# Introduction to AlphaZero

The AlphaZero algorithm elegantly combines search and learning, which are described in Rich Sutton's essay "The Bitter Lesson" as the two fundamental pillars of AI. It augments a tree search procedure with two learnt heuristics: one to evaluate board positions and one to concentrate branching on moves that are not obviously wrong.

When training starts, both heuristics are initialized randomly and tree search has only access to a meaningful signal at the level of final states, where the game outcome is known. These heuristics are then improved iteratively through self-play. More specifically:

• The heuristics are implemented by a two-headed neural network. Given a board position as an input, it estimates the probability for each player to ultimately win the game. It also provides a quantitative estimate of the relative quality of all available moves in the form of a probability distribution.
• The search component is powered by Monte-Carlo Tree Search (MCTS), which implements a good compromise between breadth-first and depth-first search and provides a principled way to manage the uncertainty introduced by the heuristics. Also, given a position, it does not return a single choice for a best move but rather a probability distribution over available moves.
• At each training iteration, AlphaZero plays a series of games against itself. The network is then updated so that it makes more accurate predictions about the outcome of these games. Also, the network's policy heuristic is updated to match the output of MCTS on all encountered positions. This way, MCTS can be seen as a powerful policy improvement operator.

For more details, we recommend the following resources.

### External resources

• A short and effective introduction to AlphaZero is Surag Nair's excellent tutorial.
• A good resource to learn about Monte Carlo Tree Search (MCTS) is this Int8 tutorial.
• Then, DeepMind's original Nature paper is a nice read.
• Finally, this series of posts from Oracle has been an important source of inspiration for AlphaZero.jl. It provides useful details on implementing asynchronous MCTS, along with an interesting discussion on hyperparameters tuning.