Alphago Paper Download

We thank Fan Hui for agreeing to play against AlphaGo; T. Manning for refereeing the match; R. Munos and T. Schaul for helpful discussions and advice; A. Cain and M. Cant for work on the visuals; P. Dayan, G. Wayne, D. Kumaran, D. Purves, H. van Hasselt, A. Barreto and G. Ostrovski for reviewing the paper; and the rest of the DeepMind team for their support, ideas and encouragement.

A.H., G.v.d.D., J.S., I.A., M.La., A.G., T.G. and D.S. designed and implemented the search in AlphaGo. C.J.M., A.G., L.S., A.H., I.A., V.P., S.D., D.G., N.K., I.S., K.K. and D.S. designed and trained the neural networks in AlphaGo. J.S., J.N., A.H. and D.S. designed and implemented the evaluation framework for AlphaGo. D.S., M.Le., T.L., T.G., K.K. and D.H. managed and advised on the project. D.S., T.G., A.G. and D.H. wrote the paper.

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I understand that their architecture was to basically pass the input as a representation of the last 8 boards in the game, as well as a bit representing whose turn it is for a total of 19x19x17 inputs. Then, you pass that through a deep residual neural network, and their output was value v, the likelihood that alphago zero will win the game, as well as a policy p which is a probability distribution over all the valid movements the player can take.

In October 2015, the distributed version of AlphaGo defeated the European Go champion Fan Hui,[21] a 2-dan (out of 9 dan possible) professional, five to zero.[6][22] This was the first time a computer Go program had beaten a professional human player on a full-sized board without handicap.[23] The announcement of the news was delayed until 27 January 2016 to coincide with the publication of a paper in the journal Nature[4] describing the algorithms used.[6]

In a paper released on arXiv on 5 December 2017, DeepMind claimed that it generalized AlphaGo Zero's approach into a single AlphaZero algorithm, which achieved within 24 hours a superhuman level of play in the games of chess, shogi, and Go by defeating world-champion programs, Stockfish, Elmo, and 3-day version of AlphaGo Zero in each case.[54]

Go is a popular game in China, Japan and Korea, and the 2016 matches were watched by perhaps a hundred million people worldwide.[69][81] Many top Go players characterized AlphaGo's unorthodox plays as seemingly-questionable moves that initially befuddled onlookers, but made sense in hindsight:[73] "All but the very best Go players craft their style by imitating top players. AlphaGo seems to have totally original moves it creates itself."[69] AlphaGo appeared to have unexpectedly become much stronger, even when compared with its October 2015 match[82] where a computer had beaten a Go professional for the first time ever without the advantage of a handicap.[83] The day after Lee's first defeat, Jeong Ahram, the lead Go correspondent for one of South Korea's biggest daily newspapers, said "Last night was very gloomy... Many people drank alcohol."[84] The Korea Baduk Association, the organization that oversees Go professionals in South Korea, awarded AlphaGo an honorary 9-dan title for exhibiting creative skills and pushing forward the game's progress.[85]

This tutorial walks through a synchronous single-thread single-GPU (read malnourished) game-agnostic implementation of the recent AlphaGo Zero paper by DeepMind. It's a beautiful piece of work that trains an agent for the game of Go through pure self-play without any human knowledge except the rules of the game. The methods are fairly simple compared to previous papers by DeepMind, and AlphaGo Zero ends up beating AlphaGo (trained using data from expert games and beat the best human Go players) convincingly. Recently, DeepMind published a preprint of Alpha Zero on arXiv that extends AlphaGo Zero methods to Chess and Shogi.

The aim of this post is to distil out the key ideas from the AlphaGo Zero paper and understand them concretely through code. It assumes basic familiarity with machine learning and reinforcement learning concepts, and should be accessible if you understand neural network basics and Monte Carlo Tree Search. Before starting out (or after finishing this tutorial), I would recommend reading the original paper. It's well-written, very readable and has beautiful illustrations! AlphaGo Zero is trained by self-play reinforcement learning. It combines a neural network and Monte Carlo Tree Search in an elegant policy iteration framework to achieve stable learning. But that's just words- let's dive into the details straightaway.

When training the network, at the end of each game of self-play, the neural network is provided training examples of the form $ (s_t, \vec{\pi}_t, z_t) $. $ \vec{\pi}_t $ is an estimate of the policy from state $s_t$ (we'll get to how $\vec{\pi}_t$ is arrived at in the next section), and $z_t \in \{-1,1\}$ is the final outcome of the game from the perspective of the player at $s_t$ (+1 if the player wins, -1 if the player loses). The neural network is then trained to minimise the following loss function (excluding regularisation terms):$$ l = \sum_t (v_\theta(s_t) - z_t)^2 - \vec{\pi}_t \cdot \log(\vec{p}_\theta(s_t)) $$ The underlying idea is that over time, the network will learn what states eventually lead to wins (or losses). In addition, learning the policy would give a good estimate of what the best action is from a given state. The neural network architecture in general would depend on the game. Most board games such as Go can use a multi-layer CNN architecture. In the paper by DeepMind, they use 20 residual blocks, each with 2 convolutional layers. I was able to get a 4-layer CNN network followed by a few feedforward layers to work for 6x6 Othello.

At the end of the iteration, the neural network is trained with the obtained training examples. The old and the new networks are pit against each other. If the new network wins more than a set threshold fraction of games (55% in the DeepMind paper), the network is updated to the new network. Otherwise, we conduct another iteration to augment the training examples.

We trained an agent for the game of Othello for a 6x6 board on a single GPU. Each iteration consisted of 100 episodes of self-play and each MCTS used 25 simulations. Note that this is orders of magnitude smaller than the computation used in the AlphaGo paper (25000 episodes per iteration, 1600 simulations per turn). The model took around 3 days (80 iterations) for training to saturate on an NVIDIA Tesla K80 GPU. We evaluated the model against random and greedy baselines, as well as a minimax agent and humans. It performed pretty well and even picked up some common strategies used by humans.

This post provides an overview of the key ideas in the AlphaGo Zero paper and excludes finer details for the sake of clarity. The AlphaGo paper describes some additional details in their implementation. Some of them are: History of State: Since Go is not completely observable from the current state of the board, the neural network also takes as input the boards from the last 7 time steps. This is a feature of the game itself, and other games such as Chess and Othello would only require the current board as input. Temperature: The stochastic policy obtained after performing the MCTS uses exponentiated counts, i.e. $\vec{\pi}(s) = N(s, \cdot)^{1/\tau}/\sum_b(N(s,b)^{1/\tau}) $, where $\tau$ is the temperature and controls the degree of exploration. AlphaGo Zero uses $\tau=1$ (simply the normalised counts) for the first 30 moves of each game, and then sets it to an infinitesimal value (picking the move with the maximum counts). Symmetry: The Go board is invariant to rotation and reflection. When MCTS reaches a leaf node, the current neural network is called with a reflected or rotated version of the board to exploit this symmetry. In general, this can be extended to other games using symmetries that hold for the game. Asynchronous MCTS: AlphaGo Zero uses an asynchronous variant of MCTS that performs the simulations in parallel. The neural network queries are batched and each search thread is locked until evaluation completes. In addition, the 3 main processes: self-play, neural network training and comparison between old and new networks are all done in parallel. Compute Power: Each neural network was trained using 64 GPUs and 19 CPUs. The compute power used for executing the self-play in unclear from the paper. Neural Network Design: The authors tried a variety of architectures including networks with and without residual networks, and with and without parameter sharing for the value and policy networks. Their best architecture used residual networks and shared the parameters for the value and policy networks.

Also, I think the main probability is you misread the paper. I bet the ablation analysis takes out the policy network used to decide on good moves during search (not just the surface-level policy network used at the top of the tree), and they used the same amount of compute in the ablations (i.e. they reduced the search depth rather than doing brute-force search to the same depth).

Unfortunately, the algorithm as described here is an inherentlysequential process. Because MCTS is deterministic, rerunning step 1 willalways return the same variation, until the updated value estimates andvisit counts have been incorporated. And yet, the supporting informationin the AGZ paper describes batching up positions in multiples of 8, foroptimal TPU throughput.

The second mindblowing part of the AGZ paper was that thisbootstrapping actually worked, even starting from random noise. The MCTSwould just be averaging a bunch of random value estimates at the start,so how would it make any progress at all?

The first AlphaGo paper trained the policy network first, thenfroze those weights while training the weights of a value branch. Thecurrent AlphaGo concurrently computes both policy and value halves, andtrains with a combined loss function. This is really elegant is severalways: the two objectives regularize each other; it halves thecomputation time required; and it integrates perfectly with MCTS, whichrequires evaluating both policy and value parts for each variationinvestigated. 2351a5e196