def plot(self,stats):
# For plotting: Create value function from action-value function
# by picking the best action at each state
V = defaultdict(float)
for state, actions in self.Q.items():
action_value = np.max(actions)
V[state] = action_value
plotting.plot_value_function(V, title="Final Value Function")
def main():
env = BlackjackEnv()
V_10k = mc_prediction(sample_policy, env, num_episodes=10000)
plotting.plot_value_function(V_10k, title="10,000 Steps")
V_500k = mc_prediction(sample_policy, env, num_episodes=500000)
plotting.plot_value_function(V_500k, title="500,000 Steps")
def main():
# V_10k, stats = mc_prediction(sample_policy, env, num_episodes=100)
# plotting.plot_value_function(V_10k, title="10,000 Steps")
V_500k, stats = mc_prediction(sample_policy, env, num_episodes=500000)
plotting.plot_value_function(V_500k, title="500,000 Steps")
def find_optimal_policy(num_episodes):
Q, policy = mc_control_epsilon_greedy(env, num_episodes=num_episodes, epsilon=0.1)
# For plotting: Create value function from action-value function
# by picking the best action at each state
V = defaultdict(float)
for state, actions in Q.items():
action_value = np.max(actions)
V[state] = action_value
plotting.plot_value_function(V, title="Optimal Value Function ({} episodes)".format(num_episodes))
def main():
Q, behaviour_policy = mc_control_importance_sampling(env,
num_episodes=50000)
V = defaultdict(float)
for state, action_values in Q.items():
action_value = np.max(action_values)
V[state] = action_value
plotting.plot_value_function(V, title="Optimal Value Function")
def main(): # Q, policy = mc_control_epsilon_greedy(env, num_episodes=500000, epsilon=0.1) Q, policy= mc_control_epsilon_greedy(env, num_episodes=300000, epsilon=0.4) # For plotting: Create value function from action-value function # by picking the best action at each state V = defaultdict(float) for state, actions in Q.items(): action_value = np.max(actions) V[state] = action_value plotting.plot_value_function(V, title="On-Policy MC Control, 30000 steps - Value Function")
def main():
random_policy = create_random_policy(env.action_space.n)
#use an epsilon-greedy policy
Q, policy = mc_control_random_off_policy(env,
num_episodes=300000,
behavior_policy=random_policy)
V = defaultdict(float)
for state, action_values in Q.items():
action_value = np.max(action_values)
V[state] = action_value
plotting.plot_value_function(V, title="Optimal Value Function")
def main():
Q, behaviour_policy = mc_control_importance_sampling(env, num_episodes=500000)
# For plotting: Create value function from action-value function
# by picking the best action at each state
V = defaultdict(float)
for state, action_values in Q.items():
action_value = np.max(action_values)
V[state] = action_value
plotting.plot_value_function(V, title="Optimal Value Function")
def main():
random_policy = create_random_policy(env.action_space.n)
#use an epsilon-greedy policy
Q, policy, Advantage_Function = mc_control_importance_sampling(
env, num_episodes=5000, behavior_policy=random_policy)
# For plotting: Create value function from action-value function
# by picking the best action at each state
V = defaultdict(float)
for state, action_values in Advantage_Function.items():
action_value = np.max(action_values)
V[state] = action_value
plotting.plot_value_function(V, title="Optimal Value Function")
obs = newObs
return (episode)
def compute_return(episode, begin, discount_factor):
output = 0
for i, transition in enumerate(episode[begin:]):
#print(transition[2]*(discount_factor**i))
output += transition[2] * (discount_factor**i)
return (output)
def plot_results(evolution, index):
fig = pl.figure()
pl.plot(evolution)
pl.title('variations of the computed means')
pl.xlabel('iteration')
pl.ylabel('L1 difference of variations')
pl.legend()
pl.savefig(index + '_evolutionMean.png')
pl.show()
V_10k, evolution = mc_prediction(sample_policy, env, num_episodes=10000)
plotting.plot_value_function(V_10k, title="10,000 Steps")
plot_results(evolution, '10K')
V_500k, evolution = mc_prediction(sample_policy, env, num_episodes=500000)
plotting.plot_value_function(V_500k, title="500,000 Steps")
plot_results(evolution, '500K')
# find its first occurrence
first_occurrence_idx = next((ith for ith, x in enumerate(episode)
if tuple(x[0:2]) == state_action))
# sum up all rewards since the first occurrence
G = sum([
observation[2] * discount_factor**ith for ith, observation in
enumerate(episode[first_occurrence_idx:])
])
# record total returns of each (state, action) pair and their first-visit numbers
returns_sum[state_action] += G
returns_count[state_action] += 1
# update Q(s,a) and epsilon-greedy policy
Q[state_action[0]][state_action[
1]] = returns_sum[state_action] / returns_count[state_action]
# our policy is updated implicitly
# policy = make_epsilon_greedy_policy(Q, epsilon, env.action_space.n)
return Q, policy
Q, policy = mc_control_epsilon_greedy(env, num_episodes=500000, epsilon=0.1)
# For plotting: Create value function from action-value function
# by picking the best action at each state
V = defaultdict(float)
for state, actions in Q.items():
print(state, actions)
action_value = np.max(actions)
V[state] = action_value
plotting.plot_value_function(V, title="Optimal Value Function")
def plot(Q):
V = defaultdict(float)
for state, actions in Q.items():
action_value = np.max(actions)
V[tuple([state[1], state[0]])] = action_value
plotting.plot_value_function(V, title="Optimal Value Function")
# Not waiting to generate one episode for TD update
for s in States:
V[s] = V[s] + alfa * delta * Z[s]
Z[s] = lmbd * discount * Z[s]
# Move to the next state
now_state = next_state
if done:
terminate = True
return V
"""Block code below evaluate a policy and return a plotted V-value
"""
print "TEMPORAL-DIFFERENCE-LAMBDA EVALUATE POLICY_0"
V = tdlambda_prediction(policy_0, n_episodes=10000)
# Delete state with player score below 12 to make it same with example
# Because we call V[next_state] in the end, to make the same plot
# we should delete some keys
new_V = defaultdict(float)
for key, data in V.iteritems():
if key[0] >= 12 and key[1]<=11:
new_V[key] = data
# Using plotting library from Denny Britz repo
plotting.plot_value_function(new_V, title="Policy_0 Evaluation")
def mc_control_epsilon_greedy(env,
num_episodes,
discount_factor=1.0,
epsilon=0.1):
"""
Monte Carlo Control using Epsilon-Greedy policies.
Finds an optimal epsilon-greedy policy.
Args:
env: OpenAI gym environment.
num_episodes: Number of episodes to sample.
discount_factor: Gamma discount factor.
epsilon: Chance the sample a random action. Float betwen 0 and 1.
Returns:
A tuple (Q, policy).
Q is a dictionary mapping state -> action values.
policy is a function that takes an observation as an argument and returns
action probabilities
"""
# Keeps track of sum and count of returns for each state
# to calculate an average. We could use an array to save all
# returns (like in the book) but that's memory inefficient.
returns_sum = defaultdict(float)
returns_count = defaultdict(float)
# The final action-value function.
# A nested dictionary that maps state -> (action -> action-value).
Q = defaultdict(lambda: np.zeros(env.action_space.n))
# The policy we're following
policy = make_epsilon_greedy_policy(Q, epsilon, env.action_space.n)
for episode in range(num_episodes):
if episode % 1000 == 0:
print("Episode: " + str(episode) + "/" + str(num_episodes))
if (episode + 1) % 100000 == 0:
print("Nice")
V = defaultdict(float)
for state, actions in Q.items():
action_value = np.max(actions)
V[state] = action_value
plotting.plot_value_function(V, title="Optimal Value Function")
states_visited = []
state = env.reset()
while True:
action_values = policy(state)
action = np.random.choice(range(env.action_space.n),
p=action_values)
next_state, reward, done, info = env.step(action)
states_visited.append([state, action, reward])
if done:
break
state = next_state
G = 0
for i, state in enumerate(reversed(states_visited)):
sa_pair = (state[0], action)
G += (discount_factor * G) + state[2]
if states_visited[0:i - 1].count(state) == 0:
returns_sum[sa_pair] += G
returns_count[sa_pair] += 1
Q[state[0]][
action] = returns_sum[sa_pair] / returns_count[sa_pair]
# policy = make_epsilon_greedy_policy(Q, epsilon, env.action_space.n)
return Q, policy
pl.legend()
pl.savefig(index + '_evolutionMean.png')
pl.show()
#on 500K iterations
Q500K, policy, evolution500K = mc_control_epsilon_greedy(env,
num_episodes=500000,
epsilon=0.1)
# For plotting: Create value function from action-value function
# by picking the best action at each state
V500K = defaultdict(float)
for state, actions in Q500K.items():
action_value = np.max(actions)
V500K[state] = action_value
plotting.plot_value_function(V500K, title="Optimal Value Function_500K")
plot_results(evolution500K, 'evolution_500K')
plot_policy(Q500K, policy, 'policy_500K')
#on 1M iterations
Q1M, policy, evolution1M = mc_control_epsilon_greedy(env,
num_episodes=1000000,
epsilon=0.1)
# For plotting: Create value function from action-value function
# by picking the best action at each state
V1M = defaultdict(float)
for state, actions in Q1M.items():
action_value = np.max(actions)
V1M[state] = action_value
plotting.plot_value_function(V1M, title="Optimal Value Function_1M")
V[state] += (episode_rewards[state] - V[state]) / returns_num[state]
return V
# In[4]:
def sample_policy(observation):
"""
A policy that sticks if the player score is > 20 and hits otherwise.
"""
player_score, dealer_score, usable_ace = observation
return np.array([1.0, 0.0]) if player_score >= 20 else np.array([0.0, 1.0])
# In[5]:
V_10k = mc_prediction(sample_policy, env, num_episodes=10000)
plotting.plot_value_function(V_10k, title="10,000 Steps")
# In[18]:
V_500k = mc_prediction(sample_policy, env, num_episodes=500000)
plotting.plot_value_function(V_500k, title="500,000 Steps")
def plot_value_function(self):
assert self.policy is not None
plot_value_function(self.q)
action = np.random.choice(np.arange(len(A)), p=A)
next_state, reward, done, info = env.step(action)
episode.append((observation, action, reward))
if done:
break
observation = next_state
temp_set = set()
for w in episode:
temp_set.add((w[0], w[1]))
for state, action in temp_set:
ind = 0
for i, w in enumerate(episode):
if w[0] == state and w[1] == action:
ind = i
returns_sum[(state, action)] += sum([w[2] * discount_factor ** i for i, w in enumerate(episode[ind:])])
returns_counts[(state, action)] += 1
Q[state][action] = returns_sum[(state, action)] / returns_counts[(state, action)]
return Q
if __name__ == "__main__":
#V_over500k = monte_carlo_prediction(env, num_eps=500000)
Q_over500k = monte_corlo_control(env, num_eps=500000)
V_over500k = defaultdict(float)
for state in Q_over500k.keys():
V_over500k[state] = np.max(Q_over500k[state])
pprint(V_over500k)
plotting.plot_value_function(V_over500k, title="5,00,000 Steps")
for t in range(len(episode))[::-1]:
state, action, reward = episode[t]
# Update the total reward since step t
G = discount_factor * G + reward
# Update weighted importance sampling formula denominator
C[state][action] += W
# Update the action-value function using the incremental update formula
# This also improves our target policy which holds a reference to Q
Q[state][action] += (W / C[state][action]) * (G - Q[state][action])
# If the action taken by the behavior policy is not the action
# taken by the traget policy then probability will be 0 and we can break
if action != np.argmax(target_policy(state)):
break
W = W * 1. / behavior_policy(state)[action]
return Q, target_policy
if __name__ == '__main__':
random_policy = create_random_policy(env.action_space.n)
Q, policy = mc_control_importance_sampling(env,
num_episodes=500000,
behavior_policy=random_policy)
# For plotting, create value function from action-value function
# by picking the best action at each state
V = defaultdict(float)
for state, action_values in Q.items():
action_value = np.max(action_values)
V[state] = action_value
plotting.plot_value_function(V, title='Optimal Value Function')
for j, e in enumerate(episode[i:])
])
returns_sum[exp[0]][exp[1]] += G
returns_count[exp[0]][exp[1]] += 1
Q[exp[0]][exp[1]] = returns_sum[exp[0]][
exp[1]] / returns_count[exp[0]][exp[1]]
#############################################Implement your code end###################################################################################################
return Q, policy
Q_first, policy_first = mc(env, num_episodes=500000, epsilon=0.1)
Q_every, policy_every = mc(env,
num_episodes=500000,
epsilon=0.1,
first_visit=0)
# For plotting: Create value function from action-value function
# by picking the best action at each state
V_first = defaultdict(float)
V_every = defaultdict(float)
for state, actions in Q_first.items():
action_value = np.max(actions)
V_first[state] = action_value
for state, actions in Q_every.items():
action_value = np.max(actions)
V_every[state] = action_value
plotting.plot_value_function(V_first,
title="(first_visit)Optimal Value Function")
plotting.plot_value_function(V_every,
title="(every_visit)Optimal Value Function")
break
state = ns
states_in_episode = set([tuple(state) for state, _, _ in episode])
for s in states_in_episode:
first_occurence_idx = next(i for i, (state, _,
_) in enumerate(episode)
if s == state)
G = sum([
gamma**i * reward
for i, (_, _,
reward) in enumerate(episode[first_occurence_idx:])
])
# sum over sample episodes
returns_sum[s] += G
returns_count[s] += 1.0
V[s] = returns_sum[s] / returns_count[s]
return V
def sample_policy(state):
score, _, _ = state
return np.array([1.0, 0.0]) if score >= 20 else np.array([0.0, 1.0])
if __name__ == '__main__':
env = BlackjackEnv()
V = mc_prediction(sample_policy, env, 10000)
plotting.plot_value_function(V, title='10,000 Steps')
episode.append((state, action, reward))
if done:
break
state = next_state
states_in_episode = set([tuple(x[0]) for x in episode])
for state in states_in_episode:
first_time_id = next(i for i, x in enumerate(episode)
if x[0] == state)
G = sum([
x[2] * (discount_factor**i)
for i, x in enumerate(episode[first_time_id:])
])
returns_sum[state] += G
returns_count[state] += 1
V[state] = returns_sum[state] / returns_count[state]
return V
def sample_policy(observation):
score, dealer_score, usable_ace = observation
return 0 if score >= 18 else 1
if __name__ == '__main__':
env = BlackjackEnv()
V_50k = mc_prediction(sample_policy, env, 500000, 1.0)
plotting.plot_value_function(V_50k, title='50k >= 18')
episode.append(state)
probs = policy(state)
action = np.random.choice(np.arange(len(probs)), p=probs)
next_state, reward, done, _ = env.step(action)
state = next_state
if done:
for state in episode:
returns_sum[state] += reward
returns_count[state] += 1.0
break
for k in returns_sum.keys():
V[k] = returns_sum[k] / returns_count[k]
return V
def sample_policy(observation):
"""
A policy that sticks if the player score is > 20 and hits otherwise.
"""
score, dealer_score, usable_ace = observation
return np.array([1.0, 0.0]) if score >= 16 else np.array([0.0, 1.0])
V_SMALL = mc_prediction(sample_policy, env, num_episodes=50000)
print(V_SMALL)
plotting.plot_value_function(V_SMALL, title="10,000 Steps")
#V_500k = mc_prediction(sample_policy, env, num_episodes=500000)
#plotting.plot_value_function(V_500k, title="500,000 Steps")
# Find the first occurance of the state in the episode
first_occurance_idx = next(i for i, x in enumerate(episode)
if x[0] == state)
print(episode[first_occurance_idx][0])
# Sum up all rewards since the first occurance
G = sum([
x[2] * (discount_factor**i)
for i, x in enumerate(episode[first_occurance_idx:])
])
# Calculate average return for this state over all sampled episodes
returns_sum[state] += G
returns_count[state] += 1.0
V[state] = returns_sum[state] / returns_count[state]
return V
def sample_policy(observation):
"""
A policy that sticks if the player score is over 20 and hits otherwise.
"""
score, deal_score, usable_ace = observation
return 0 if score >= 20 else 1
if __name__ == '__main__':
v_10k = mc_prediction(sample_policy, env, num_episodes=10000)
plotting.plot_value_function(v_10k, title='10000 Steps')
v_500k = mc_prediction(sample_policy, env, num_episodes=500000)
plotting.plot_value_function(v_500k, title='500000 Steps')