我刚刚开始学习Q学习，并且我一直可以使用表格方法来获得不错的结果。我发现使用Q学习非常有趣的一款游戏是Blackjack，这似乎是一个完美的MDP类型问题。
我一直想将其扩展到使用神经网络作为函数逼近器，但是我一点也没有运气。该方法是计算给定状态下每个动作的期望值，然后选择最佳动作，而随机选择某些东西的可能性很小（ε贪婪）。什么都没收敛，它学到了愚蠢的Q值，甚至在甲板上只有5张卡片时也无法弄清楚怎么玩。
在花了几个小时并调整了超参数以及我能想到的所有其他东西之后，我真的陷入了困境。我觉得我一定在Q学习中犯了一个根本看不到的错误。我的代码如下：
import gym
from gym import spaces
from gym.utils import seeding
import numpy as np
import random
import pandas as pd
import sklearn
import math
import itertools
import tensorflow as tf
from matplotlib import pyplot as plt
############################ START BLACKJACK CLASS ############################
class Blackjack(gym.Env):
"""Simple Blackjack environment"""
def __init__(self, natural=False):
self.action_space = spaces.Discrete(2)
self._seed()
# Start the first game
self.prevState = self.reset()
def _seed(self, seed=None):
self.np_random, seed = seeding.np_random(seed)
return seed
# Returns a tuple of the form (str, int) where str is "H" or "S" depending on if its a
# Soft or Hard hand and int is the sum total of the cards in hand
# Example output: ("H", 15)
def getTotal(cards):
running_total = 0
softs = 0
for c in cards:
running_total += c
if c == 11:
softs += 1
if running_total > 21 and softs > 0:
softs -= 1
running_total -= 10
return "H" if softs == 0 else "S", running_total
def drawCard():
# Draw a random card from the deck with replacement. 11 is ACE
# I've set it to always draw a 5. In theory this should be very easy to learn and
# The only possible states, and their correct Q values should be:
# Q[10_5, stand] = -1 Q[10_5, hit] = 0
# Q[15_5, stand] = -1 Q[15_5, hit] = 0
# Q[20_5, stand] = 0 Q[20_5, hit] = -1
# The network can't even learn this!
return 5
return random.choice([5,6])
return random.choice([2,3,4,5,6,7,8,9,10,10,10,10,11])
def isBlackjack(cards):
return sum(cards) == 21 and len(cards) == 2
def getState(self):
# Defines the state of the current game
pstate, ptotal = Blackjack.getTotal(self.player)
dstate, dtotal = Blackjack.getTotal(self.dealer)
return "{}_{}".format("BJ" if Blackjack.isBlackjack(self.player) else pstate+str(ptotal), dtotal)
def reset(self):
# Resets the game - Dealer is dealt 1 card, player is dealt 2 cards
# The player and dealer are represented by an array of numbers, which are the cards they were
# dealt in order
self.soft = "H"
self.dealer = [Blackjack.drawCard()]
self.player = [Blackjack.drawCard() for _ in range(2)]
pstate, ptotal = Blackjack.getTotal(self.player)
dstate, dtotal = Blackjack.getTotal(self.dealer)
# Returns the current state of the game
return self.getState()
def step(self, action):
assert self.action_space.contains(action)
# Action should be 0 or 1.
# If standing, the dealer will draw all cards until they are >= 17. This will end the episode
# If hitting, a new card will be added to the player, if over 21, reward is -1 and episode ends
# Stand
if action == 0:
pstate, ptotal = Blackjack.getTotal(self.player)
dstate, dtotal = Blackjack.getTotal(self.dealer)
while dtotal < 17:
self.dealer.append(Blackjack.drawCard())
dstate, dtotal = Blackjack.getTotal(self.dealer)
# if player won with blackjack
if Blackjack.isBlackjack(self.player) and not Blackjack.isBlackjack(self.dealer):
rw = 1.5
# if dealer bust or if the player has a higher number than dealer
elif dtotal > 21 or (dtotal <= 21 and ptotal > dtotal and ptotal <= 21):
rw = 1
# if theres a draw
elif dtotal == ptotal:
rw = 0
# player loses in all other situations
else:
rw = -1
state = self.getState()
# Returns (current_state, reward, boolean_true_if_episode_ended, empty_dict)
return state, rw, True, {}
# Hit
else:
# Player draws another card
self.player.append(Blackjack.drawCard())
# Calc new total for player
pstate, ptotal = Blackjack.getTotal(self.player)
state = self.getState()
# Player went bust and episode is over
if ptotal > 21:
return state, -1, True, {}
# Player is still in the game, but no observed reward yet
else:
return state, 0, False, {}
############################ END BLACKJACK CLASS ############################
# Converts a player or dealers hand into an array of 10 cards
# that keep track of how many of each card are held. The card is identified
# through its index:
# Index: 0 1 2 3 4 5 6 7 9 10
# Card: 2 3 4 5 6 7 8 9 T A
def cardsToX(cards):
ans = [0] * 12
for c in cards:
ans[c] += 1
ans = ans[2:12]
return ans
# Easy way to convert Q values into weighted decision probabilities via softmax.
# This is useful if we probablistically choose actions based on their values rather
# than always choosing the max.
# eg Q[s,0] = -1
# Q[s,1] = -2
# softmax([-1,-2]) = [0.731, 0.269] --> 73% chance of standing, 27% chance of hitting
def softmax(x):
"""Compute softmax values for each sets of scores in x."""
e_x = np.exp(x - np.max(x))
return e_x / e_x.sum()
plt.ion()
# Define number of Neurons per layer
K = 20 # Layer 1
L = 10 # Layer 2
M = 5 # Layer 2
N_IN = 20 # 10 unique cards for player, and 10 for dealer = 20 total inputs
N_OUT = 2
SDEV = 0.000001
# Input / Output place holders
X = tf.placeholder(tf.float32, [None, N_IN])
X = tf.reshape(X, [-1, N_IN])
# This will be the observed reward + decay_factor * max(Q[s+1, 0], Q[s+1, 1]).
# This should be an estimate of the 'correct' Q-value with the ony caveat being that
# the Q-value of the next state is a biased estimate of the true value.
Q_TARGET = tf.placeholder(tf.float32, [None, N_OUT])
# LAYER 1
W1 = tf.Variable(tf.random_normal([N_IN, K], stddev = SDEV))
B1 = tf.Variable(tf.random_normal([K], stddev = SDEV))
# LAYER 2
W2 = tf.Variable(tf.random_normal([K, L], stddev = SDEV))
B2 = tf.Variable(tf.random_normal([L], stddev = SDEV))
# LAYER 3
W3 = tf.Variable(tf.random_normal([L, M], stddev = SDEV))
B3 = tf.Variable(tf.random_normal([M], stddev = SDEV))
# LAYER 4
W4 = tf.Variable(tf.random_normal([M, N_OUT], stddev = SDEV))
B4 = tf.Variable(tf.random_normal([N_OUT], stddev = SDEV))
H1 = tf.nn.relu(tf.matmul(X, W1) + B1)
H2 = tf.nn.relu(tf.matmul(H1, W2) + B2)
H3 = tf.nn.relu(tf.matmul(H2, W3) + B3)
# The predicted Q value, as determined by our network (function approximator)
# outputs expected reward for standing and hitting in the form [stand, hit] given the
# current game state
Q_PREDICT = (tf.matmul(H3, W4) + B4)
# Is this correct? The Q_TARGET should be a combination of the real reward and the discounted
# future rewards of the future state as predicted by the network. Q_TARGET - Q_PREDICT should be
# the error in prediction, which we want to minimise. Does this loss function work to help the network
# converge to the true Q values with sufficient training?
loss_func = tf.reduce_sum(tf.square(Q_TARGET - Q_PREDICT))
# This are some placeholder values to enable manually set decayed learning rates. For now, use
# the same learning rate all the time.
LR_START = 0.001
#LR_END = 0.000002
#LR_DECAY = 0.999
# Optimizer
LEARNING_RATE = tf.Variable(LR_START, trainable=False)
optimizer = tf.train.GradientDescentOptimizer(LEARNING_RATE)#(LEARNING_RATE)
train_step = optimizer.minimize(loss_func)
init = tf.global_variables_initializer()
sess = tf.Session()
sess.run(init)
# Initialise the game environment
game = Blackjack()
# Number of episodes (games) to play
num_eps = 10000000
# probability of picking a random action. This decays over time
epsilon = 0.1
# discount factor. For blackjack, future rewards are equally important as immediate rewards.
discount = 1.0
all_rewards = [] # Holds all observed rewards. The rolling mean of rewards should improve as the network learns
all_Qs = [] # Holds all predicted Q values. Useful as a sanity check once the network is trained
all_losses = [] # Holds all the (Q_TARGET - Q_PREDICTED) values. The rolling mean of this should decrease
hands = [] # Holds a summary of all hands played. (game_state, Q[stand], Q[hit], action_taken)
# boolean switch to use the highest action value instead of a stochastic decision via softmax on Q-values
use_argmax = True
# Begin generating episodes
for ep in range(num_eps):
game.reset()
# Keep looping until the episode is not over
while True:
# x is the array of 20 numbers. The player cards, and the dealer cards.
x = cardsToX(game.player) + cardsToX(game.dealer)
# Q1 refers to the predicted Q-values before any action was taken
Q1 = sess.run(Q_PREDICT, feed_dict = {X : np.reshape( np.array(x), (-1, N_IN) )})
all_Qs.append(Q1)
if use_argmax:
# action is selected to be the one with the highest Q-value
act = np.argmax(Q1)
else:
# action is a weighted selection based on predicted Q_values
act = np.random.choice(range(N_OUT), p = softmax(Q1)[0])
if random.random() < epsilon:
# action is selected randomly
act = random.randint(0, N_OUT-1)
# Get game state before action is taken
game_state = game.getState()
# Take action! Observe new state, reward, and if the game is over
game_state_new, reward, done, _ = game.step(act)
hands.append( (game_state, Q1[0][0], Q1[0][1], act, reward) )
# Store the new state vector to feed into our network.
# x2 corresponds to the x vector observed in state s+1
x2 = cardsToX(game.player) + cardsToX(game.dealer)
# Q2 refers to the predicted Q-values in the new s+1 state. This is used for the 'SARSA' update.
Q2 = sess.run(Q_PREDICT,feed_dict = {X : np.reshape( np.array(x2), (-1, N_IN) )})
# Store the maximum Q-value in this new state. This should be the expected reward from this new state
maxQ2 = np.max(Q2)
# targetQ is the same as our predicted one initially. The index of the action we took will be
# updated to be [observed reward] + [discount_factor] * max(Q[s+1])
targetQ = np.copy(Q1)
# If the game is done, then there is no future state
if done:
targetQ[0,act] = reward
all_rewards.append(reward)
else:
targetQ[0,act] = reward + discount * maxQ2
# Perform one gradient descent update, filling the placeholder value for Q_TARGET with targetQ.
# The returned loss is the difference between the predicted Q-values and the targetQ we just calculated
loss, _, _ = sess.run([loss_func, Q_PREDICT, train_step],
feed_dict = {X : np.reshape( np.array(x), (-1, N_IN) ),
Q_TARGET : targetQ}
)
all_losses.append(loss)
# Every 1000 episodes, show how the q-values moved after the gradient descent update
if ep % 1000 == 0 and ep > 0:
Q_NEW = sess.run(Q_PREDICT, feed_dict = {X : np.reshape( np.array(x), (-1, N_IN) ),
Q_TARGET : targetQ})
#print(game_state, targetQ[0], Q1[0], (Q_NEW-Q1)[0], loss, ep, epsilon, act)
rolling_window = 1000
rolling_mean = np.mean( all_rewards[-rolling_window:] )
rolling_loss = np.mean( all_losses[-rolling_window:] )
print("Rolling mean reward: {:<10.4f}, Rolling loss: {:<10.4f}".format(rolling_mean, rolling_loss))
if done:
# Reduce chance of random action as we train the model.
epsilon = 2/((ep/500) + 10)
epsilon = max(0.02, epsilon)
# rolling mean of rewards should increase over time!
if ep % 1000 == 0 and ep > 0:
pass# Show the rolling mean of all losses. This should decrease over time!
#plt.plot(pd.rolling_mean(pd.Series(all_losses), 5000))
#plt.pause(0.02)
#plt.show()
break
print(cardsToX(game.player))
print(game.dealer)
有什么想法吗？我被困住了：（