AbstractPlayer

Abstract type for a game player.

AbstractSchedule{R}

Abstract type for a parameter schedule, which represents a function from nonnegative integers to numbers of type R. Subtypes must implement the getindex(s::AbstractSchedule, i::Int) operator.

ArenaParams

Parameters that govern the evaluation process that compares the current neural network with the best one seen so far (which is used to generate data).

Explanation (two-player games)

• The two competing networks are instantiated into two MCTS players of parameter mcts and then play sim.num_games games.
• The evaluated network replaces the current best one if its average collected reward is greater or equal than update_threshold.

Explanation (single-player games)

• The two competing networks play sim.num_games games each.
• The evaluated network replaces the current best one if its average collected rewards exceeds the average collected reward of the old one by update_threshold at least.

Remarks

• See necessary_samples to make an informed choice for sim.num_games.

AlphaGo Zero Parameters

In the original AlphaGo Zero paper, 400 games are played to evaluate a network and the update_threshold parameter is set to a value that corresponds to a 55% win rate.

Env

Type for an AlphZero environment.

The environment features the current neural network, the best neural network seen so far that is used for data generation, a memory buffer and an iteration counter.

Constructor

Env(game_spec, params, curnn, bestnn=copy(curnn), experience=[], itc=0)

Construct a new AlphaZero environment:

• game_spec specified the game being played
• params has type Params
• curnn is the current neural network and has type AbstractNetwork
• bestnn is the best neural network so far, which is used for data generation
• experience is the initial content of the memory buffer as a vector of TrainingSample
• itc is the value of the iteration counter (0 at the start of training)

EpsilonGreedyPlayer{Player} <: AbstractPlayer

A wrapper on a player that makes it choose a random move with a fixed $ϵ$ probability.

Human <: AbstractPlayer

Human player that queries the standard input for actions.

Does not implement think but instead implements select_move directly.

LearningParams

Parameters governing the learning phase of a training iteration, where the neural network is updated to fit the data in the memory buffer.

Description

The neural network goes through num_checkpoints series of n updates using batches of size batch_size drawn from memory, where n is defined as follows:

n = min(max_batches_per_checkpoint, ntotal ÷ min_checkpoints_per_epoch)

with ntotal the total number of batches in memory. Between each series, the current network is evaluated against the best network so far (see ArenaParams).

• nonvalidity_penalty is the multiplicative constant of a loss term that corresponds to the average probability weight that the network puts on invalid actions.
• batch_size is the batch size used for gradient descent.
• loss_computation_batch_size is the batch size that is used to compute the loss between each epochs.
• All rewards are divided by rewards_renormalization before the MSE loss is computed.
• If use_position_averaging is set to true, samples in memory that correspond to the same board position are averaged together. The merged sample is reweighted according to samples_weighing_policy.

AlphaGo Zero Parameters

In the original AlphaGo Zero paper:

• The batch size for gradient updates is $2048$.
• The L2 regularization parameter is set to $10^{-4}$.
• Checkpoints are produced every 1000 training steps, which corresponds to seeing about 20% of the samples in the memory buffer: $(1000 × 2048) / 10^7 ≈ 0.2$.
• It is unclear how many checkpoints are taken or how many training steps are performed in total.

Parameters of an MCTS player.

Explanation

An MCTS player picks an action as follows. Given a game state, it launches num_iters_per_turn MCTS iterations, with UCT exploration constant cpuct. Rewards are discounted using the gamma factor.

Then, an action is picked according to the distribution $π$ where $π_i ∝ n_i^{1/τ}$ with $n_i$ the number of times that the $i^{\text{th}}$ action was visited and $τ$ the temperature parameter.

It is typical to use a high value of the temperature parameter $τ$ during the first moves of a game to increase exploration and then switch to a small value. Therefore, temperature is am AbstractSchedule.

For information on parameters cpuct, dirichlet_noise_ϵ, dirichlet_noise_α and prior_temperature, see MCTS.Env.

AlphaGo Zero Parameters

In the original AlphaGo Zero paper:

• The discount factor gamma is set to 1.
• The number of MCTS iterations per move is 1600, which corresponds to 0.4s of computation time.
• The temperature is set to 1 for the 30 first moves and then to an infinitesimal value.
• The $ϵ$ parameter for the Dirichlet noise is set to $0.25$ and the $α$ parameter to $0.03$, which is consistent with the heuristic of using $α = 10/n$ with $n$ the maximum number of possibles moves, which is $19 × 19 + 1 = 362$ in the case of Go.

MctsPlayer{MctsEnv} <: AbstractPlayer

A player that selects actions using MCTS.

Constructors

MctsPlayer(mcts::MCTS.Env; τ, niters, timeout=nothing)

Construct a player from an MCTS environment. When computing each move:

• if timeout is provided, MCTS simulations are executed for timeout seconds by groups of niters
• otherwise, niters MCTS simulations are run

The temperature parameter τ can be either a real number or a AbstractSchedule.

MctsPlayer(game_spec::AbstractGameSpec, oracle,
           params::MctsParams; timeout=nothing)

Construct an MCTS player from an oracle and an MctsParams structure.

MemAnalysisParams

Parameters governing the analysis of the memory buffer (for debugging and profiling purposes).

Explanation

The memory analysis consists in partitioning the memory buffer in num_game_stages parts of equal size, according to the number of remaining moves until the end of the game for each sample. Then, the quality of the predictions of the current neural network is evaluated on each subset (see Report.Memory).

This is useful to get an idea of how the neural network performance varies depending on the game stage (typically, good value estimates for endgame board positions are available earlier in the training process than good values for middlegame positions).

MemoryBuffer(game_spec, size, experience=[])

A circular buffer to hold memory samples.

NetworkPlayer{Net} <: AbstractPlayer

A player that uses the policy output by a neural network directly, instead of relying on MCTS. The given neural network must be in test mode.

PLSchedule{R} <: AbstractSchedule{R}

Type for piecewise linear schedules.

Constructors

PLSchedule(cst)

Return a schedule with a constant value cst.

PLSchedule(xs, ys)

Return a piecewise linear schedule such that:

• For all i, (xs[i], ys[i]) belongs to the schedule's graph.
• Before xs[1], the schedule has value ys[1].
• After xs[end], the schedule has value ys[end].

Params

The AlphaZero training hyperparameters.

Explanation

The AlphaZero training process consists in num_iters iterations. Each iteration can be decomposed into a self-play phase (see SelfPlayParams) and a learning phase (see LearningParams).

• ternary_rewards: set to true if the rewards issued by the game environment always belong to $\{-1, 0, 1\}$ so that the logging and profiling tools can take advantage of this property.
• use_symmetries: if set to true, board symmetries are used for data augmentation before learning.
• mem_buffer_size: size schedule of the memory buffer, in terms of number of samples. It is typical to start with a small memory buffer that is grown progressively so as to wash out the initial low-quality self-play data more quickly.
• memory_analysis: parameters for the memory analysis step that is performed at each iteration (see MemAnalysisParams), or nothing if no analysis is to be performed.

AlphaGo Zero Parameters

In the original AlphaGo Zero paper:

• About 5 millions games of self-play are played across 200 iterations.
• The memory buffer contains 500K games, which makes about 100M samples as an average game of Go lasts about 200 turns.

PlayerWithTemperature{Player} <: AbstractPlayer

A wrapper on a player that enables overwriting the temperature schedule.

RandomPlayer <: AbstractPlayer

A player that picks actions uniformly at random.

SamplesWeighingPolicy

During self-play, early board positions are possibly encountered many times across several games. The corresponding samples can be merged together and given a weight $W$ that is a nondecreasing function of the number $n$ of merged samples:

• CONSTANT_WEIGHT: $W(n) = 1$
• LOG_WEIGHT: $W(n) = \log_2(n) + 1$
• LINEAR_WEIGHT: $W(n) = n$

SelfPlayParams

Parameters governing self-play.

AlphaGo Zero Parameters

In the original AlphaGo Zero paper, sim.num_games=25_000 (5 millions games of self-play across 200 iterations).

SimParams

Parameters for parallel game simulations.

These parameters are common to self-play data generation, neural network evaluation and benchmarking.

Explanations

• On each machine (process), num_workers simulation tasks are spawned. Inference requests are processed by an inference server by batch of size batch_size. Note that we must have batch_size <= num_workers.
• If fill_batches is set to true, we make sure that batches sent to the neural network for inference have constant size.
• Both players are reset (e.g. their MCTS trees are emptied) every reset_every games (or never if nothing is passed).
• To add randomization and before every game turn, the game board is "flipped" according to a symmetric transformation with probability flip_probability.
• In the case of (symmetric) two-player games and if alternate_colors is set totrue, then the colors of both players are swapped between each simulated game.

Simulator(make_player, make_oracles, measure)

A distributed simulator that encapsulates the details of running simulations across multiple threads and multiple machines.

Arguments

• make_oracles: a function that takes no argument and returns the oracles used by the player, which can be either nothing, a single oracle or a pair of oracles.
• make_player: a function that takes as an argument the result of make_oracles and builds a player from it. In practice, an oracle returned by make_oracles may be replaced by a BatchedOracle before it is passed to make_player, which is why these two functions are specified separately.
• measure(trace, colors_flipped, player): the function that is used to take measurements after each game simulation.

StepSchedule{R} <: AbstractSchedule{R}

Type for step function schedules.

Constructor

StepSchedule(;start, change_at, values)

Return a schedule that has initial value start. For all i, the schedule takes value values[i] at step change_at[i].

Trace{State}

An object that collects all states visited during a game, along with the rewards obtained at each step and the successive player policies to be used as targets for the neural network.

Constructor

Trace(initial_state)

TrainingSample{State}

Type of a training sample. A sample features the following fields:

• s::State is the state
• π::Vector{Float64} is the recorded MCTS policy for this position
• z::Float64 is the discounted reward cumulated from state s
• t::Float64 is the (average) number of moves remaining before the end of the game
• n::Int is the number of times the state s was recorded

As revealed by the last field n, several samples that correspond to the same state can be merged, in which case the π, z and t fields are averaged together.

TwoPlayers <: AbstractPlayer

If white and black are two AbstractPlayer, then TwoPlayers(white, black) is a player that behaves as white when white is to play and as black when black is to play.

AlphaZeroPlayer(::Env; [timeout, mcts_params, use_gpu])

Create an AlphaZero player from the current training environment.

Note that the returned player may be slow as it does not batch MCTS requests.

CyclicSchedule(base, mid, term; n, xmid=0.45, xback=0.90)

Return the PLSchedule that is typically used for cyclic learning rate scheduling.

get_experience(env::Env)

Return the content of the agent's memory as a vector of TrainingSample.

get_experience(::MemoryBuffer) :: Vector{<:TrainingSample}

Return all samples in the memory buffer.

initial_report(env::Env)

Return a report summarizing the configuration of agent before training starts, as an object of type Report.Initial.

interactive!(game)
interactive!(gspec)
interactive!(game, player)
interactive!(gspec, player)
interactive!(game, white, black)
interactive!(gspec, white, black)

Launch a possibly interactive game session.

This function takes either an AbstractGameSpec or AbstractGameEnv as an argument.

necessary_samples(ϵ, β) = log(1 / β) / (2 * ϵ^2)

Compute the number of times $N$ that a random variable $X \sim \text{Ber}(p)$ has to be sampled so that if the empirical average of $X$ is greather than $1/2 + ϵ$, then $p > 1/2$ with probability at least $1-β$.

This bound is based on Hoeffding's inequality .

play_game(gspec::AbstractGameSpec, player; flip_probability=0.) :: Trace

Simulate a game by an AbstractPlayer.

• For two-player games, please use TwoPlayers.
• If the flip_probability argument is set to $p$, the board is flipped randomly at every turn with probability $p$, using GI.apply_random_symmetry!.

player_temperature(::AbstractPlayer, game, turn_number)

Return the player temperature, given the number of actions that have been played before by both players in the current game.

A default implementation is provided that always returns 1.

push_trace!(mem::MemoryBuffer, trace::Trace, gamma)

Collect samples out of a game trace and add them to the memory buffer.

Here, gamma is the reward discount factor.

record_trace

A measurement function to be passed to a Simulator that produces named tuples with two fields: trace::Trace and colors_flipped::Bool.

reset_player!(::AbstractPlayer)

Reset the internal memory of a player (e.g. the MCTS tree). The default implementation does nothing.

select_move(player::AbstractPlayer, game, turn_number)

Return a single action. A default implementation is provided that samples an action according to the distribution computed by think, with a temperature given by player_temperature.

simulate(::Simulator, ::AbstractGameSpec; ::SimParams; <kwargs>)

Play a series of games using a given Simulator.

Keyword Arguments

• game_simulated is called every time a game simulation is completed (with no arguments)

Return

Return a vector of objects computed by simulator.measure.

simulate_distributed(::Simulator, ::AbstractGameSpec, ::SimParams; <kwargs>)

Identical to simulate but splits the work across all available distributed workers, whose number is given by Distributed.nworkers().

think(::AbstractPlayer, game)

Return a probability distribution over available actions as a (actions, π) pair.

train!(env::Env, handler=nothing)

Start or resume the training of an AlphaZero agent.

A handler object can be passed that implements a subset of the callback functions defined in Handlers.

Base.push!(t::Trace, π, r, s)

Add a (target policy, reward, new state) quadruple to a trace.