# Bonus Tutorial: Planning with Monte Carlo Tree Search

## Contents

# Bonus Tutorial: Planning with Monte Carlo Tree Search¶

**Week 3, Day 5: Reinforcement Learning for Games & DL Thinking 3**

**By Neuromatch Academy**

**Content creators:** Mandana Samiei, Raymond Chua, Kushaan Gupta, Tim Lilicrap, Blake Richards

**Content reviewers:** Arush Tagade, Lily Cheng, Melvin Selim Atay, Kelson Shilling-Scrivo

**Content editors:** Melvin Selim Atay, Spiros Chavlis, Gunnar Blohm

**Production editors:** Namrata Bafna, Gagana B, Spiros Chavlis

# Tutorial Objectives¶

In this tutorial, you will learn about Monte Carlo Tree Search (MCTS) and compare its performance to policy-based, value-based players, and Monte Carlo planners.

These are the slides for the videos in the tutorial. If you want to locally download the slides, click here.

# Setup¶

## Install dependencies¶

```
# @title Install dependencies
!pip install coloredlogs --quiet
```

## Install and import feedback gadget¶

```
# @title Install and import feedback gadget
!pip3 install vibecheck datatops --quiet
from vibecheck import DatatopsContentReviewContainer
def content_review(notebook_section: str):
return DatatopsContentReviewContainer(
"", # No text prompt
notebook_section,
{
"url": "https://pmyvdlilci.execute-api.us-east-1.amazonaws.com/klab",
"name": "neuromatch_dl",
"user_key": "f379rz8y",
},
).render()
feedback_prefix = "W3D5_T3_Bonus"
```

```
# Imports
import os
import math
import random
import time
import torch
import random
import logging
import coloredlogs
import numpy as np
import torch.nn as nn
import torch.optim as optim
import torch.nn.functional as F
from tqdm.notebook import tqdm
log = logging.getLogger(__name__)
coloredlogs.install(level='INFO') # Change this to DEBUG to see more info.
```

## Set random seed¶

Executing `set_seed(seed=seed)`

you are setting the seed

```
# @title Set random seed
# @markdown Executing `set_seed(seed=seed)` you are setting the seed
# For DL its critical to set the random seed so that students can have a
# baseline to compare their results to expected results.
# Read more here: https://pytorch.org/docs/stable/notes/randomness.html
# Call `set_seed` function in the exercises to ensure reproducibility.
def set_seed(seed=None, seed_torch=True):
"""
Function that controls randomness. NumPy and random modules must be imported.
Args:
seed : Integer
A non-negative integer that defines the random state. Default is `None`.
seed_torch : Boolean
If `True` sets the random seed for pytorch tensors, so pytorch module
must be imported. Default is `True`.
Returns:
Nothing.
"""
if seed is None:
seed = np.random.choice(2 ** 32)
random.seed(seed)
np.random.seed(seed)
if seed_torch:
torch.manual_seed(seed)
torch.cuda.manual_seed_all(seed)
torch.cuda.manual_seed(seed)
torch.backends.cudnn.benchmark = False
torch.backends.cudnn.deterministic = True
print(f'Random seed {seed} has been set.')
# In case that `DataLoader` is used
def seed_worker(worker_id):
"""
DataLoader will reseed workers following randomness in
multi-process data loading algorithm.
Args:
worker_id: integer
ID of subprocess to seed. 0 means that
the data will be loaded in the main process
Refer: https://pytorch.org/docs/stable/data.html#data-loading-randomness for more details
Returns:
Nothing
"""
worker_seed = torch.initial_seed() % 2**32
np.random.seed(worker_seed)
random.seed(worker_seed)
```

## Set device (GPU or CPU). Execute `set_device()`

¶

```
# @title Set device (GPU or CPU). Execute `set_device()`
# especially if torch modules used.
# Inform the user if the notebook uses GPU or CPU.
def set_device():
"""
Set the device. CUDA if available, CPU otherwise
Args:
None
Returns:
Nothing
"""
device = "cuda" if torch.cuda.is_available() else "cpu"
if device != "cuda":
print("WARNING: For this notebook to perform best, "
"if possible, in the menu under `Runtime` -> "
"`Change runtime type.` select `GPU` ")
else:
print("GPU is enabled in this notebook.")
return device
```

```
SEED = 2023
set_seed(seed=SEED)
DEVICE = set_device()
```

```
Random seed 2023 has been set.
GPU is enabled in this notebook.
```

## Download the modules¶

```
# @title Download the modules
# @markdown Run this cell!
# @markdown Download from OSF. The original repo is https://github.com/raymondchua/nma_rl_games.git
import os, io, sys, shutil, zipfile
from urllib.request import urlopen
# download from github repo directly
#!git clone git://github.com/raymondchua/nma_rl_games.git --quiet
REPO_PATH = 'nma_rl_games'
if not os.path.exists(REPO_PATH):
download_string = "Downloading"
zipurl = 'https://osf.io/kf4p9/download'
print(f"{download_string} and unzipping the file... Please wait.")
with urlopen(zipurl) as zipresp:
with zipfile.ZipFile(io.BytesIO(zipresp.read())) as zfile:
zfile.extractall()
print("Download completed.")
print(f"Add the {REPO_PATH} in the path and import the modules.")
# add the repo in the path
sys.path.append('nma_rl_games/alpha-zero')
# @markdown Import modules designed for use in this notebook
import Arena
from utils import *
from Game import Game
from MCTS import MCTS
from NeuralNet import NeuralNet
# from othello.OthelloPlayers import *
from othello.OthelloLogic import Board
# from othello.OthelloGame import OthelloGame
from othello.pytorch.NNet import NNetWrapper as NNet
```

```
Add the nma_rl_games in the path and import the modules.
```

## Helper functions from previous tutorials¶

```
# @title Helper functions from previous tutorials
def loadTrainExamples(folder, filename):
"""
Helper function to load training examples
Args:
folder: string
Path specifying training examples
filename: string
File name of training examples
Returns:
trainExamplesHistory: list
Returns examples based on the model were already collected (loaded)
"""
trainExamplesHistory = []
modelFile = os.path.join(folder, filename)
examplesFile = modelFile + ".examples"
if not os.path.isfile(examplesFile):
print(f'File "{examplesFile}" with trainExamples not found!')
r = input("Continue? [y|n]")
if r != "y":
sys.exit()
else:
print("File with train examples found. Loading it...")
with open(examplesFile, "rb") as f:
trainExamplesHistory = Unpickler(f).load()
print('Loading done!')
return trainExamplesHistory
def save_model_checkpoint(folder, filename, nnet):
filepath = os.path.join(folder, filename)
if not os.path.exists(folder):
print("Checkpoint Directory does not exist! Making directory {}".format(folder))
os.mkdir(folder)
else:
print("Checkpoint Directory exists!")
torch.save({'state_dict': nnet.state_dict()}, filepath)
print("Model saved!")
def load_model_checkpoint(folder, filename, nnet, device):
filepath = os.path.join(folder, filename)
if not os.path.exists(filepath):
raise FileNotFoundError("No model in path {}".format(filepath))
checkpoint = torch.load(filepath, map_location=device)
nnet.load_state_dict(checkpoint['state_dict'])
class OthelloGame(Game):
"""
Othello game board
"""
square_content = {
-1: "X",
+0: "-",
+1: "O"
}
@staticmethod
def getSquarePiece(piece):
return OthelloGame.square_content[piece]
def __init__(self, n):
self.n = n
def getInitBoard(self):
b = Board(self.n)
return np.array(b.pieces)
def getBoardSize(self):
return (self.n, self.n)
def getActionSize(self):
# Return number of actions, n is the board size and +1 is for no-op action
return self.n * self.n + 1
def getCanonicalForm(self, board, player):
# Return state if player==1, else return -state if player==-1
return player * board
def stringRepresentation(self, board):
return board.tobytes()
def stringRepresentationReadable(self, board):
board_s = "".join(self.square_content[square] for row in board for square in row)
return board_s
def getScore(self, board, player):
b = Board(self.n)
b.pieces = np.copy(board)
return b.countDiff(player)
@staticmethod
def display(board):
n = board.shape[0]
print(" ", end="")
for y in range(n):
print(y, end=" ")
print("")
print("-----------------------")
for y in range(n):
print(y, "|", end="") # Print the row
for x in range(n):
piece = board[y][x] # Get the piece to print
print(OthelloGame.square_content[piece], end=" ")
print("|")
print("-----------------------")
@staticmethod
def displayValidMoves(moves):
A=np.reshape(moves[0:-1], board.shape)
n = board.shape[0]
print(" ")
print("possible moves")
print(" ", end="")
for y in range(n):
print(y, end=" ")
print("")
print("-----------------------")
for y in range(n):
print(y, "|", end="") # Print the row
for x in range(n):
piece = A[y][x] # Get the piece to print
print(OthelloGame.square_content[piece], end=" ")
print("|")
print("-----------------------")
def getNextState(self, board, player, action):
"""
Make valid move. If player takes action on board, return next (board,player)
and action must be a valid move
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
player: Integer
ID of current player
action: np.ndarray
Space of actions
Returns:
(board, player): tuple
Next state representation
"""
if action == self.n*self.n:
return (board, -player)
b = Board(self.n)
b.pieces = np.copy(board)
move = (int(action/self.n), action%self.n)
b.execute_move(move, player)
return (b.pieces, -player)
def getValidMoves(self, board, player):
"""
Get all valid moves for player
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
player: Integer
ID of current player
action: np.ndarray
Space of action
Returns:
valids: np.ndarray
Valid moves for player
"""
valids = [0]*self.getActionSize()
b = Board(self.n)
b.pieces = np.copy(board)
legalMoves = b.get_legal_moves(player)
if len(legalMoves)==0:
valids[-1]=1
return np.array(valids)
for x, y in legalMoves:
valids[self.n*x+y]=1
return np.array(valids)
def getGameEnded(self, board, player):
"""
Check if game ended
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
player: Integer
ID of current player
Returns:
0 if not ended, 1 if player 1 won, -1 if player 1 lost
"""
b = Board(self.n)
b.pieces = np.copy(board)
if b.has_legal_moves(player):
return 0
if b.has_legal_moves(-player):
return 0
if b.countDiff(player) > 0:
return 1
return -1
def getSymmetries(self, board, pi):
"""
Get mirror/rotational configurations of board
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
pi: np.ndarray
Dimension of board
Returns:
l: list
90 degree of board, 90 degree of pi_board
"""
assert(len(pi) == self.n**2+1) # 1 for pass
pi_board = np.reshape(pi[:-1], (self.n, self.n))
l = []
for i in range(1, 5):
for j in [True, False]:
newB = np.rot90(board, i)
newPi = np.rot90(pi_board, i)
if j:
newB = np.fliplr(newB)
newPi = np.fliplr(newPi)
l += [(newB, list(newPi.ravel()) + [pi[-1]])]
return l
class RandomPlayer():
def __init__(self, game):
self.game = game
def play(self, board):
"""
Simulates game play
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
Returns:
a: int
Randomly chosen move
"""
# Compute the valid moves using getValidMoves()
valids = self.game.getValidMoves(board, 1)
# Compute the probability of each move being played (random player means this should
# be uniform for valid moves, 0 for others)
prob = valids/valids.sum()
# Pick an action based on the probabilities (hint: np.choice is useful)
a = np.random.choice(self.game.getActionSize(), p=prob)
return a
class OthelloNNet(nn.Module):
def __init__(self, game, args):
"""
Initialise game parameters
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
args: dictionary
Instantiates number of iterations and episodes, controls temperature threshold, queue length,
arena, checkpointing, and neural network parameters:
learning-rate: 0.001, dropout: 0.3, epochs: 10, batch_size: 64,
num_channels: 512
"""
self.board_x, self.board_y = game.getBoardSize()
self.action_size = game.getActionSize()
self.args = args
super(OthelloNNet, self).__init__()
self.conv1 = nn.Conv2d(in_channels=1, out_channels=args.num_channels,
kernel_size=3, stride=1, padding=1)
self.conv2 = nn.Conv2d(in_channels=args.num_channels,
out_channels=args.num_channels, kernel_size=3,
stride=1, padding=1)
self.conv3 = nn.Conv2d(in_channels=args.num_channels,
out_channels=args.num_channels, kernel_size=3,
stride=1)
self.conv4 = nn.Conv2d(in_channels=args.num_channels,
out_channels=args.num_channels, kernel_size=3,
stride=1)
self.bn1 = nn.BatchNorm2d(num_features=args.num_channels)
self.bn2 = nn.BatchNorm2d(num_features=args.num_channels)
self.bn3 = nn.BatchNorm2d(num_features=args.num_channels)
self.bn4 = nn.BatchNorm2d(num_features=args.num_channels)
self.fc1 = nn.Linear(in_features=args.num_channels * (self.board_x - 4) * (self.board_y - 4),
out_features=1024)
self.fc_bn1 = nn.BatchNorm1d(num_features=1024)
self.fc2 = nn.Linear(in_features=1024, out_features=512)
self.fc_bn2 = nn.BatchNorm1d(num_features=512)
self.fc3 = nn.Linear(in_features=512, out_features=self.action_size)
self.fc4 = nn.Linear(in_features=512, out_features=1)
def forward(self, s):
"""
Controls forward pass of OthelloNNet
Args:
s: np.ndarray
Array of size (batch_size x board_x x board_y)
Returns:
prob, v: tuple of torch.Tensor
Probability distribution over actions at the current state and the value
of the current state.
"""
s = s.view(-1, 1, self.board_x, self.board_y) # batch_size x 1 x board_x x board_y
s = F.relu(self.bn1(self.conv1(s))) # batch_size x num_channels x board_x x board_y
s = F.relu(self.bn2(self.conv2(s))) # batch_size x num_channels x board_x x board_y
s = F.relu(self.bn3(self.conv3(s))) # batch_size x num_channels x (board_x-2) x (board_y-2)
s = F.relu(self.bn4(self.conv4(s))) # batch_size x num_channels x (board_x-4) x (board_y-4)
s = s.view(-1, self.args.num_channels * (self.board_x - 4) * (self.board_y - 4))
s = F.dropout(F.relu(self.fc_bn1(self.fc1(s))), p=self.args.dropout, training=self.training) # batch_size x 1024
s = F.dropout(F.relu(self.fc_bn2(self.fc2(s))), p=self.args.dropout, training=self.training) # batch_size x 512
pi = self.fc3(s) # batch_size x action_size
v = self.fc4(s) # batch_size x 1
return F.log_softmax(pi, dim=1), torch.tanh(v)
class ValueNetwork(NeuralNet):
def __init__(self, game):
"""
Args:
game: OthelloGame
Instance of the OthelloGame class above
"""
self.nnet = OthelloNNet(game, args)
self.board_x, self.board_y = game.getBoardSize()
self.action_size = game.getActionSize()
self.nnet.to(args.device)
def train(self, games):
"""
Args:
games: list
List of examples with each example is of form (board, pi, v)
"""
optimizer = optim.Adam(self.nnet.parameters())
for examples in games:
for epoch in range(args.epochs):
print('EPOCH ::: ' + str(epoch + 1))
self.nnet.train()
v_losses = [] # To store the losses per epoch
batch_count = int(len(examples) / args.batch_size) # len(examples)=200, batch-size=64, batch_count=3
t = tqdm(range(batch_count), desc='Training Value Network')
for _ in t:
sample_ids = np.random.randint(len(examples), size=args.batch_size) # Read the ground truth information from MCTS simulation using the loaded examples
boards, pis, vs = list(zip(*[examples[i] for i in sample_ids])) # Length of boards, pis, vis = 64
boards = torch.FloatTensor(np.array(boards).astype(np.float64))
target_vs = torch.FloatTensor(np.array(vs).astype(np.float64))
# Predict
# To run on GPU if available
boards, target_vs = boards.contiguous().to(args.device), target_vs.contiguous().to(args.device)
# Compute output
_, out_v = self.nnet(boards)
l_v = self.loss_v(target_vs, out_v) # Total loss
# Record loss
v_losses.append(l_v.item())
t.set_postfix(Loss_v=l_v.item())
# Compute gradient and do SGD step
optimizer.zero_grad()
l_v.backward()
optimizer.step()
def predict(self, board):
"""
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
Returns:
v: OthelloNet instance
Data of the OthelloNet class instance above;
"""
# Timing
start = time.time()
# Preparing input
board = torch.FloatTensor(board.astype(np.float64))
board = board.contiguous().to(args.device)
board = board.view(1, self.board_x, self.board_y)
self.nnet.eval()
with torch.no_grad():
_, v = self.nnet(board)
return v.data.cpu().numpy()[0]
def loss_v(self, targets, outputs):
"""
Args:
targets: np.ndarray
Ground Truth variables corresponding to input
outputs: np.ndarray
Predictions of Network
Returns:
MSE Loss averaged across the whole dataset
"""
# Mean squared error (MSE)
return torch.sum((targets - outputs.view(-1)) ** 2) / targets.size()[0]
def save_checkpoint(self, folder='checkpoint', filename='checkpoint.pth.tar'):
save_model_checkpoint(folder, filename, self.nnet)
def load_checkpoint(self, folder='checkpoint', filename='checkpoint.pth.tar'):
load_model_checkpoint(folder, filename, self.nnet, args.device)
class ValueBasedPlayer():
def __init__(self, game, vnet):
"""
Args:
game: OthelloGame instance
Instance of the OthelloGame class
vnet: Value Network instance
Instance of the Value Network class
"""
self.game = game
self.vnet = vnet
def play(self, board):
"""
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
Returns:
candidates: List
Collection of tuples describing action and values of future predicted
states
"""
valids = self.game.getValidMoves(board, 1)
candidates = []
max_num_actions = 4
va = np.where(valids)[0]
va_list = va.tolist()
random.shuffle(va_list)
for a in va_list:
# Return next board state using getNextState() function
nextBoard, _ = self.game.getNextState(board, 1, a)
# Predict the value of next state using value network
value = self.vnet.predict(nextBoard)
# Add the value and the action as a tuple to the candidate lists, note that you might need to change the sign of the value based on the player
candidates += [(-value, a)]
if len(candidates) == max_num_actions:
break
# Sort by the values
candidates.sort()
# Return action associated with highest value
return candidates[0][1]
class PolicyNetwork(NeuralNet):
def __init__(self, game):
"""
Args:
game: OthelloGame
Instance of the OthelloGame class
"""
self.nnet = OthelloNNet(game, args)
self.board_x, self.board_y = game.getBoardSize()
self.action_size = game.getActionSize()
self.nnet.to(args.device)
def train(self, games):
"""
Args:
games: list
List of examples where each example is of form (board, pi, v)
"""
optimizer = optim.Adam(self.nnet.parameters())
for examples in games:
for epoch in range(args.epochs):
print('EPOCH ::: ' + str(epoch + 1))
self.nnet.train()
pi_losses = []
batch_count = int(len(examples) / args.batch_size)
t = tqdm(range(batch_count), desc='Training Policy Network')
for _ in t:
sample_ids = np.random.randint(len(examples), size=args.batch_size)
boards, pis, _ = list(zip(*[examples[i] for i in sample_ids]))
boards = torch.FloatTensor(np.array(boards).astype(np.float64))
target_pis = torch.FloatTensor(np.array(pis))
# Predict
boards, target_pis = boards.contiguous().to(args.device), target_pis.contiguous().to(args.device)
# Compute output
out_pi, _ = self.nnet(boards)
l_pi = self.loss_pi(target_pis, out_pi)
# Record loss
pi_losses.append(l_pi.item())
t.set_postfix(Loss_pi=l_pi.item())
# Compute gradient and do SGD step
optimizer.zero_grad()
l_pi.backward()
optimizer.step()
def predict(self, board):
"""
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
Returns:
Data from the OthelloNet instance
"""
# Timing
start = time.time()
# Preparing input
board = torch.FloatTensor(board.astype(np.float64))
board = board.contiguous().to(args.device)
board = board.view(1, self.board_x, self.board_y)
self.nnet.eval()
with torch.no_grad():
pi,_ = self.nnet(board)
return torch.exp(pi).data.cpu().numpy()[0]
def loss_pi(self, targets, outputs):
"""
Calculates Negative Log Likelihood(NLL) of Targets
Args:
targets: np.ndarray
Ground Truth variables corresponding to input
outputs: np.ndarray
Predictions of Network
Returns:
Negative Log Likelihood calculated as: When training a model, we aspire to
find the minima of a loss function given a set of parameters (in a neural
network, these are the weights and biases).
Sum the loss function to all the correct classes. So, whenever the network
assigns high confidence at the correct class, the NLL is low, but when the
network assigns low confidence at the correct class, the NLL is high.
"""
## For more information, here is a reference that connects the expression to
# the neg-log-prob: https://gombru.github.io/2018/05/23/cross_entropy_loss/
return -torch.sum(targets * outputs) / targets.size()[0]
def save_checkpoint(self, folder='checkpoint', filename='checkpoint.pth.tar'):
save_model_checkpoint(folder, filename, self.nnet)
def load_checkpoint(self, folder='checkpoint', filename='checkpoint.pth.tar'):
load_model_checkpoint(folder, filename, self.nnet, args.device)
class PolicyBasedPlayer():
def __init__(self, game, pnet, greedy=True):
"""
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
pnet: Policy Network instance
Instance of the Policy Network class above
greedy: Boolean
If true, implement greedy approach
Else, implement random sample policy based player
"""
self.game = game
self.pnet = pnet
self.greedy = greedy
def play(self, board):
"""
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
Returns:
a: np.ndarray
If greedy, implement greedy policy player
Else, implement random sample policy based player
"""
valids = self.game.getValidMoves(board, 1)
action_probs = self.pnet.predict(board)
vap = action_probs*valids # Masking invalid moves
sum_vap = np.sum(vap)
if sum_vap > 0:
vap /= sum_vap # Renormalize
else:
# If all valid moves were masked we make all valid moves equally probable
print("All valid moves were masked, doing a workaround.")
vap = vap + valids
vap /= np.sum(vap)
if self.greedy:
# Greedy policy player
a = np.where(vap == np.max(vap))[0][0]
else:
# Sample-based policy player
a = np.random.choice(self.game.getActionSize(), p=vap)
return a
class MonteCarlo():
def __init__(self, game, nnet, args):
"""
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
nnet: OthelloNet instance
Instance of the OthelloNNet class above;
args: dictionary
Instantiates number of iterations and episodes, controls temperature threshold, queue length,
arena, checkpointing, and neural network parameters:
learning-rate: 0.001, dropout: 0.3, epochs: 10, batch_size: 64,
num_channels: 512
"""
self.game = game
self.nnet = nnet
self.args = args
self.Ps = {} # Stores initial policy (returned by neural net)
self.Es = {} # Stores game.getGameEnded ended for board s
# Call this rollout
def simulate(self, canonicalBoard):
"""
Simulate one Monte Carlo rollout
Args:
canonicalBoard: np.ndarray
Canonical Board of size n x n [6x6 in this case]
Returns:
temp_v:
Terminal State
"""
s = self.game.stringRepresentation(canonicalBoard)
init_start_state = s
temp_v = 0
isfirstAction = None
current_player = -1 # opponent's turn (the agent has already taken an action before the simulation)
self.Ps[s], _ = self.nnet.predict(canonicalBoard)
for i in range(self.args.maxDepth): # maxDepth
if s not in self.Es:
self.Es[s] = self.game.getGameEnded(canonicalBoard, 1)
if self.Es[s] != 0:
# Terminal state
temp_v = self.Es[s] * current_player
break
self.Ps[s], v = self.nnet.predict(canonicalBoard)
valids = self.game.getValidMoves(canonicalBoard, 1)
self.Ps[s] = self.Ps[s] * valids # Masking invalid moves
sum_Ps_s = np.sum(self.Ps[s])
if sum_Ps_s > 0:
self.Ps[s] /= sum_Ps_s # Renormalize
else:
# If all valid moves were masked make all valid moves equally probable
# NB! All valid moves may be masked if either your NNet architecture is insufficient or you've get overfitting or something else.
# If you have got dozens or hundreds of these messages you should pay attention to your NNet and/or training process.
log.error("All valid moves were masked, doing a workaround.")
self.Ps[s] = self.Ps[s] + valids
self.Ps[s] /= np.sum(self.Ps[s])
# Choose action according to the policy distribution
a = np.random.choice(self.game.getActionSize(), p=self.Ps[s])
# Find the next state and the next player
next_s, next_player = self.game.getNextState(canonicalBoard, 1, a)
canonicalBoard = self.game.getCanonicalForm(next_s, next_player)
s = self.game.stringRepresentation(next_s)
current_player *= -1
# Initial policy
self.Ps[s], v = self.nnet.predict(canonicalBoard)
temp_v = v.item() * current_player
return temp_v
class MonteCarloBasedPlayer():
"""
Simulate Player based on Monte Carlo Algorithm
"""
def __init__(self, game, nnet, args):
"""
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
nnet: OthelloNet instance
Instance of the OthelloNNet class above;
args: dictionary
Instantiates number of iterations and episodes, controls temperature threshold, queue length,
arena, checkpointing, and neural network parameters:
learning-rate: 0.001, dropout: 0.3, epochs: 10, batch_size: 64,
num_channels: 512
"""
self.game = game
self.nnet = nnet
self.args = args
self.mc = MonteCarlo(game, nnet, args)
self.K = self.args.mc_topk
def play(self, canonicalBoard):
"""
Simulate Play on Canonical Board
Args:
canonicalBoard: np.ndarray
Canonical Board of size n x n [6x6 in this case]
Returns:
best_action: tuple
(avg_value, action) i.e., Average value associated with corresponding action
i.e., Action with the highest topK probability
"""
self.qsa = []
s = self.game.stringRepresentation(canonicalBoard)
Ps, v = self.nnet.predict(canonicalBoard)
valids = self.game.getValidMoves(canonicalBoard, 1)
Ps = Ps * valids # Masking invalid moves
sum_Ps_s = np.sum(Ps)
if sum_Ps_s > 0:
Ps /= sum_Ps_s # Renormalize
else:
# If all valid moves were masked make all valid moves equally probable
# NB! All valid moves may be masked if either your NNet architecture is insufficient or you've get overfitting or something else.
# If you have got dozens or hundreds of these messages you should pay attention to your NNet and/or training process.
log = logging.getLogger(__name__)
log.error("All valid moves were masked, doing a workaround.")
Ps = Ps + valids
Ps /= np.sum(Ps)
num_valid_actions = np.shape(np.nonzero(Ps))[1]
if num_valid_actions < self.K:
top_k_actions = np.argpartition(Ps,-num_valid_actions)[-num_valid_actions:]
else:
top_k_actions = np.argpartition(Ps,-self.K)[-self.K:] # To get actions that belongs to top k prob
for action in top_k_actions:
next_s, next_player = self.game.getNextState(canonicalBoard, 1, action)
next_s = self.game.getCanonicalForm(next_s, next_player)
values = []
# Do some rollouts
for rollout in range(self.args.numMCsims):
value = self.mc.simulate(next_s)
values.append(value)
# Average out values
avg_value = np.mean(values)
self.qsa.append((avg_value, action))
self.qsa.sort(key=lambda a: a[0])
self.qsa.reverse()
best_action = self.qsa[0][1]
return best_action
def getActionProb(self, canonicalBoard, temp=1):
"""
Get probabilities associated with each action
Args:
canonicalBoard: np.ndarray
Canonical Board of size n x n [6x6 in this case]
temp: Integer
Signifies if game is in terminal state
Returns:
action_probs: List
Probability associated with corresponding action
"""
if self.game.getGameEnded(canonicalBoard, 1) != 0:
return np.zeros((self.game.getActionSize()))
else:
action_probs = np.zeros((self.game.getActionSize()))
best_action = self.play(canonicalBoard)
action_probs[best_action] = 1
return action_probs
```

The hyperparameters used throughout the notebook.

```
args = dotdict({
'numIters': 1, # In training, number of iterations = 1000 and num of episodes = 100
'numEps': 1, # Number of complete self-play games to simulate during a new iteration.
'tempThreshold': 15, # To control exploration and exploitation
'updateThreshold': 0.6, # During arena playoff, new neural net will be accepted if threshold or more of games are won.
'maxlenOfQueue': 200, # Number of game examples to train the neural networks.
'numMCTSSims': 15, # Number of games moves for MCTS to simulate.
'arenaCompare': 10, # Number of games to play during arena play to determine if new net will be accepted.
'cpuct': 1,
'maxDepth':5, # Maximum number of rollouts
'numMCsims': 5, # Number of monte carlo simulations
'mc_topk': 3, # Top k actions for monte carlo rollout
'checkpoint': './temp/',
'load_model': False,
'load_folder_file': ('/dev/models/8x100x50','best.pth.tar'),
'numItersForTrainExamplesHistory': 20,
# Define neural network arguments
'lr': 0.001, # learning rate
'dropout': 0.3,
'epochs': 10,
'batch_size': 64,
'device': DEVICE,
'num_channels': 512,
})
```

# Section 1: Plan using Monte Carlo Tree Search (MCTS)¶

*Time estimate: ~30 mins*

**Goal:** Teach students to understand the core ideas behind Monte Carlo Tree Search (MCTS).

## Video 1: Plan with MCTS¶

## Submit your feedback¶

```
# @title Submit your feedback
content_review(f"{feedback_prefix}_Plan_with_MCTS_Video")
```

## Coding Exercise 1: MCTS planner¶

In building the MCTS planner, we will focus on the action selection part, particularly the objective function used. MCTS will use a combination of the current action-value function \(Q\) and the policy prior as follows:

with \(u(s_t, a)=c_{puct} \cdot P(s,a) \cdot \frac{\sqrt{\sum_b N(s,b)}}{1+N(s,a)}\). This effectively implements an Upper Confidence bound applied to Trees (UCT). UCT balances exploration and exploitation by taking the values stored from the MCTS into account. The trade-off is parametrized by \(c_{puct}\).

**Note**: Polynomial Upper Confidence Trees (PUCT) is the technical term for the alorithm below in which we sequentially run MCTS and store/use information from previous runs to explore and find optimal actions).

**Exercise**:

Finish the MCTS planner by using UCT to select actions to build the tree.

Deploy the MCTS planner to build a tree search for a given board position, producing value estimates and action counts for that position.

```
class MCTS():
def __init__(self, game, nnet, args):
"""
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
nnet: OthelloNet instance
Instance of the OthelloNNet class above;
args: dictionary
Instantiates number of iterations and episodes, controls temperature threshold, queue length,
arena, checkpointing, and neural network parameters:
learning-rate: 0.001, dropout: 0.3, epochs: 10, batch_size: 64,
num_channels: 512
"""
self.game = game
self.nnet = nnet
self.args = args
self.Qsa = {} # Stores Q values for s,a (as defined in the paper)
self.Nsa = {} # Stores #times edge s,a was visited
self.Ns = {} # Stores #times board s was visited
self.Ps = {} # Stores initial policy (returned by neural net)
self.Es = {} # Stores game.getGameEnded ended for board s
self.Vs = {} # Stores game.getValidMoves for board s
def search(self, canonicalBoard):
"""
Perform one iteration of MCTS.
It is recursively called till a leaf node is found. The action chosen at
each node is one that has the maximum upper confidence bound.
Once a leaf node is found, the neural network is called to return an
initial policy P and a value v for the state. This value is propagated
up the search path. In case the leaf node is a terminal state, the
outcome is propagated up the search path. The values of Ns, Nsa, Qsa are
updated.
NOTE: the return values are the negative of the value of the current
state. This is done since v is in [-1,1] and if v is the value of a
state for the current player, then its value is -v for the other player.
Args:
canonicalBoard: np.ndarray
Canonical Board of size n x n [6x6 in this case]
Returns:
v: Float
The negative of the value of the current canonicalBoard
"""
s = self.game.stringRepresentation(canonicalBoard)
if s not in self.Es:
self.Es[s] = self.game.getGameEnded(canonicalBoard, 1)
if self.Es[s] != 0:
# Terminal node
return -self.Es[s]
if s not in self.Ps:
# Leaf node
self.Ps[s], v = self.nnet.predict(canonicalBoard)
valids = self.game.getValidMoves(canonicalBoard, 1)
self.Ps[s] = self.Ps[s] * valids # Masking invalid moves
sum_Ps_s = np.sum(self.Ps[s])
if sum_Ps_s > 0:
self.Ps[s] /= sum_Ps_s # Renormalize
else:
# If all valid moves were masked make all valid moves equally probable
# NB! All valid moves may be masked if either your NNet architecture is
# insufficient or you've get overfitting or something else.
# If you have got dozens or hundreds of these messages you should
# pay attention to your NNet and/or training process.
log = logging.getLogger(__name__)
log.error("All valid moves were masked, doing a workaround.")
self.Ps[s] = self.Ps[s] + valids
self.Ps[s] /= np.sum(self.Ps[s])
self.Vs[s] = valids
self.Ns[s] = 0
return -v
valids = self.Vs[s]
cur_best = -float('inf')
best_act = -1
############################################################################
## TODO for students:
# Implement the highest upper confidence bound depending whether we observed
# the state-action pair which is stored in self.Qsa[(s, a)].
# You can find the formula in the slide 52 in video 8 above.
# Fill out function and remove
raise NotImplementedError("Complete the for loop")
############################################################################
# Pick the action with the highest upper confidence bound
for a in range(self.game.getActionSize()):
if valids[a]:
if (s, a) in self.Qsa:
u = ... + ... * ... * math.sqrt(...) / (1 + ...)
else:
u = ... * ... * math.sqrt(... + 1e-8)
if u > cur_best:
cur_best = u
best_act = a
a = best_act
next_s, next_player = self.game.getNextState(canonicalBoard, 1, a)
next_s = self.game.getCanonicalForm(next_s, next_player)
v = self.search(next_s)
if (s, a) in self.Qsa:
self.Qsa[(s, a)] = (self.Nsa[(s, a)] * self.Qsa[(s, a)] + v) / (self.Nsa[(s, a)] + 1)
self.Nsa[(s, a)] += 1
else:
self.Qsa[(s, a)] = v
self.Nsa[(s, a)] = 1
self.Ns[s] += 1
return -v
def getNsa(self):
return self.Nsa
```

### Submit your feedback¶

```
# @title Submit your feedback
content_review(f"{feedback_prefix}_MCTS_Planner_Exercise")
```

# Section 2: Use MCTS to play games¶

*Time estimate: ~10 mins*

**Goal:** Learn how to use the results of MCTS to play games.

**Exercise:**

Plug the MCTS planner into an agent.

Play games against other agents.

Explore the contributions of prior network, value function, number of simulations/time to play and explore/exploit parameters.

## Video 2: Play with MCTS¶

## Submit your feedback¶

```
# @title Submit your feedback
content_review(f"{feedback_prefix}_Play_with_MCTS_Video")
```

## Coding Exercise 2: Agent that uses an MCTS planner¶

Now we can use the MCTS planner and play the game! We will again let the MCTS planner play against players with other policies.

```
# Load MCTS model from the repository
mcts_model_save_name = 'MCTS.pth.tar'
path = "nma_rl_games/alpha-zero/pretrained_models/models/"
```

```
class MonteCarloTreeSearchBasedPlayer():
def __init__(self, game, nnet, args):
"""
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
nnet: OthelloNet instance
Instance of the OthelloNNet class above;
args: dictionary
Instantiates number of iterations and episodes, controls temperature threshold, queue length,
arena, checkpointing, and neural network parameters:
learning-rate: 0.001, dropout: 0.3, epochs: 10, batch_size: 64,
num_channels: 512
"""
self.game = game
self.nnet = nnet
self.args = args
self.mcts = MCTS(game, nnet, args)
def play(self, canonicalBoard, temp=1):
"""
Args:
canonicalBoard: np.ndarray
Canonical Board of size n x n [6x6 in this case]
temp: Integer
Signifies if game is in terminal state
Returns:
List of probabilities for all actions if temp is 0
Best action based on max probability otherwise
"""
for i in range(self.args.numMCTSSims):
##########################################################################
## TODO for students:
# Run MCTS search function.
# Fill out function and remove
raise NotImplementedError("Plug the planner")
##########################################################################
...
s = self.game.stringRepresentation(canonicalBoard)
############################################################################
## TODO for students:
# Call the Nsa function from MCTS class and store it in the self.Nsa
# Fill out function and remove
raise NotImplementedError("Compute Nsa (number of times edge s,a was visited)")
############################################################################
self.Nsa = ...
self.counts = [self.Nsa[(s, a)] if (s, a) in self.Nsa else 0 for a in range(self.game.getActionSize())]
if temp == 0:
bestAs = np.array(np.argwhere(self.counts == np.max(self.counts))).flatten()
bestA = np.random.choice(bestAs)
probs = [0] * len(self.counts)
probs[bestA] = 1
return probs
self.counts = [x ** (1. / temp) for x in self.counts]
self.counts_sum = float(sum(self.counts))
probs = [x / self.counts_sum for x in self.counts]
return np.argmax(probs)
def getActionProb(self, canonicalBoard, temp=1):
"""
Args:
canonicalBoard: np.ndarray
Canonical Board of size n x n [6x6 in this case]
temp: Integer
Signifies if game is in terminal state
Returns:
action_probs: List
Probability associated with corresponding action
"""
action_probs = np.zeros((self.game.getActionSize()))
best_action = self.play(canonicalBoard)
action_probs[best_action] = 1
return action_probs
set_seed(seed=SEED)
game = OthelloGame(6)
rp = RandomPlayer(game).play # All players
num_games = 20 # Games
n1 = NNet(game) # nnet players
n1.load_checkpoint(folder=path, filename=mcts_model_save_name)
args1 = dotdict({'numMCTSSims': 50, 'cpuct':1.0})
## Uncomment below to check your agent!
# print('\n******MCTS player versus random player******')
# mcts1 = MonteCarloTreeSearchBasedPlayer(game, n1, args1)
# n1p = lambda x: np.argmax(mcts1.getActionProb(x, temp=0))
# arena = Arena.Arena(n1p, rp, game, display=OthelloGame.display)
# MCTS_result = arena.playGames(num_games, verbose=False)
# print(f"\nNumber of games won by player1 = {MCTS_result[0]}, "
# f"number of games won by player2 = {MCTS_result[1]}, out of {num_games} games")
# win_rate_player1 = MCTS_result[0]/num_games
# print(f"\nWin rate for player1 over {num_games} games: {round(win_rate_player1*100, 1)}%")
```

```
Random seed 2023 has been set.
```

```
Number of games won by player1 = 19, num of games won by player2 = 1, out of 20 games
Win rate for player1 over 20 games: 95.0%
```

### Load in trained value and policy networks¶

```
# @title Load in trained value and policy networks
model_save_name = 'ValueNetwork.pth.tar'
path = "nma_rl_games/alpha-zero/pretrained_models/models/"
set_seed(seed=SEED)
game = OthelloGame(6)
vnet = ValueNetwork(game)
vnet.load_checkpoint(folder=path, filename=model_save_name)
model_save_name = 'PolicyNetwork.pth.tar'
path = "nma_rl_games/alpha-zero/pretrained_models/models/"
set_seed(seed=SEED)
game = OthelloGame(6)
pnet = PolicyNetwork(game)
pnet.load_checkpoint(folder=path, filename=model_save_name)
# Alternative if the downloading of trained model didn't work (will train the model)
if not os.listdir('nma_rl_games/alpha-zero/pretrained_models/models/'):
path = "nma_rl_games/alpha-zero/pretrained_models/data/"
loaded_games = loadTrainExamples(folder=path, filename='checkpoint_1.pth.tar')
set_seed(seed=SEED)
game = OthelloGame(6)
vnet = ValueNetwork(game)
vnet.train(loaded_games)
set_seed(seed=SEED)
game = OthelloGame(6)
pnet = PolicyNetwork(game)
pnet.train(loaded_games)
```

```
Random seed 2023 has been set.
Random seed 2023 has been set.
```

### MCTS player against Value-based player¶

```
print('\n******MCTS player versus value-based player******')
set_seed(seed=SEED)
vp = ValueBasedPlayer(game, vnet).play # Value-based player
arena = Arena.Arena(n1p, vp, game, display=OthelloGame.display)
MC_result = arena.playGames(num_games, verbose=False)
print(f"\nNumber of games won by player1 = {MC_result[0]}, "
f"number of games won by player2 = {MC_result[1]}, out of {num_games} games")
win_rate_player1 = MC_result[0]/num_games
print(f"\nWin rate for player1 over {num_games} games: {round(win_rate_player1*100, 1)}%")
```

```
******MCTS player versus value-based player******
Random seed 2023 has been set.
```

```
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In[20], line 4
2 set_seed(seed=SEED)
3 vp = ValueBasedPlayer(game, vnet).play # Value-based player
----> 4 arena = Arena.Arena(n1p, vp, game, display=OthelloGame.display)
5 MC_result = arena.playGames(num_games, verbose=False)
7 print(f"\nNumber of games won by player1 = {MC_result[0]}, "
8 f"number of games won by player2 = {MC_result[1]}, out of {num_games} games")
NameError: name 'n1p' is not defined
```

```
Number of games won by player1 = 17, number of games won by player2 = 3, out of 20 games
Win rate for player1 over 20 games: 85.0%
```

### MCTS player against Policy-based player¶

```
print('\n******MCTS player versus policy-based player******')
set_seed(seed=SEED)
pp = PolicyBasedPlayer(game, pnet).play # Policy-based player
arena = Arena.Arena(n1p, pp, game, display=OthelloGame.display)
MC_result = arena.playGames(num_games, verbose=False)
print(f"\nNumber of games won by player1 = {MC_result[0]}, "
f"number of games won by player2 = {MC_result[1]}, out of {num_games} games")
win_rate_player1 = MC_result[0]/num_games
print(f"\nWin rate for player1 over {num_games} games: {round(win_rate_player1*100, 1)}%")
```

```
******MCTS player versus policy-based player******
Random seed 2023 has been set.
```

```
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In[21], line 4
2 set_seed(seed=SEED)
3 pp = PolicyBasedPlayer(game, pnet).play # Policy-based player
----> 4 arena = Arena.Arena(n1p, pp, game, display=OthelloGame.display)
5 MC_result = arena.playGames(num_games, verbose=False)
7 print(f"\nNumber of games won by player1 = {MC_result[0]}, "
8 f"number of games won by player2 = {MC_result[1]}, out of {num_games} games")
NameError: name 'n1p' is not defined
```

```
Number of games won by player1 = 20, number of games won by player2 = 0, out of 20 games
Win rate for player1 over 20 games: 100.0%
```

### MCTS player against Monte-Carlo player¶

```
mc_model_save_name = 'MC.pth.tar'
path = "nma_rl_games/alpha-zero/pretrained_models/models/"
n2 = NNet(game) # nNet players
n2.load_checkpoint(folder=path, filename=mc_model_save_name)
args2 = dotdict({'numMCsims': 10, 'maxRollouts':5, 'maxDepth':5, 'mc_topk': 3})
```

```
print('\n******MCTS player versus MC player******')
set_seed(seed=SEED)
mc = MonteCarloBasedPlayer(game, n2, args2)
n2p = lambda x: np.argmax(mc.getActionProb(x))
arena = Arena.Arena(n1p, n2p, game, display=OthelloGame.display)
MC_result = arena.playGames(num_games, verbose=False)
print(f"\nNumber of games won by player1 = {MC_result[0]}, "
f"number of games won by player2 = {MC_result[1]}, out of {num_games} games")
win_rate_player1 = MC_result[0]/num_games
print(f"\nWin rate for player1 over {num_games} games: {round(win_rate_player1*100, 1)}%")
```

```
******MCTS player versus MC player******
Random seed 2023 has been set.
```

```
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In[23], line 5
3 mc = MonteCarloBasedPlayer(game, n2, args2)
4 n2p = lambda x: np.argmax(mc.getActionProb(x))
----> 5 arena = Arena.Arena(n1p, n2p, game, display=OthelloGame.display)
6 MC_result = arena.playGames(num_games, verbose=False)
8 print(f"\nNumber of games won by player1 = {MC_result[0]}, "
9 f"number of games won by player2 = {MC_result[1]}, out of {num_games} games")
NameError: name 'n1p' is not defined
```

```
Number of games won by player1 = 16, number of games won by player2 = 4, out of 20 games
Win rate for player1 over 20 games: 80.0%
```

#### Submit your feedback¶

```
# @title Submit your feedback
content_review(f"{feedback_prefix}_Play_Games_MCTS_Exercise")
```

# Summary¶

In this tutorial, you have learned about players with Monte Carlo Tree Search planner and compared them to random, value-based, policy-based, and Monte-Carlo players.