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learn.py
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learn.py
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'''
This file implements learning agents for the goal domain.
'''
import numpy as np
import pickle
from numpy.linalg import norm
from simulator import Simulator, Enemy, Player, scale_state, STATE_DIM, platform_features
def softmax(values):
''' Returns the softmax weighting of a set of values. '''
maxval = max(values)
values = [np.exp(value - maxval) for value in values]
total = sum(values)
return [value / total for value in values]
def weighted_selection(values):
''' Select an index with probabilities given by values. '''
rand = np.random.rand()
for index, value in enumerate(values):
if rand <= value:
return index
rand -= value
return 0
def formatf(value):
''' Format a float to 5 decimal places. '''
return '{0:.5f}'.format(value)
def formatd(value):
''' Format an integer to 6 places. '''
return '{0:6d}'.format(int(value))
def format_array(values):
''' Format a float array. '''
return [formatf(value) for value in values]
FOURIER_DIM = 6
COUPLING = STATE_DIM - 2
def generate_coefficients(coeffs, vector, depth=0, count=0):
''' Generate all coefficient vectors. '''
if depth == STATE_DIM or count == COUPLING:
coeffs.append(vector)
else:
for j in range(FOURIER_DIM):
new_vector = np.copy(vector)
new_vector[depth] = np.pi * j
generate_coefficients(coeffs, new_vector, depth+1, count + (j > 0))
def get_coeffs():
''' Compute coeffs, scale, count. '''
coeffs = []
generate_coefficients(coeffs, np.zeros((STATE_DIM,)))
count = len(coeffs)
scale = np.ones(count)
for i in range(1, count):
scale[i] = norm(coeffs[i])
return coeffs, scale, count
COEFFS, COEFF_SCALE, BASIS_COUNT = get_coeffs()
print "Basis Functions:", BASIS_COUNT
INITIAL_RUN = 3.0
INITIAL_HOP = 10.0
INITIAL_LEAP = 400.0
def fourier_basis(state):
''' Defines a fourier basis function. '''
basis = np.zeros((BASIS_COUNT,))
scaled = scale_state(state)
for i, coeff in enumerate(COEFFS):
basis[i] = np.cos(coeff.dot(scaled))
return basis
def polynomial_basis(state):
''' Defines a polynomial basis using the current COEFFS. '''
basis = np.zeros((BASIS_COUNT,))
scaled = scale_state(state)
for i, coeff in enumerate(COEFFS):
basis[i] = coeff.dot(scaled)
basis[0] = 1.0
return basis
def param_features(state):
''' Defines a simple linear set of state variables. '''
array = np.ones(state.size + 1)
array[1:] = scale_state(state)
array = np.append(array, platform_features(state))
return array
def initial_features(state):
''' Computes the initial features phi(s_0) for enac. '''
return np.array([1])
def load(agent_class, run):
''' Load the given class. '''
agent = agent_class(run)
file_handle = file(agent.filename + '.obj', 'r')
agent = pickle.load(file_handle)
return agent
def save(agent):
''' Save the agent. '''
file_handle = file(agent.filename + '.obj', 'w')
pickle.dump(agent, file_handle)
class FixedSarsaAgent:
'''
Implements a fixed parameter weight gradient-descent SARSA agent.
'''
name = 'fixedsarsa'
legend = 'Fixed Sarsa'
colour = '-k'
action_count = 3
lmb = 0.5
gamma = 0.999
variances = [0.1, 0.1, 0.01]
action_names = ['run', 'hop', 'leap']
parameter_features = [param_features, param_features, param_features]
action_features = [fourier_basis, fourier_basis, fourier_basis]
def __init__(self, run):
self.run = run
self.action_weights = []
self.filename = 'runs/' + self.name +'/'+ str(run)
self.parameter_weights = [
INITIAL_RUN*np.eye(self.get_param_size(0), 1)[:, 0],
INITIAL_HOP*np.eye(self.get_param_size(1), 1)[:, 0],
INITIAL_LEAP*np.eye(self.get_param_size(2), 1)[:, 0]]
for _ in range(self.action_count):
self.action_weights.append(np.zeros((BASIS_COUNT,)))
self.steps = 0.0
self.tdiff = 0.0
self.tdiffs = []
self.total = 0.0
self.episodes = 0.0
self.returns = []
self.alpha = 1.0
self.temperature = 1.0
self.cooling = 0.996
def get_param_size(self, act):
return self.parameter_features[act](np.zeros((STATE_DIM,))).size
def run_episode(self, simulator=None):
''' Run a single episode for a maximum number of steps. '''
if simulator == None:
simulator = Simulator()
state = simulator.get_state()
states = [state]
rewards = []
actions = []
end_ep = False
act = self.action_policy(state)
acts = [act]
while not end_ep:
action = self.policy(state, act)
new_state, reward, end_ep, steps = simulator.take_action(action)
new_act = self.action_policy(new_state)
delta = reward - self.state_quality(state, act)
if not end_ep:
delta += (self.gamma**steps) * self.state_quality(new_state, new_act)
self.tdiff += abs(delta)
self.steps += 1.0
state = new_state
states.append(state)
actions.append(action)
rewards.append(reward)
act = new_act
acts.append(act)
self.tdiffs.append(self.tdiff / self.steps)
self.episodes += 1
self.total += sum(rewards)
self.returns.append(sum(rewards))
return states, actions, rewards, acts
def discount(self, rewards):
''' Computes the discounted sum of rewards. '''
return sum([(self.gamma**t)*reward for t, reward in enumerate(rewards)])
def value_function(self, state):
''' Computes V(s) = E_a[pi(s,a)Q(s,a)] '''
value = 0
action_prob = self.action_prob(state)
for act in range(self.action_count):
value += action_prob[act] * self.state_quality(state, act)
return value
def state_quality(self, state, act):
''' Returns Q(s, a). '''
feat = self.action_features[act](state)
return self.feat_quality(feat, act)
def feat_quality(self, feat, act):
''' Returns w_a * phi. '''
return self.action_weights[act].dot(feat)
def evaluate_policy(self, runs):
''' Evaluate the current policy. '''
average_reward = 0
for _ in range(runs):
rewards = self.run_episode()[2]
average_reward += sum(rewards) / runs
return average_reward
def follow_action(self, act):
''' Computes the expected return after taking action a. '''
sim = Simulator()
action = self.policy(sim.get_state(), act)
reward, end = sim.take_action(action)[1:3]
if end:
return reward
else:
rewards = self.run_episode(sim)[2]
return reward + self.gamma * self.discount(rewards)
def compare_value_function(self, runs):
''' Compares the value function to the expected rewards. '''
ret = 0.0
rets = [0]*self.action_count
quality = [0]*self.action_count
sim = Simulator()
state = sim.get_state()
vf0 = self.value_function(state)
for j in range(self.action_count):
quality[j] = self.state_quality(state, j)
for i in range(1, runs + 1):
ret += self.discount(self.run_episode()[2]) / runs
for j in range(self.action_count):
rets[j] += self.follow_action(j) / runs
print 'Step: ', formatd(i), 'V(s0): ', formatf(vf0), 'R: ', formatf(ret * runs / i)
print "V: ", formatf(vf0)
print "R:", formatf(ret)
print "Q:", [formatf(qual) for qual in quality]
print "RQ:", [formatf(retn) for retn in rets]
def load_runs(self):
''' Load the saved results for the agent. '''
return np.load(self.filename + '.npy')
def save_runs(self, returns):
''' Save the returns. '''
np.save(self.filename + '.npy', np.array(returns))
def policy(self, state, action=None):
''' Policy selects an action based on its internal policies. '''
if action == None:
action = self.action_policy(state)
parameters = self.parameter_policy(state, action)
return (self.action_names[action], parameters)
def action_prob(self, state):
''' Computes the probability of selecting each action. '''
values = [self.state_quality(state, i) for i in range(self.action_count)]
if self.temperature == 0.0:
prob = [0]*self.action_count
prob[np.argmax(values)] = 1.0
else:
prob = softmax([val / self.temperature for val in values])
return prob
def action_policy(self, state):
''' Selects an action based on action probabilities. '''
values = self.action_prob(state)
return weighted_selection(values)
def parameter_policy(self, state, action):
''' Computes the parameters for the given action. '''
features = self.parameter_features[action](state)
weights = self.parameter_weights[action]
mean = weights.dot(features)
if self.variances[action] == 0.0:
return mean
else:
return np.random.normal(mean, self.variances[action])
def update(self):
''' Learn for a single episode. '''
simulator = Simulator()
state = simulator.get_state()
act = self.action_policy(state)
feat = self.action_features[act](state)
end_episode = False
rewards = []
traces = []
for _ in range(self.action_count):
traces.append(np.zeros((BASIS_COUNT,)))
while not end_episode:
action = self.policy(state, act)
state, reward, end_episode, steps = simulator.take_action(action)
new_act = self.action_policy(state)
new_feat = self.action_features[new_act](state)
rewards.append(reward)
delta = reward - self.feat_quality(feat, act)
if not end_episode:
delta += (self.gamma)**steps * self.feat_quality(new_feat, new_act)
self.tdiff += abs(delta)
self.steps += 1.0
for i in range(self.action_count):
traces[i] *= self.lmb * self.gamma
traces[act] += feat
alpha_bound = self.gamma * traces[new_act].dot(new_feat) - traces[act].dot(feat)
self.alpha = min(self.alpha, 1.0 / abs(alpha_bound))
for i in range(self.action_count):
self.action_weights[i] += self.alpha * delta * traces[i] / COEFF_SCALE
act = new_act
feat = new_feat
self.episodes += 1
total_ret = sum(rewards)
self.total += total_ret
self.temperature *= self.cooling
self.returns.append(total_ret)
self.tdiffs.append(self.tdiff / self.steps)
av_ret = self.total / self.episodes
av_diff = self.tdiff / self.steps
print 'Step:', formatd(self.episodes), 'r:', formatf(total_ret), 'R:', formatf(av_ret), 'Delta:', formatf(av_diff)
return rewards
def learn(self, steps):
''' Learn for the given number of update steps. '''
for step in range(steps):
rets = self.update()
return self.returns
class QpamdpAgent(FixedSarsaAgent):
''' Defines an agent to optimize H(theta) using eNAC. '''
relearn = 10
runs = 50
name = 'qpamdp'
legend = 'Q-PAMDP(1)'
colour = '-.g'
beta = 1.0
qsteps = 10000
opt_omega = False
norm_grad = False
def get_parameters(self):
''' Returns all the parameters in a vector. '''
parameters = np.zeros((0,))
for action in range(self.action_count):
if self.opt_omega:
parameters = np.append(parameters, self.action_weights[action])
parameters = np.append(parameters, self.parameter_weights[action])
return parameters
def set_parameters(self, parameters):
''' Set the parameters using a vector. '''
index = 0
for action in range(self.action_count):
if self.opt_omega:
size = self.action_weights[action].size
self.action_weights[action] = parameters[index: index+size]
index += size
rows = self.parameter_weights[action].size
self.parameter_weights[action] = parameters[index: index+rows]
index += rows
def log_action_gradient(self, state, action, selection):
''' Returns the log gradient for action,
given the state and the selection used. '''
features = self.action_features[action](state)
prob = self.action_prob(state)[action]
if action == selection:
return (1 - prob)*features / self.temperature
else:
return - prob * features / self.temperature
def log_parameter_gradient(self, state, action, value):
''' Returns the log gradient for the parameter,
given the state and the value. '''
features = self.parameter_features[action](state)
mean = self.parameter_weights[action].dot(features)
grad = (value - mean) * features / self.variances[action]
return grad
def log_gradient(self, state, action, value):
''' Returns the log gradient for the entire policy. '''
grad = np.zeros((0,))
for i in range(self.action_count):
if self.opt_omega:
action_grad = self.log_action_gradient(state, i, action)
grad = np.append(grad, action_grad)
rows = self.parameter_weights[i].size
if i == action:
parameter_grad = self.log_parameter_gradient(state, i, value)
grad = np.append(grad, parameter_grad)
else:
grad = np.append(grad, np.zeros((rows,)))
return grad
def enac_gradient(self):
''' Compute the episodic NAC gradient. '''
returns = np.zeros((self.runs, 1))
param_size = self.get_parameters().size
feat_size = initial_features(np.zeros((STATE_DIM,))).size
psi = np.zeros((self.runs, param_size+feat_size))
for run in range(self.runs):
states, actions, rewards, acts = self.run_episode()
returns[run, 0] = sum(rewards)
log_grad = np.zeros((param_size,))
for state, act, action in zip(states, acts, actions):
log_grad += self.log_gradient(state, act, action[1])
psi[run, :] = np.append(log_grad, initial_features(states[0]))
av_ret = self.total / self.episodes
av_diff = self.tdiff / self.steps
print 'Step:', formatd(self.episodes), 'r:', formatf(sum(rewards)), 'R:', formatf(av_ret), 'Delta:', formatf(av_diff)
grad = np.linalg.pinv(psi).dot(returns)[0:param_size, 0]
return grad, returns
def parameter_update(self):
''' Perform a single gradient update. '''
grad, returns = self.enac_gradient()
if norm(grad) > 0 and self.norm_grad:
grad /= norm(grad)
self.set_parameters(self.get_parameters() + self.beta * grad)
return returns
def learn(self, steps):
''' Learn for a given number of steps. '''
for step in range(self.qsteps):
new_ret = self.update()
updates = int((steps - self.qsteps) / (self.runs + self.relearn))
for step in range(updates):
self.temperature = 0.0
new_ret = self.parameter_update()
self.temperature = 1.0
self.cooling = 0.95
for _ in range(self.relearn):
new_ret = self.update()
return self.returns
class EnacAoAgent(QpamdpAgent):
''' Defines an alternating agent using eNAC. '''
name = 'enacao'
legend = 'Q-PAMDP($\infty$)'
colour = '--b'
gradsteps = 180
relearn = 1000
one_iteration = False
def learn(self, steps):
''' Learn for a given number of steps. '''
if self.one_iteration:
self.gradsteps = (steps - self.qsteps) / self.runs
self.relearn = 0
updates = int((steps - self.qsteps) / (self.relearn + self.gradsteps * self.runs))
for _ in range(self.qsteps):
new_ret = self.update()
self.cooling = 0.995
for _ in range(updates):
self.temperature = 0.0
for i in range(self.gradsteps):
new_ret = self.parameter_update()
self.temperature = 1.0
for i in range(self.relearn):
new_ret = self.update()
return self.returns
class EnacAgent(QpamdpAgent):
''' Defines an agent to optimize J(theta, omega) using eNAC. '''
name = 'enac'
legend = 'eNAC'
colour = ':r'
opt_omega = True
def learn(self, steps):
''' Learn for a given number of steps. '''
updates = int(steps / self.runs)
self.temperature = 0.01
for step in range(updates):
new_ret = self.parameter_update()
return self.returns
def determine_variance(agent, steps, runs=1):
''' Determine the variance of parameterized policy agent. '''
rewards = []
for _ in range(steps):
reward = agent.evaluate_policy(runs)
rewards.append(reward)
print reward
mean = sum(rewards) / steps
variance = 0
for reward in rewards:
variance += (reward - mean)**2 / steps
print
print 'Mean:', mean
print 'Variance:', variance
def save_run(agent_class, steps, run):
''' Save a single run. '''
agent = agent_class(run)
returns = agent.learn(steps)
agent.save_runs(returns)
save(agent)
def extend_run(agent_class, steps, run):
''' Extend an existing run for a given number of steps. '''
agent = load(agent_class, run)
returns = agent.load_runs()
returns = np.append(returns, agent.learn(steps))
agent.save_runs(returns)
save(agent)
def random_sample(runs):
''' Randomly tests parameters around the current parameters. '''
print 0, sum(QpamdpAgent().learn(0)) / QpamdpAgent.qsteps
for i in range(1, runs):
agent = QpamdpAgent()
params = agent.get_parameters()
params += 2*np.random.randn(params.size)
agent.set_parameters(params)
rets = agent.learn(0)
print i, sum(rets) / QpamdpAgent.qsteps
print agent.get_parameters()
def gradient_variance(runs):
''' Compute the variance of the gradient estimate. '''
agent = load(QpamdpAgent, 999)
grads = []
for _ in range(runs):
grad = agent.enac_gradient()[0]
grad /= norm(grad)
grads.append(grad)
print grad
print
mean = np.mean(grads, 0)
print 'Mean:'
print mean
var = np.var(grads, 0)
print 'Var:'
print var
print 'Relative Var:'
print mean / var
print 'Norm Var:', norm(var)