def Q_learning(gamma, numRounds, alpha):
states = darts.get_states()
actions = darts.get_actions()
Q = {}
for s in states:
Q[s] = [0] * len(actions)
totaliter = 0
for i in range(numRounds):
s = throw.START_SCORE
numiterations = 0
while s > 0:
randAction = random.randint(0, len(actions) - 1)
maxAction = Q[s].index(max(Q[s]))
a = ex_strategy_one(numRounds, i, randAction, maxAction)
#a = ex_strategy_two(numRounds, i, Q, len(actions), s)
action = actions[a]
s_prime = s - throw.location_to_score(action)
if s_prime < 0:
s_prime = s
maxQ = 0.0
for a_prime in range(len(actions)):
if Q[s_prime][a_prime] > maxQ:
maxQ = Q[s_prime][a_prime]
Q[s][a] = Q[s][a] + alpha * (darts.R(s, actions[a]) + (gamma * maxQ) - Q[s][a])
s = s_prime
numiterations += 1
totaliter += numiterations
print "Average number of throws: " + str(float(totaliter) / numRounds)
def Q_learning(gamma, numRounds, alpha):
states = darts.get_states()
actions = darts.get_actions()
currentRound = 0
Q = {}
for s in states:
Q[s] = [0] * len(actions)
for i in range(numRounds):
s = throw.START_SCORE
numiterations = 0
while s > 0:
randAction = random.randint(0, len(actions))
maxAction = Q[score].index(max(Q[s]))
#a = ex_strategy_one(Q, randAction, maxAction)
a = ex_strategy_two(numRounds, currentRound, Q, len(actions), s)
action = actions[a]
s_prime = s - throw.location_to_score(action)
if s_prime < 0:
s_prime = s
maxQ = 0.0
for a_prime in range(len(actions)):
if Q[s_prime][a_prime] > maxQ:
maxQ = Q[s_prime][a_prime]
Q[s][a] = Q[s][a] + alpha * (darts.R(s, actions[a]) + (gamma * maxQ) - Q[s][a])
s = s_prime
currentRound += 1
def Q_learning(gamma, numRounds, alpha):
states = darts.get_states()
actions = darts.get_actions()
Q = {}
for s in states:
Q[s] = [0] * len(actions)
for i in range(numRounds):
s = throw.START_SCORE
numiterations = 0
while s > 0:
randAction = random.randint(0, len(actions))
maxAction = Q[score].index(max(Q[s]))
#a = ex_strategy_one(Q, randAction, maxAction)
a = ex_strategy_two(Q, randAction, maxAction)
action = actions[a]
s_prime = s - throw.location_to_score(action)
if s_prime < 0:
s_prime = s
maxQ = 0.0
for a_prime in range(len(actions)):
if Q[s_prime][a_prime] > maxQ:
maxQ = Q[s_prime][a_prime]
Q[s][a] = Q[s][a] + alpha * (darts.R(s, actions[a]) + (gamma * maxQ) - Q[s][a])
s = s_prime
def infiniteValueIteration(gamma):
# takes a discount factor gamma and convergence cutoff epislon
# returns
V = {}
Q = {}
V_prime = {}
states = darts.get_states()
actions = darts.get_actions()
notConverged = True
# intialize value of each state to 0
for s in states:
V[s] = 0
Q[s] = {}
# until convergence is reached
while notConverged:
# store values from previous iteration
for s in states:
V_prime[s] = V[s]
# update Q, pi, and V
for s in states:
for a in actions:
# given current state and action, sum product of T and V over all states
summand = 0
for s_prime in states:
summand += T(a, s, s_prime)*V_prime[s_prime]
# update Q
Q[s][a] = darts.R(s, a) + gamma*summand
# given current state, store the action that maximizes V in pi and the corresponding value in V
PI[s] = actions[0]
V[s] = Q[s][PI[s]]
for a in actions:
if V[s] <= Q[s][a]:
V[s] = Q[s][a]
PI[s] = a
notConverged = False
for s in states:
if abs(V[s] - V_prime[s]) > EPSILON:
notConverged = True
# Print table of optimal policy, for writeup purposes
def print_table():
for s in [9, 8, 7, 6, 5, 4, 3, 2, 1]:
EPs = map(lambda a : EPoints(a, s), actions)
print " " + str(s) + " & (" + str(PI[s].wedge) + ", " + str(PI[s].ring) + ") & " + str(EPoints(PI[s], s)) + " & [" + str(min(EPs)) + ", " + str(max(EPs)) + "] & " + str(s - EPoints(PI[s], s)) + " \\\\"
print V
print_table()
def start_game(gamma, learning_rate, num_games):
actions = darts.get_actions()
states = darts.get_states()
Q_learning(gamma, learning_rate, num_games)
a = q_values[throw.START_SCORE].index(max(q_values[throw.START_SCORE]))
return actions[a]
def start_game():
global states, actions, Q
states = darts.get_states()
actions = darts.get_actions()
for s in states:
Q[s] = {}
for a in range(len(actions)):
Q[s][a] = 0
return throw.location(throw.INNER_RING, throw.NUM_WEDGES)
def infiniteValueIteration(gamma):
# takes a discount factor gamma and convergence cutoff epislon
# returns
V = {}
Q = {}
V_prime = {}
states = darts.get_states()
actions = darts.get_actions()
notConverged = True
# intialize value of each state to 0
for s in states:
V[s] = 0
Q[s] = {}
# until convergence is reached
while notConverged:
# store values from previous iteration
for s in states:
V_prime[s] = V[s]
# update Q, pi, and V
for s in states:
for a in actions:
# given current state and action, sum product of T and V over all states
summand = 0
for s_prime in states:
summand += T(a, s, s_prime)*V_prime[s_prime]
# update Q
Q[s][a] = darts.R(s, a) + gamma*summand
# given current state, store the action that maximizes V in pi and the corresponding value in V
PI[s] = actions[0]
V[s] = Q[s][PI[s]]
for a in actions:
if V[s] <= Q[s][a]:
V[s] = Q[s][a]
PI[s] = a
notConverged = False
for s in states:
if abs(V[s] - V_prime[s]) > EPSILON:
notConverged = True
# test_score = 9
# test_action = throw.location(throw.OUTER_RING,4)
# print T(test_action,test_score,5)
def modelbased_value_iteration(gamma, T_matrix, pi_star, V_n={}):
V = {}
V[0] = {}
V[1] = {}
converging = 0
num_iterations = 0
Q = {}
# Get all possible actions
actions = darts.get_actions()
states = darts.get_states()
# initialize v
if len(V_n) == 0:
for s in states:
V[0][s] = 0
V[1][s] = 0
else:
for s in states:
V[0][s] = V_n[s]
V[1][s] = V_n[s]
# iterate until all state values (v[s]) converge
while not(converging):
num_iterations += 1
for s in states:
for a in range(len(actions)):
# find the value of each action, given state s
Q[a] = darts.R(s, actions[a])
for s_prime in states:
Q[a] += gamma * T_matrix[s][s_prime][a] * V[0][s_prime]
# find the action that maximizes Q and the maximum value of Q
if a == 0 or (Q[a] >= V[1][s]):
pi_star[s] = a
V[1][s] = Q[a]
# values of v for iteration k become the values of v for iteration k-1
converging = True
for s in states:
# check for one component that does not converge
if EPSILON_VI < abs(V[0][s] - V[1][s]):
converging = False
V[0][s] = V[1][s]
return T_matrix, pi_star, Q, V[1]
def infiniteValueIteration(gamma):
# takes a discount factor gamma and convergence cutoff epislon
# returns
V = {}
Q = {}
V_prime = {}
states = darts.get_states()
actions = darts.get_actions()
notConverged = True
# intialize value of each state to 0
for s in states:
V[s] = 0
Q[s] = {}
# until convergence is reached
while notConverged:
# store values from previous iteration
for s in states:
V_prime[s] = V[s]
# update Q, pi, and V
for s in states:
for a in actions:
# given current state and action, sum product of T and V over all states
summand = 0
for s_prime in states:
summand += T(a, s, s_prime) * V_prime[s_prime]
# update Q
Q[s][a] = darts.R(s, a) + gamma * summand
# given current state, store the action that maximizes V in pi and the corresponding value in V
PI[s] = actions[0]
# bug fix from piazza post 283
V[s] = Q[s][PI[s]]
for a in actions:
if V[s] <= Q[s][a]:
V[s] = Q[s][a]
PI[s] = a
notConverged = False
for s in states:
if abs(V[s] - V_prime[s]) > EPSILON:
notConverged = True
def start_game(gamma):
global GAMMA
global Q
global actions
GAMMA = gamma
states = darts.get_states()
actions = darts.get_actions()
for s in states:
Q[s] = {}
for a in actions:
Q[s][a]=100
return choice(actions)#(throw.location(throw.INNER_RING, throw.NUM_WEDGES))
def start_game():
global actions, s_old, a_old
if actions == None:
print "GAMMA: ", darts.GAMMA
print "LEARNING_RATE: ", LEARNING_RATE
print "strategy: ", darts.strategy
actions = darts.get_actions()
for s in darts.get_states():
Q[s] = {}
for a in actions:
Q[s][a] = 0.
s_old = throw.START_SCORE
a_old = actions[-15]
return a_old
def modelfree(alpha, gamma, num_games):
# store all actions (targets on dartboard) in actions array
actions = darts.get_actions()
states = darts.get_states()
pi_star = {}
g = 0
num_iterations = 0
Q = [[]] * len(states)
# Initialize all arrays to 0 except the policy, which should be assigned a random action for each state.
for s in states:
pi_star[s] = random.randint(0, len(actions)-1)
Q[s] = [0] * len(actions)
# play num_games games
for g in range(1, num_games + 1):
#print str(g) + "/" + str(num_games)
# run a single game
s = throw.START_SCORE
while s > 0:
num_iterations += 1
# The following two statements implement two exploration-exploitation
# strategies. Comment out the strategy that you wish not to use.
a = ex_strategy_one(num_iterations, actions, pi_star, s)
#a = ex_strategy_two(num_iterations, Q, actions, s, pi_star)
action = actions[a]
# Get result of throw from dart thrower; update score if necessary
loc = throw.throw(action)
s_prime = int(s - throw.location_to_score(loc))
if s_prime < 0:
s_prime = s
max_Q = max(Q[s_prime])
Q[s][a] += alpha * (darts.R(s, actions[a]) + gamma * max(Q[s_prime]) - Q[s][a])
pi_star[s] = Q[s].index(max(Q[s]))
# Next state becomes current state
s = s_prime
print "Average turns = ", float(num_iterations)/float(num_games)
def start_game():
global last_score, last_action, actions
if last_score is None:
actions = darts.get_actions()
for s in darts.get_states():
Q[s] = {}
for a in actions:
Q[s][a] = 0.
last_score = throw.START_SCORE
print >> sys.stderr, 'start'
last_action = throw.location(throw.INNER_RING, throw.NUM_WEDGES)
print >> sys.stderr, last_action
return last_action
def start_game():
global last_score, last_action, actions
if last_score is None:
actions = darts.get_actions()
for s in darts.get_states():
Q[s] = {}
for a in actions:
Q[s][a] = 0.
last_score = throw.START_SCORE
print >>sys.stderr, 'start'
last_action = throw.location(throw.INNER_RING, throw.NUM_WEDGES)
print >>sys.stderr, last_action
return last_action
def modelbased_value_iteration(gamma, T_matrix, pi_star):
V = {}
V[0] = {}
V[1] = {}
converging = 0
num_iterations = 0
Q = {}
# Get all possible actions
actions = darts.get_actions()
states = darts.get_states()
# initialize v
for s in states:
V[0][s] = 0
V[1][s] = 0
# iterate until all state values (v[s]) converge
while not (converging):
num_iterations += 1
for s in states:
for a in range(len(actions)):
# find the value of each action, given state s
Q[a] = darts.R(s, actions[a])
for s_prime in states:
Q[a] += gamma * T_matrix[s][s_prime][a] * V[0][s_prime]
# find the action that maximizes Q and the maximum value of Q
if a == 0 or (Q[a] >= V[1][s]):
pi_star[s] = a
V[1][s] = Q[a]
# values of v for iteration k become the values of v for iteration k-1
converging = True
for s in states:
# check for one component that does not converge
if EPSILON_VI < abs(V[0][s] - V[1][s]):
converging = False
V[0][s] = V[1][s]
return T_matrix, pi_star
def Q_learning(gamma, learning_rate, num_games):
g = 0
num_iterations = 0
# store all actions (targets on dartboard) in actions array
# actions = darts.get_actions()
# states = darts.get_states()
actions = darts.get_actions()
states = darts.get_states()
# Initialize all arrays to 0 except the policy, which should be assigned a random action for each state.
for s in states:
list_a = []
for a in range(len(actions)):
list_a.append(0)
q_values.append(list_a)
for g in range(1, num_games + 1):
# run a single game
s = throw.START_SCORE
while s > 0:
num_iterations += 1
# which strategy to use
#to_explore = ex_strategy_one(num_iterations)
to_explore = ex_strategy_two(num_iterations)
if to_explore:
# explore
a = random.randint(0, len(actions)-1)
action = actions[a]
else:
# exploit
a = q_values[s].index(max(q_values[s]))
action = actions[a]
def start_game():
global Q, states, actions, cur_s, last_a, throws
cur_s = throw.START_SCORE
throws = 1
# only initialize states, actions, and Q once
if states == None:
states = darts.get_states()
if actions == None:
actions = darts.get_actions()
if len(Q) == 0:
for s in states:
Q[s] = {}
for a in actions:
Q[s][a] = 0.0
# start by returning uniform random action
last_a = choice(actions)
return last_a
def start_game():
global Q, states, actions, cur_s, last_a, throws
cur_s = throw.START_SCORE
throws = 1
# only initialize states, actions, and Q once
if states == None:
states = darts.get_states()
if actions == None:
actions = darts.get_actions()
if len(Q) == 0:
for s in states:
Q[s] = {}
for a in actions:
Q[s][a] = 0.0
# start by returning uniform random action
last_a = choice(actions)
return last_a
def test_get_states(self):
x = throw.START_SCORE
self.assertTrue(x / 2 < len(darts.get_states()))
self.assertTrue(0.75 * x < len(darts.get_states()))
def modelfree(gamma, learning_rate, num_games, strategy_idx):
actions = darts.get_actions()
states = darts.get_states()
pi_star = {}
g = 0
num_actions = {}
num_transitions = {}
T_matrix = {}
Q = {}
num_iterations = 0
# Initialize all arrays to 0 except the policy, which should be assigned a random action for each state.
for s in states:
pi_star[s] = random.randint(0, len(actions)-1)
num_actions[s] = {}
Q[s] = {}
num_transitions[s] = {}
T_matrix[s] = {}
for a in range(len(actions)):
Q[s][a] = 1.0
num_actions[s][a] = 0
for s_prime in states:
num_transitions[s][s_prime] = {}
T_matrix[s][s_prime] = {}
for a in range(len(actions)):
num_transitions[s][s_prime][a] = 0
T_matrix[s][s_prime][a] = 0
# play num_games games, updating policy after every EPOCH_SIZE number of throws
for g in range(1, num_games + 1):
# run a single game
s = throw.START_SCORE
throws = 0
explores = 0
exploits = 0
while s > 0:
num_iterations += 1
throws += 1
# The following two statements implement two exploration-exploitation
# strategies. Comment out the strategy that you wish not to use.
if(strategy_idx==1):
to_explore = ex_strategy_one(s,g)
else:
to_explore = ex_strategy_two(s,g)
if to_explore:
# explore
a = random.randint(0, len(actions)-1)
action = actions[a]
explores += 1
else:
# exploit
a = bestAction(Q, s)
action = actions[a]
exploits += 1
#print "a", a, "action",action
# Get result of throw from dart thrower; update score if necessary
loc = throw.throw(action)
delta = throw.location_to_score(loc)
s_prime = s - delta
if s_prime < 0:
s_prime = s
# Update experience:
# increment number of times this action was taken in this state;
# increment number of times we moved from this state to next state on this action.
num_actions[s][a] += 1
num_transitions[s][s_prime][a] += 1
this_lr = 1 / num_actions[s][a]
Q[s][a] = newQ(Q, s, a, s_prime, gamma, this_lr)
# Next state becomes current state
s = s_prime
# Update our learned MDP and optimal policy after every EPOCH_SIZE throws,
# using infinite-horizon value iteration.
#print "Game",g,"took",throws,"throws (explore ratio %1.4f)" % (float(explores)/(explores+exploits))
print g,throws,"%1.4f" % (float(explores)/(explores+exploits))
avg = float(num_iterations)/float(num_games)
return avg
import random import throw import darts # The default player aims for the maximum score, unless the # current score is less than the number of wedges, in which # case it aims for the exact score it needs. # # You may use the following functions as a basis for # implementing the Q learning algorithm or define your own # functions. ACTIVE_STRATEGY=1; actions = darts.get_actions() states = darts.get_states() gamma = .5 learning_rate = .1 num_games = 10 #def start_game(): # num_throws_this = 1 # last_action = throw.location(throw.INNER_RING, throw.NUM_WEDGES) # return(last_action) #def update_counts(score): # last_delta = score - last_state # update_T(last_state, last_action, last_delta) #def get_target(score):
import random import throw import darts # The default player aims for the maximum score, unless the # current score is less than the number of wedges, in which # case it aims for the exact score it needs. # # You may use the following functions as a basis for # implementing the Q learning algorithm or define your own # functions. ACTIVE_STRATEGY = 1 actions = darts.get_actions() states = darts.get_states() gamma = .5 learning_rate = .1 num_games = 10 #def start_game(): # num_throws_this = 1 # last_action = throw.location(throw.INNER_RING, throw.NUM_WEDGES) # return(last_action) #def update_counts(score): # last_delta = score - last_state # update_T(last_state, last_action, last_delta) #def get_target(score):
def modelfree(gamma, learning_rate, num_games, strategy_idx):
actions = darts.get_actions()
states = darts.get_states()
pi_star = {}
g = 0
num_actions = {}
num_transitions = {}
T_matrix = {}
Q = {}
num_iterations = 0
# Initialize all arrays to 0 except the policy, which should be assigned a random action for each state.
for s in states:
pi_star[s] = random.randint(0, len(actions) - 1)
num_actions[s] = {}
Q[s] = {}
num_transitions[s] = {}
T_matrix[s] = {}
for a in range(len(actions)):
Q[s][a] = 1.0
num_actions[s][a] = 0
for s_prime in states:
num_transitions[s][s_prime] = {}
T_matrix[s][s_prime] = {}
for a in range(len(actions)):
num_transitions[s][s_prime][a] = 0
T_matrix[s][s_prime][a] = 0
# play num_games games, updating policy after every EPOCH_SIZE number of throws
for g in range(1, num_games + 1):
# run a single game
s = throw.START_SCORE
throws = 0
explores = 0
exploits = 0
while s > 0:
num_iterations += 1
throws += 1
# The following two statements implement two exploration-exploitation
# strategies. Comment out the strategy that you wish not to use.
if (strategy_idx == 1):
to_explore = ex_strategy_one(s, g)
else:
to_explore = ex_strategy_two(s, g)
if to_explore:
# explore
a = random.randint(0, len(actions) - 1)
action = actions[a]
explores += 1
else:
# exploit
a = bestAction(Q, s)
action = actions[a]
exploits += 1
#print "a", a, "action",action
# Get result of throw from dart thrower; update score if necessary
loc = throw.throw(action)
delta = throw.location_to_score(loc)
s_prime = s - delta
if s_prime < 0:
s_prime = s
# Update experience:
# increment number of times this action was taken in this state;
# increment number of times we moved from this state to next state on this action.
num_actions[s][a] += 1
num_transitions[s][s_prime][a] += 1
this_lr = 1 / num_actions[s][a]
Q[s][a] = newQ(Q, s, a, s_prime, gamma, this_lr)
# Next state becomes current state
s = s_prime
# Update our learned MDP and optimal policy after every EPOCH_SIZE throws,
# using infinite-horizon value iteration.
#print "Game",g,"took",throws,"throws (explore ratio %1.4f)" % (float(explores)/(explores+exploits))
print g, throws, "%1.4f" % (float(explores) / (explores + exploits))
avg = float(num_iterations) / float(num_games)
return avg
def test_get_states(self):
x = throw.START_SCORE;
self.assertTrue(x/2 < len(darts.get_states() ));
self.assertTrue(0.75* x < len(darts.get_states()));
def modelbased(gamma, epoch_size, num_games):
# store all actions (targets on dartboard) in actions array
actions = darts.get_actions()
states = darts.get_states()
pi_star = {}
g = 0
num_actions = {}
num_transitions = {}
T_matrix = {}
num_iterations = 0
# initialize v
V = {}
V[0] = {}
V[1] = {}
for s in states:
V[0][s] = 0
V[1][s] = 0
# Initialize all arrays to 0 except the policy, which should be assigned a random action for each state.
for s in states:
pi_star[s] = random.randint(0, len(actions) - 1)
num_actions[s] = {}
num_transitions[s] = {}
T_matrix[s] = {}
for a in range(len(actions)):
num_actions[s][a] = 0
for s_prime in states:
num_transitions[s][s_prime] = {}
T_matrix[s][s_prime] = {}
for a in range(len(actions)):
num_transitions[s][s_prime][a] = 0
T_matrix[s][s_prime][a] = 0
# play num_games games, updating policy after every EPOCH_SIZE number of throws
for g in range(1, num_games + 1):
iterations_this_game = 0
Q = {}
# run a single game
s = throw.START_SCORE
while s > 0:
iterations_this_game += 1
num_iterations += 1
# The following two statements implement two exploration-exploitation
# strategies. Comment out the strategy that you wish not to use.
a = ex_strategy_one(actions, pi_star, s, iterations_this_game)
# a = ex_strategy_two(actions, Q, s, iterations_this_game)
action = actions[a]
# Get result of throw from dart thrower; update score if necessary
loc = throw.throw(action)
s_prime = s - throw.location_to_score(loc)
if s_prime < 0:
s_prime = s
# Update experience:
# increment number of times this action was taken in this state;
# increment number of times we moved from this state to next state on this action.
num_actions[s][a] += 1
num_transitions[s][s_prime][a] += 1
# Next state becomes current state
s = s_prime
# Update our learned MDP and optimal policy after every EPOCH_SIZE throws,
# using infinite-horizon value iteration.
if num_iterations % epoch_size == 0:
# Update transition probabilities
for i in states:
for j in states:
for k in range(len(actions)):
if num_actions[i][k] != 0:
T_matrix[i][j][k] = float(
num_transitions[i][j][k]) / float(
num_actions[i][k])
# Update strategy (stored in pi) based on newly updated reward function and transition
# probabilities
T_matrix, pi_star, Q, V = modelbased_value_iteration(
gamma, T_matrix, pi_star, actions, states, V)
avg_turns = float(num_iterations) / float(num_games)
print "Average turns = ", avg_turns
return avg_turns
def modelbased(gamma, epoch_size, num_games):
# store all actions (targets on dartboard) in actions array
actions = darts.get_actions()
states = darts.get_states()
pi_star = {}
g = 0
num_actions = {}
num_transitions = {}
T_matrix = {}
num_iterations = 0
Q = {}
# Initialize all arrays to 0 except the policy, which should be assigned a random action for each state.
for s in states:
pi_star[s] = random.randint(0, len(actions)-1)
num_actions[s] = {}
num_transitions[s] = {}
T_matrix[s] = {}
Q[s] = {}
for a in range(len(actions)):
num_actions[s][a] = 0
Q[s][a] = 0
for s_prime in states:
num_transitions[s][s_prime] = {}
T_matrix[s][s_prime] = {}
for a in range(len(actions)):
num_transitions[s][s_prime][a] = 0
T_matrix[s][s_prime][a] = 0
# play num_games games, updating policy after every EPOCH_SIZE number of throws
for g in range(1, num_games + 1):
# run a single game
s = throw.START_SCORE
while s > 0:
num_iterations += 1
# The following two statements implement two exploration-exploitation
# strategies. Comment out the strategy that you wish not to use.
#to_explore = ex_strategy_one(s, num_iterations)
# Second strategy
to_explore = 2
newindex, newaction = ex_strategy_two(s, num_iterations, Q, actions)
if to_explore == 2:
a = newindex
action = newaction
elif to_explore:
# explore
a = random.randint(0, len(actions)-1)
action = actions[a]
else:
# exploit
a = pi_star[s]
action = actions[a]
# Get result of throw from dart thrower; update score if necessary
loc = throw.throw(action)
s_prime = s - throw.location_to_score(loc)
if s_prime < 0:
s_prime = s
# Update experience:
# increment number of times this action was taken in this state;
# increment number of times we moved from this state to next state on this action.
num_actions[s][a] += 1
num_transitions[s][s_prime][a] += 1
# Next state becomes current state
s = s_prime
# Update our learned MDP and optimal policy after every EPOCH_SIZE throws,
# using infinite-horizon value iteration.
if num_iterations % epoch_size == 0:
# Update transition probabilities
for i in states:
for j in states:
for k in range(len(actions)):
if num_actions[i][k] != 0:
T_matrix[i][j][k] = float(num_transitions[i][j][k]) / float(num_actions[i][k])
# Update strategy (stored in pi) based on newly updated reward function and transition
# probabilities
T_matrix, pi_star, Q = modelbased_value_iteration(gamma, T_matrix, pi_star)
print "Average turns = ", float(num_iterations)/float(num_games)
def Q_learning(gamma, alpha, num_games):
# set these to values that make sense!
#alpha = .5
#gamma = .3
Q = {}
states = darts.get_states()
actions = darts.get_actions()
num_iterations = 0
num_total_iterations = 1
# Initialize all the Q values to zero
for s in states:
Q[s]= {}
for a in actions:
Q[s][a] = 0
for g in range(1, num_games + 1):
#print "Average turns = ", float(num_iterations)/float(g)
#print "GAME {}".format(g)
# run a single game
s = throw.START_SCORE
gamethrows = 0;
while s > 0:
num_total_iterations += 1
gamethrows += 1
# The following two statements implement two exploration-exploitation
# strategies. Comment out the strategy that you wish not to use.
#to_explore = ex_strategy_one(num_iterations)
to_explore = ex_strategy_two(num_total_iterations)
#to_explore = ex_strategy_three(g, num_games)
action = 0
if to_explore:
#explore
#print "explore\n"
a = random.randint(0, len(actions)-1)
action = actions[a]
# print "action {}".format(action)
else:
# exploit
num_iterations += 1
#print "exploit\n"
action = lookup_max_a(Q,s, actions)
#print "action {}".format(action)
#action = a # actions[a]
# Get result of throw from dart thrower; update score if necessary
loc = throw.throw(action)
#print "score {}".format(s)
#print "throw value:{}".format(throw.location_to_score(loc))
#should reward be based on action of loc?
reward = darts.R(s,action)
#print "reward {}".format(reward)
s_prime = s - throw.location_to_score(loc)
if s_prime < 0:
s_prime = s
# now we update the q score table
#oldQ = copy.deepcopy(Q[s][a])
oldQ = (Q[s][action])
#print "oldQ {}".format(oldQ)
nextQaction = lookup_max_a(Q, s_prime, actions)
#print "nextQaction {}".format(nextQaction)
newQ = oldQ + alpha*(reward + gamma*(Q[s_prime][nextQaction]) - oldQ)
#print "newQ {}".format(newQ)
Q[s][action] = newQ
#print "Q[s][a] {}".format(Q[s][a])
#print "in game {},score {}, throw value {}, oldQ {}, newQ{}".format(g,s,throw.location_to_score(loc),oldQ,newQ)
s = s_prime
#print gamethrows
print "Average turns = ", float(num_iterations)/float(num_games/2)