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ez21.py
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ez21.py
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import random
from collections import defaultdict
import operator
import copy
from mpl_toolkits import mplot3d
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
from matplotlib import cm
HIT = "hit"
STICK = "stick"
N0 = 100
FEATURES = 36
DECK_MAX = 21
CARD_MAX = 10
CARD_MIN = 1
DEALER_STICK = 17
def draw_card():
n = random.choice([i for i in range(CARD_MIN, CARD_MAX + 1)])
return n if random.choice(["red", "black", "black"]) == "black" else -n
def draw_blacks():
player = abs(draw_card())
dealer = abs(draw_card())
return player, dealer
def is_bust(deck):
return deck > DECK_MAX or deck < CARD_MIN
def easy21(state, action):
player, dealer = state
if action == HIT:
player += draw_card()
return (None, -1) if is_bust(player) else ((player, dealer), 0)
while dealer < DEALER_STICK:
dealer += draw_card()
if is_bust(dealer):
return None, 1
return None, int(dealer < player) - int(dealer > player)
def mse(Q_a, Q_b):
err = 0
n = 0
for player in range(CARD_MIN, DECK_MAX + 1):
for dealer in range(CARD_MIN, CARD_MAX + 1):
state = player, dealer
for action in HIT, STICK:
err += (Q_a(state, action) - Q_b(state, action))**2
n += 1
return err/n
def epsilon_policy(actions, e):
m = len(actions)
best = max((q, a) for a, q in actions)[1]
weighted = [(a, (e/m + 1 - e) if a == best else e/m) for a, q in actions]
tip = random.random()
mass = 0
for a, w in weighted:
mass += w
if tip <= mass:
return a
assert False
def mc(episodes):
Q = defaultdict(lambda:{HIT:0, STICK:0})
N = defaultdict(lambda:defaultdict(int))
for _ in range(episodes):
state = draw_blacks()
episode = []
reward = 0
while state is not None:
epsilon = N0/(N0 + sum(N[state].values()))
action = epsilon_policy(Q[state].items(), epsilon)
episode.append((state, action))
state, reward = easy21(state, action)
for s, a in episode:
N[s][a] += 1
q = Q[s][a]
alf = 1/N[s][a]
Q[s][a] = q + alf*(reward - q)
return Q
def td(episodes, lmbda, Q_ref):
Q = defaultdict(lambda:{HIT:0, STICK:0})
N = defaultdict(lambda:defaultdict(int))
mses = []
for _ in range(episodes):
E = defaultdict(lambda:defaultdict(int))
state = draw_blacks()
action = epsilon_policy(Q[state].items(), 1.0)
while state is not None:
E[state][action] += 1
N[state][action] += 1
q = Q[state][action]
state, reward = easy21(state, action)
action = epsilon_policy(Q[state].items(), N0/(N0 + sum(N[state].values())))
err = reward + Q[state][action] - q
for s in E:
for a in E[s]:
alf = 1/N[s][a]
Q[s][a] += alf*err*E[s][a]
E[s][a] *= lmbda
mses.append(mse(lambda s, a: Q_ref[s][a], lambda s, a: Q[s][a]))
return Q, mses
def feature(state, action):
DEAL = [(1, 4), (4, 7), (7, 10)]
PLAY = [(1, 6), (4, 9), (7, 12), (10, 15), (13, 18), (16, 21)]
ACT = [HIT, STICK]
player, dealer = state
def indicator(d, p, a):
if action != a:
return 0
if dealer < d[0] or dealer > d[1]:
return 0
if player < p[0] or player > p[1]:
return 0
return 1
return [indicator(d, p, a) for d in DEAL for p in PLAY for a in ACT]
def qfa(state, action, w):
return sum(map(operator.mul, feature(state, action), w)) if state is not None else 0
def fa(episodes, lmbda, Q_ref):
W = [0]*FEATURES
ALF = 0.01
ETA = 0.05
actions = lambda state: [(HIT, qfa(state, HIT, W)), (STICK, qfa(state, STICK, W))]
mses = []
for _ in range(episodes):
state = draw_blacks()
action = epsilon_policy(actions(state), ETA)
E = [0]*FEATURES
while state is not None:
X = feature(state, action)
q = qfa(state, action, W)
state, reward = easy21(state, action)
action = epsilon_policy(actions(state), ETA)
err = reward + qfa(state, action, W) - q
E = [lmbda*e + x for x, e in zip(X, E)]
W = [w + ALF*err*e for w, e in zip(W, E)]
mses.append(mse(lambda s, a: Q_ref[s][a], lambda s, a: qfa(s, a, W)))
return W, mses
def eye_candy(Q_mc, Q_td, Q_fa):
td_lmbda = lambda t: t[1]
td_mses = lambda t: t[0][1]
fig = plt.figure(num="Easy21 eyecandy")
gs = fig.add_gridspec(2, 2)
ax = fig.add_subplot(gs[:, 0], projection='3d')
ax.set_title("GLIE-MC state-value ({} episodes)".format(Q_MC_EPS))
ax.set_xlabel("Player sum")
ax.set_ylabel("Dealer showing")
ax.set_zlabel("V")
ax.xaxis.set_major_locator(ticker.MultipleLocator(5))
ax.yaxis.set_major_locator(ticker.MultipleLocator(5))
ax.zaxis.set_major_locator(ticker.MultipleLocator(1))
def v(x, y):
return max((q, a) for a, q in Q_mc[(x, y)].items())[0]
player, dealer, reward = zip(
*((x, y, v(x, y)) for x in range(CARD_MIN, DECK_MAX + 1) for y in range(CARD_MIN, CARD_MAX + 1)))
ax.plot_trisurf(player, dealer, reward, cmap=cm.coolwarm)
ax = fig.add_subplot(gs[0, 1])
ax.set_title("TD(λ) ↔ GLIE-MC mean squared error ({} episodes)".format(Q_TD_EPS))
ax.plot([td_lmbda(qs) for qs in Q_td], [td_mses(qs)[-1] for qs in Q_td], label = "TD")
ax.plot([td_lmbda(qs) for qs in Q_fa], [td_mses(qs)[-1] for qs in Q_fa], label = "TD-FA")
ax.set_xlabel("λ")
ax.set_ylabel("MSE")
plt.legend()
ax = fig.add_subplot(gs[1, 1])
ax.set_title("TD(λ) ↔ GLIE-MC mean squared error per episode".format(Q_TD_EPS))
ax.plot([mse for mse in td_mses(Q_td[0])], label="TD({})".format(0))
ax.plot([mse for mse in td_mses(Q_td[-1])], label="TD({})".format(1))
ax.plot([mse for mse in td_mses(Q_fa[0])], label="TD-FA({})".format(0))
ax.plot([mse for mse in td_mses(Q_fa[-1])], label="TD-FA({})".format(1))
ax.set_xlabel("Episode")
ax.set_ylabel("MSE")
plt.legend()
plt.show()
if __name__ == "__main__":
Q_MC_EPS = int(1e6)
Q_TD_EPS = int(1e3)
LAMBDAS = (0.0, 0.2, 0.4, 0.6, 0.8, 1.0)
print("Learning MC agent...")
Q_mc = mc(episodes=Q_MC_EPS)
print("Learning TD(λ) agents...")
Q_td = [(td(episodes=Q_TD_EPS, lmbda=lmbda, Q_ref=Q_mc), lmbda) for lmbda in LAMBDAS]
print("Learning TD-FA(λ) agents...")
Q_fa = [(fa(episodes=Q_TD_EPS, lmbda=lmbda, Q_ref=Q_mc), lmbda) for lmbda in LAMBDAS]
eye_candy(Q_mc, Q_td, Q_fa)