knowledge without the need to construct and manage game databases for training purposes. The UCT-NN algorithm is outlined for pruning in the game of Go-Moku as a candidate case-study for this research. The UCT-NN algorithm contained three major parameters which emerged from the UCT algorithm, the use of NNs and the pruning schemes considered. Suitable methods for finding candidate values for these three parameters were outlined and applied to the game of Go-Moku on a 5 by 5 board. An empirical investigation of the playing performance of UCT-NN was conducted in comparison to UCT through three benchmarks. The benchmarks comprise a common randomly moving opponent, a common UCTmax player which is given a large amount of playing time, and a pair-wise tournament between UCT-NN and UCT. The results of the performance evaluation for 5 by 5 Go-Moku were promising, which prompted an evaluation of a larger 9 by 9 Go-Moku board. The results of both evaluations indicate that the time allocated to the UCT-NN algorithm directly affects its performance when compared to UCT. The UCT-NN algorithm generally performs better than UCT in games with very limited time-constraints in all benchmarks considered except when playing against a randomly moving player in 9 by 9 Go-Moku. In real-time and near-real-time Go-Moku games, UCT-NN provides statistically significant improvements compared to UCT. The findings of this research contribute to the realisation of applying game-specific knowledge to the UCT algorithm

Complexity, Heuristic, and Search Analysis for the Games of Crossings and Epaminondas

Games provide fertile research domains for algorithmic research. Often, game research helps solve real-world problems through the testing and refinement of search algorithms in game domains. Other times, game research finds limits for certain algorithms. For example, the game of Go proved intractable for the Min-Max with Alpha-Beta pruning algorithm leading to the popularity of Monte-Carlo based search algorithms. Although effective in Go, and game domains once ruled by Alpha-Beta such as Lines of Action, Monte-Carlo methods appear to have limits too as they fall short in tactical domains such as Hex and Chess. In a continuation of this type of research, two new games, Crossings and Epaminondas, are presented, analyzed and used to test two Monte-Carlo based algorithms: Upper Confidence Bounds applied to Trees (UCT) and Heuristic Guided UCT (HUCT). Results indicate that heuristic knowledge can positively affect UCT\u27s performance in the lower complexity domain of Crossings. However, both agents perform worse in the higher complexity domain of Epaminondas. This identifies Epaminondas as another domain that poses difficulties for Monte Carlo agents

Learning From Geometry In Learning For Tactical And Strategic Decision Domains

Artificial neural networks (ANNs) are an abstraction of the low-level architecture of biological brains that are often applied in general problem solving and function approximation. Neuroevolution (NE), i.e. the evolution of ANNs, has proven effective at solving problems in a variety of domains. Information from the domain is input to the ANN, which outputs its desired actions. This dissertation presents a new NE algorithm called Hypercube-based NeuroEvolution of Augmenting Topologies (HyperNEAT), based on a novel indirect encoding of ANNs. The key insight in HyperNEAT is to make the algorithm aware of the geometry in which the ANNs are embedded and thereby exploit such domain geometry to evolve ANNs more effectively. The dissertation focuses on applying HyperNEAT to tactical and strategic decision domains. These domains involve simultaneously considering short-term tactics while also balancing long-term strategies. Board games such as checkers and Go are canonical examples of such domains; however, they also include real-time strategy games and military scenarios. The dissertation details three proposed extensions to HyperNEAT designed to work in tactical and strategic decision domains. The first is an action selector ANN architecture that allows the ANN to indicate its judgements on every possible action all at once. The second technique is called substrate extrapolation. It allows learning basic concepts at a low resolution, and then increasing the resolution to learn more advanced concepts. The iii final extension is geometric game-tree pruning, whereby HyperNEAT can endow the ANN the ability to focus on specific areas of a domain (such as a checkers board) that deserve more inspection. The culminating contribution is to demonstrate the ability of HyperNEAT with these extensions to play Go, a most challenging game for artificial intelligence, by combining HyperNEAT with UC

Spatial regression in large datasets: problem set solution

In this dissertation we investigate a possible attempt to combine the Data Mining methods and traditional Spatial Autoregressive models, in the context of large spatial datasets. We start to considere the numerical difficulties to handle massive datasets by the usual approach based on Maximum Likelihood estimation for spatial models and Spatial Two-Stage Least Squares. So, we conduct an experiment by Monte Carlo simulations to compare the accuracy and computational complexity for decomposition and approximation techniques to solve the problem of computing the Jacobian in spatial models, for various regular lattice structures. In particular, we consider one of the most common spatial econometric models: spatial lag (or SAR, spatial autoregressive model). Also, we provide new evidences in the literature, by examining the double effect on computational complexity of these methods: the influence of "size effect" and "sparsity effect". To overcome this computational problem, we propose a data mining methodology as CART (Classification and Regression Tree) that explicitly considers the phenomenon of spatial autocorrelation on pseudo-residuals, in order to remove this effect and to improve the accuracy, with significant saving in computational complexity in wide range of spatial datasets: realand simulated data

Guiding Monte Carlo tree searches with neural networks in the game of go

A dissertation submitted in fulfillment of the requirements to the degree of Master in Computer Science and Computer EngineeringO jogo de tabuleiro Go é um dos poucos jogos determinísticos em que os computadores ainda não conseguem vencer jogadores humanos profissionais consistentemente. Neste trabalho dois métodos de aprendizagem – por um algoritmo genético e por treino por propagação do erro – são utilizados para criar redes neuronais capazes de assistir um algoritmo de pesquisa em árvore de Monte Carlo. Este último algoritmo tem sido o mais bem sucedido na última década de investigação sobre Go. A utilização de uma rede neuronal é uma abordagem que está a sofrer uma revitalização, com os recentes sucessos de redes neuronais profundas de convolução. Estas necessitam, contudo, de recursos que ainda são muitas vezes proibitivos. Este trabalho explora o impacto de redes neuronais mais simples e a produção de um software representativo do estado da arte. Para isto é complementado com técnicas para pesquisas em árvore de Monte Carlo, aquisição automática de conhecimento, paralelismo em árvore, otimização e outros problemas presentes na computação aplicada ao jogo de Go. O software produzido – Matilda – é por isso o culminar de um conjunto de experiências nesta área.Abstract: The game of Go remains one of the few deterministic perfect information games where computer players still struggle against professional human players. In this work two methods of derivation of artificial neural networks – by genetic evolution of symbiotic populations, and by training of multilayer perceptron networks with backpropagation – are analyzed for the production of a neural network suitable for guiding a Monte Carlo tree search algorithm. This last family of algorithms has been the most successful in computer Go software in the last decade. Using a neural network to reduce the branching complexity of the search is an approach to the problema that is currently being revitalized, with the advent of the application of deep convolution neural networks. DCNN however require computational facilities that many computers still don’t have. This work explores the impact of simpler neural networks for the purpose of guiding Monte Carlo tree searches, and the production of a state-of-the-art computer Go program. For this several improvements to Monte Carlo tree searches are also explored. The work is further built upon with considerations related to the parallelization of the search, and the addition of other componentes necessary for competitive programs such as time control mechanisms and opening books. Time considerations for playing against humans are also proposed for na extra psychological advantage. The final software – named Matilda– is not only the sum of a series of experimental parts surrounding Monte Carlo Tree Search applied to Go, but also an attempt at the strongest possible solution for shared memory systems

Symbolic Search in Planning and General Game Playing

Search is an important topic in many areas of AI. Search problems often result in an immense number of states. This work addresses this by using a special datastructure, BDDs, which can represent large sets of states efficiently, often saving space compared to explicit representations. The first part is concerned with an analysis of the complexity of BDDs for some search problems, resulting in lower or upper bounds on BDD sizes for these. The second part is concerned with action planning, an area where the programmer does not know in advance what the search problem will look like. This part presents symbolic algorithms for finding optimal solutions for two different settings, classical and net-benefit planning, as well as several improvements to these algorithms. The resulting planner was able to win the International Planning Competition IPC 2008. The third part is concerned with general game playing, which is similar to planning in that the programmer does not know in advance what game will be played. This work proposes algorithms for instantiating the input and solving games symbolically. For playing, a hybrid player based on UCT and the solver is presented

On forward pruning in game-tree search

Ph.DDOCTOR OF PHILOSOPH

Graph Value Iteration

In recent years, deep Reinforcement Learning (RL) has been successful in various combinatorial search domains, such as two-player games and scientific discovery. However, directly applying deep RL in planning domains is still challenging. One major difficulty is that without a human-crafted heuristic function, reward signals remain zero unless the learning framework discovers any solution plan. Search space becomes \emph{exponentially larger} as the minimum length of plans grows, which is a serious limitation for planning instances with a minimum plan length of hundreds to thousands of steps. Previous learning frameworks that augment graph search with deep neural networks and extra generated subgoals have achieved success in various challenging planning domains. However, generating useful subgoals requires extensive domain knowledge. We propose a domain-independent method that augments graph search with graph value iteration to solve hard planning instances that are out of reach for domain-specialized solvers. In particular, instead of receiving learning signals only from discovered plans, our approach also learns from failed search attempts where no goal state has been reached. The graph value iteration component can exploit the graph structure of local search space and provide more informative learning signals. We also show how we use a curriculum strategy to smooth the learning process and perform a full analysis of how graph value iteration scales and enables learning

A novel computer Scrabble engine based on probability that performs at championship leve

The thesis starts by giving an introduction to the game of Scrabble, then mentions state-of-the-art computer Scrabble programs and presents some characteristics of our developed Scrabble engine Heuri. Some brief notions of Game Theory are given, along with history of some games in Artificial Intelligence; the fundamental algorithms for game playing, as well as state-of-the-art engines and the algorithms used by them, are presented. Basic elements of Scrabble, such as the Scrabble rules and the letter distribution, are given. Some history and state-of-the-art of Computer Scrabble are commented. For instance, the generation methods of valid moves based on the data structure DAWG (Directed Acyclic Word Graph) and also the variant GADDAG are recalled. These methods are used by the state-of-the-art Scrabble engines Quackle and Maven. Then, the contributions of this thesis are presented. A Spanish lexicon for playing Scrabble has been built that is used by Heuri engines. From this construction, a detailed study and classification of Spanish irregular verbs has been provided. A novel Scrabble move generator based on anagrams has been designed and implemented, which has been shown to be faster than the GADDAG-based generator used in Quackle engine. This method is similar to the way Scrabble players look for a move, searching for anagrams and a spot to play on the board. Next, we address the evaluation of moves when playing Scrabble; the quality of your game depends on deciding what move should be played given a certain board and a rack with tiles. This decision was made initially by Heuri trying several heuristics which ended up with the construction of several engines. We give the explanation of the heuristics used in these engines, all of them based on probabilities. All these initial heuristic evaluation functions (up to six) do not use forward looking, they are static evaluators. They have shown, after testing, an increasing playing performance, which allow Heuri to beat (top-level) expert human players in Spanish, without the need of using sampling and simulation techniques. These heuristics mainly consider the possibility of achieving a bingo on the actual board, whereas Quackle used pre-calculated values (superleaves) regardless of the latter. Then, in order to improve the quality of play of Heuri even more, some additional engines are presented in which look ahead is employed. The HeuriSamp engine, which evaluates a 2-ply search, permits to obtain a defense value. The HeuriSim engine uses a 3-ply adversarial search tree; it contemplates the best first moves (according to Heuri sixth engine heuristic) from Player 1, then some replies to these moves (Player 2 moves) and then some replies to these replies (Player 1 moves). Finally, to improve these engines, opponent modeling is used; this technique makes predictions on some of the opponents' tiles based on the last play made by the opponent. We present results obtained by playing thousands of Heuri vs Heuri games, collecting important information: general statistics of Scrabble game, like a 16 point handicap of the second player, and word statistics in Spanish, like a list of the most frequently played bingos (words that use all 7 tiles of a player's rack). In addition, we present results of matches played by Heuri against top-level humans in Spanish and results obtained by massive playing of different Heuri engines against the Quackle engine in Spanish, French and English. All these match results demonstrate the championship level performance of the Heuri engines in the three languages, especially of the last developed engine that includes simulation and opponent modeling techniques. From here, conclusions of the thesis are drawn and work for the future is envisaged.La tesi comença introduint el joc del Scrabble, esmentant els programes d’ordinador de l’estat de l’art que juguen Scrabble, i presentant algunes característiques del motor de joc de Scrabble que s’ha desenvolupat anomenat Heuri. Es donen breus nocions de la Teoria de Jocs, junt amb la història d’alguns jocs en Intel·ligència Artificial; es presenten els algorismes fonamentals per jugar, així com els motors de joc de l’estat de l’art en diferents jocs i els algorismes que usen. Es comenta també la història i estat de l’art del Computer Scrabble. Es recorden els mètodes de generació de moviments vàlids basats en l’estructura de dades DAWG (Directed Acyclic Word Graph) i en la variant GADDAG, que són usats pels motors de joc de Scrabble Quackle i Maven. A continuació es presenten les contribucions de la tesi. S’ha construït un diccionari per jugar Scrabble en espanyol, el qual és usat per les diferentes versions del motor de joc Heuri. S’ha fet un estudi detallat i una classificació dels verbs irregulars en espanyol. S’ha dissenyat i implementat un nou generador de moviments de Scrabble basat en anagrames, que ha demostrat ser més ràpid que el generador basat en GADDAG usat al motor Quackle. Aquest mètode és similar a la manera en la que els jugadors de Scrabble cerquen un moviment, buscant anagrames i un lloc del tauler on col·locar-los. Seguidament, es tracta l’evacuació dels moviments quan es juga Scrabble; la qualitat del joc depèn de decidir quin moviment cal jugar donat un cert tauler i un faristol amb fitxes. En Heuri, inicialment, aquesta decisió es va prendre provant diferents heurístiques que van dur a la construcció de diversos motors. Donem l’explicació de les heurístiques usades en aquests motors, totes elles basades en probabilitats. Totes aquestes funcions d’avaluació heurística inicials (fins a sis) no miren cap endavant, fan avaluacions estàtiques. Han mostrat, després de ser provades, un rendiment creixent de nivell de joc, el que ha permès Heuri derrotar a jugadors humans experts de màxim nivell en espanyol, sense necessitat d’usar tècniques de mostreig i de simulació. Aquestes heurístiques consideren principalment la possibilitat d’aconseguir un bingo en el tauler actual, mentre que Quackle usa uns valors pre-calculats (superleaves) que no tenen en compte l’anterior. Amb l’objectiu de millorar la qualitat de joc de Heuri encara més, es presenten uns motors de joc addicionals que sí miren cap endavant. El motor HeuriSamp, que realitza una cerca 2-ply, permet obtenir un valor de defensa. El motor HeuriSim usa un arbre de cerca 3-ply; contempla els millors primers moviments (d’acord al sisè motor heurístic d’Heuri) del Jugador 1, després algunes respostes a aquests moviments (moviments del Jugador 2) i llavors algunes rèpliques a aquestes respostes (moviments del Jugador 1). Finalment, per a millorar aquests motors, es proposa usar modelatge d’oponents; aquesta tècnica realitza prediccions d’algunes de les fitxes de l’oponent basant-se en l’últim moviment jugat per aquest. Es presenten resultats obtinguts de jugar milers de partides d’Heuri contra Heuri, que recullen important informació: estadístiques generals del joc del Scrabble, com un handicap de 16 punts del segon jugador, i estadístiques de paraules en espanyol, com una llista dels bingos (paraules que usen les 7 fitxes del faristol d’un jugador) que es juguen més freqüentment. A més, es presenten resultats de partides jugades per Heuri contra jugadors humans de màxim nivell en espanyol i resultats obtinguts d'un gran nombre d’enfrontaments entre els diferents motors de joc d’Heuri contra el motor Quackle en espanyol, francès i anglès. Tots aquests resultats de partides jugades demostren el rendiment de nivell de campió dels motors d’Heuri en les tres llengües, especialment el de l’últim motor desenvolupat que inclou tècniques de de simulació i modelatge d'oponents. A partir d'aquí s'extreuen les conclusions de la tesi i es preveu treballar de cara al futur.Postprint (published version

Applying Artificial Intelligence and Machine Learning Techniques to Create Varying Play Style in Artificial Game Opponents

Artificial Intelligence is quickly becoming an integral part of the modern world, employed in almost every modern industry we interact with. Whether it be self-drive cars, integration with our web clients or the creation of actual intelligent companions such as Xiaoice1, artificial intelligence is now an integrated and critical part of our daily existence. The application of artificial intelligence to games has been explored for several decades, with many agents now competing at a high level in strategic games which prove challenging for human players (e.g. Go and Chess). With artificial intelligence now able to produce strong opponents for many games, we are more concerned with the style of play of artificial agents, rather than simply their strength. Our work here focusses on the modification of artificial game opponents to create varied playstyle in complex games. We explore several techniques of modifying Monte Carlo Tree Search in an attempt to create different styles of play, thus changing the experience for human opponents playing against them. We also explore improving artificial agent strength, both by investigating parallelization of MCTS and by using Association Rule Mining to predict opponent’s choices, thus improving our ability to play well against them