Statistical Feature Combination for the Evaluation of Game Positions

This article describes an application of three well-known statistical methods in the field of game-tree search: using a large number of classified Othello positions, feature weights for evaluation functions with a game-phase-independent meaning are estimated by means of logistic regression, Fisher's linear discriminant, and the quadratic discriminant function for normally distributed features. Thereafter, the playing strengths are compared by means of tournaments between the resulting versions of a world-class Othello program. In this application, logistic regression - which is used here for the first time in the context of game playing - leads to better results than the other approaches.Comment: See http://www.jair.org/ for any accompanying file

Nagging: A scalable, fault-tolerant, paradigm for distributed search

This paper describes Nagging, a technique for parallelizing search in a heterogeneous distributed computing environment. Nagging exploits the speedup anomaly often observed when parallelizing problems by playing multiple reformulations of the problem or portions of the problem against each other. Nagging is both fault tolerant and robust to long message latencies. In this paper, we show how nagging can be used to parallelize several different algorithms drawn from the artificial intelligence literature, and describe how nagging can be combined with partitioning, the more traditional search parallelization strategy. We present a theoretical analysis of the advantage of nagging with respect to partitioning, and give empirical results obtained on a cluster of 64 processors that demonstrate nagging\u27s effectiveness and scalability as applied to A* search, $alpha beta$ minimax game tree search, and the Davis-Putnam algorithm

Visualisasi Algoritma Kruskal dan Prim dalam Mencari Rute Terpendek Berbasis Unity 3D

Algoritma Kruskal dan Prim adalah dua algoritma pencarian Minimum Spanning Tree pada suatu graf yang mempunyai kemiripan. Seiring dengan perkembangan teknologi, muncul sebuah media pembelajaran baru yaitu game. Riset ini dilakukan untuk merancang suatu game yang dapat menjelaskan dan memvisualisasikan cara kerja algoritma Kruskal dan Prim. Data yang digunakan dalam riset ini diambil dari angket yang disebarkan pada pengguna game yang masih berstatus pelajar atau mahasiswa. Hasil penelitian memperlihatkan adanya peningkatan jumlah pengguna game yang memahami algoritma Kruskal dan Prim.Kruskal and Prim algorithms are two Minimum Spanning Tree search algorithms on a graph that has similarities. Along with the development of technology, a new learning media emerged, namely games. This research was conducted to design a game that can explain and visualize how Kruskal and Prim's algorithm works. The data used in this research was taken from a questionnaire distributed to game users who are still students or students. The results showed an increasing number of game users who understood the Kruskal and Prim algorithms

Scaling Monte Carlo Tree Search on Intel Xeon Phi

Many algorithms have been parallelized successfully on the Intel Xeon Phi coprocessor, especially those with regular, balanced, and predictable data access patterns and instruction flows. Irregular and unbalanced algorithms are harder to parallelize efficiently. They are, for instance, present in artificial intelligence search algorithms such as Monte Carlo Tree Search (MCTS). In this paper we study the scaling behavior of MCTS, on a highly optimized real-world application, on real hardware. The Intel Xeon Phi allows shared memory scaling studies up to 61 cores and 244 hardware threads. We compare work-stealing (Cilk Plus and TBB) and work-sharing (FIFO scheduling) approaches. Interestingly, we find that a straightforward thread pool with a work-sharing FIFO queue shows the best performance. A crucial element for this high performance is the controlling of the grain size, an approach that we call Grain Size Controlled Parallel MCTS. Our subsequent comparing with the Xeon CPUs shows an even more comprehensible distinction in performance between different threading libraries. We achieve, to the best of our knowledge, the fastest implementation of a parallel MCTS on the 61 core Intel Xeon Phi using a real application (47 relative to a sequential run).Comment: 8 pages, 9 figure

Thinking Fast and Slow with Deep Learning and Tree Search

Sequential decision making problems, such as structured prediction, robotic control, and game playing, require a combination of planning policies and generalisation of those plans. In this paper, we present Expert Iteration (ExIt), a novel reinforcement learning algorithm which decomposes the problem into separate planning and generalisation tasks. Planning new policies is performed by tree search, while a deep neural network generalises those plans. Subsequently, tree search is improved by using the neural network policy to guide search, increasing the strength of new plans. In contrast, standard deep Reinforcement Learning algorithms rely on a neural network not only to generalise plans, but to discover them too. We show that ExIt outperforms REINFORCE for training a neural network to play the board game Hex, and our final tree search agent, trained tabula rasa, defeats MoHex 1.0, the most recent Olympiad Champion player to be publicly released.Comment: v1 to v2: - Add a value function in MCTS - Some MCTS hyper-parameters changed - Repetition of experiments: improved accuracy and errors shown. (note the reduction in effect size for the tpt/cat experiment) - Results from a longer training run, including changes in expert strength in training - Comparison to MoHex. v3: clarify independence of ExIt and AG0. v4: see appendix