Mctx is a library with a JAX-native implementation of Monte Carlo tree search (MCTS) algorithms such as AlphaZero, MuZero, and Gumbel MuZero. For computation speed up, the implementation fully supports JIT-compilation. Search algorithms in Mctx are defined for and operate on batches of inputs, in parallel. This allows to make the most of the accelerators and enables the algorithms to work with large learned environment models parameterized by deep neural networks.

You can install the latest released version of Mctx from PyPI via:

pip install mctx

or you can install the latest development version from GitHub:

pip install git+https://github.com/google-deepmind/mctx.git

Learning and search have been important topics since the early days of AI research. In the words of Rich Sutton:

One thing that should be learned [...] is the great power of general purpose methods, of methods that continue to scale with increased computation even as the available computation becomes very great. The two methods that seem to scale arbitrarily in this way are search and learning.

Recently, search algorithms have been successfully combined with learned models parameterized by deep neural networks, resulting in some of the most powerful and general reinforcement learning algorithms to date (e.g. MuZero). However, using search algorithms in combination with deep neural networks requires efficient implementations, typically written in fast compiled languages; this can come at the expense of usability and hackability, especially for researchers that are not familiar with C++. In turn, this limits adoption and further research on this critical topic.

Through this library, we hope to help researchers everywhere to contribute to such an exciting area of research. We provide JAX-native implementations of core search algorithms such as MCTS, that we believe strike a good balance between performance and usability for researchers that want to investigate search-based algorithms in Python. The search methods provided by Mctx are heavily configurable to allow researchers to explore a variety of ideas in this space, and contribute to the next generation of search based agents.

In Reinforcement Learning the agent must learn to interact with the environment in order to maximize a scalar reward signal. On each step the agent must select an action and receives in exchange an observation and a reward. We may call whatever mechanism the agent uses to select the action the agent's policy.

Classically, policies are parameterized directly by a function approximator (as in REINFORCE), or policies are inferred by inspecting a set of learned estimates of the value of each action (as in Q-learning). Alternatively, search allows to select actions by constructing on the fly, in each state, a policy or a value function local to the current state, by searching using a learned model of the environment.

Exhaustive search over all possible future courses of actions is computationally prohibitive in any non trivial environment, hence we need search algorithms that can make the best use of a finite computational budget. Typically priors are needed to guide which nodes in the search tree to expand (to reduce the breadth of the tree that we construct), and value functions are used to estimate the value of incomplete paths in the tree that don't reach an episode termination (to reduce the depth of the search tree).

Mctx provides a low-level generic search function and high-level concrete policies: muzero_policy and gumbel_muzero_policy.

The user needs to provide several learned components to specify the representation, dynamics and prediction used by MuZero. In the context of the Mctx library, the representation of the root state is specified by a RootFnOutput. The RootFnOutput contains the prior_logits from a policy network, the estimated value of the root state, and any embedding suitable to represent the root state for the environment model.

The dynamics environment model needs to be specified by a recurrent_fn. A recurrent_fn(params, rng_key, action, embedding) call takes an action and a state embedding. The call should return a tuple (recurrent_fn_output, new_embedding) with a RecurrentFnOutput and the embedding of the next state. The RecurrentFnOutput contains the reward and discount for the transition, and prior_logits and value for the new state.

In examples/visualization_demo.py, you can see calls to a policy:

policy_output = mctx.gumbel_muzero_policy(params, rng_key, root, recurrent_fn,
                                          num_simulations=32)

The policy_output.action contains the action proposed by the search. That action can be passed to the environment. To improve the policy, the policy_output.action_weights contain targets usable to train the policy probabilities.

We recommend to use the gumbel_muzero_policy. Gumbel MuZero guarantees a policy improvement if the action values are correctly evaluated. The policy improvement is demonstrated in examples/policy_improvement_demo.py.

The following projects demonstrate the Mctx usage:

• Pgx — A collection of 20+ vectorized JAX environments, including backgammon, chess, shogi, Go, and an AlphaZero example.
• Basic Learning Demo with Mctx — AlphaZero on random mazes.
• a0-jax — AlphaZero on Connect Four, Gomoku, and Go.
• muax — MuZero on gym-style environments (CartPole, LunarLander).
• Classic MCTS — A simple example on Connect Four.
• mctx-az — Mctx with AlphaZero subtree persistence.

Tell us about your project.

This repository is part of the DeepMind JAX Ecosystem, to cite Mctx please use the citation:

@software{deepmind2020jax,
  title = {The {D}eep{M}ind {JAX} {E}cosystem},
  author = {DeepMind and Babuschkin, Igor and Baumli, Kate and Bell, Alison and Bhupatiraju, Surya and Bruce, Jake and Buchlovsky, Peter and Budden, David and Cai, Trevor and Clark, Aidan and Danihelka, Ivo and Dedieu, Antoine and Fantacci, Claudio and Godwin, Jonathan and Jones, Chris and Hemsley, Ross and Hennigan, Tom and Hessel, Matteo and Hou, Shaobo and Kapturowski, Steven and Keck, Thomas and Kemaev, Iurii and King, Michael and Kunesch, Markus and Martens, Lena and Merzic, Hamza and Mikulik, Vladimir and Norman, Tamara and Papamakarios, George and Quan, John and Ring, Roman and Ruiz, Francisco and Sanchez, Alvaro and Sartran, Laurent and Schneider, Rosalia and Sezener, Eren and Spencer, Stephen and Srinivasan, Srivatsan and Stanojevi\'{c}, Milo\v{s} and Stokowiec, Wojciech and Wang, Luyu and Zhou, Guangyao and Viola, Fabio},
  url = {http://github.com/deepmind},
  year = {2020},
}