def policyEvaluation(self, policy):
'''
Evaluate a given policy: this is done by applying the Bellman backup over all states until the change is less than
a given threshold.
Returns: convergence status as a boolean
'''
converged = False
policy_evaluation_iteration = 0
while (not converged and self.hasTime()
and policy_evaluation_iteration < self.max_PE_iterations):
policy_evaluation_iteration += 1
# Sweep The State Space
for i in range(0, self.representation.agg_states_num):
# Check for solver time
if not self.hasTime(): break
# Map an state ID to state
s = self.representation.stateID2state(i)
# Skip terminal states and states with no possible action
possible_actions = self.domain.possibleActions(s=s)
if (self.domain.isTerminal(s) or len(possible_actions) == 0):
continue
# Apply Bellman Backup
self.BellmanBackup(s, policy.pi(s, False, possible_actions),
self.ns_samples, policy)
# Update number of backups
self.bellmanUpdates += 1
# Check for the performance
if self.bellmanUpdates % self.log_interval == 0:
performance_return = self.performanceRun()[0]
self.logger.info('[%s]: BellmanUpdates=%d, Return=%0.4f' %
(hhmmss(deltaT(self.start_time)),
self.bellmanUpdates, performance_return))
# check for convergence: L_infinity norm of the difference between the to the weight vector of representation
weight_vec_change = l_norm(
policy.representation.weight_vec -
self.representation.weight_vec, np.inf)
converged = weight_vec_change < self.convergence_threshold
# Log Status
self.logger.info(
'PE #%d [%s]: BellmanUpdates=%d, ||delta-weight_vec||=%0.4f' %
(policy_evaluation_iteration, hhmmss(deltaT(
self.start_time)), self.bellmanUpdates, weight_vec_change))
# Show Plots
if self.show:
self.domain.show(policy.pi(s, False, possible_actions),
self.representation,
s=s)
return converged
def evaluate(self, total_steps, episode_number, visualize=0):
"""
Evaluate the current agent within an experiment
:param total_steps: (int)
number of steps used in learning so far
:param episode_number: (int)
number of episodes used in learning so far
"""
# TODO resolve this hack
if className(self.agent) == 'PolicyEvaluation':
# Policy Evaluation Case
self.result = self.agent.STATS
return
random_state = np.random.get_state()
#random_state_domain = copy(self.domain.random_state)
elapsedTime = deltaT(self.start_time)
performance_return = 0.
performance_steps = 0.
performance_term = 0.
performance_discounted_return = 0.
for j in range(self.checks_per_policy):
p_ret, p_step, p_term, p_dret = self.performanceRun(
total_steps, visualize=visualize > j)
performance_return += p_ret
performance_steps += p_step
performance_term += p_term
performance_discounted_return += p_dret
performance_return /= self.checks_per_policy
performance_steps /= self.checks_per_policy
performance_term /= self.checks_per_policy
performance_discounted_return /= self.checks_per_policy
self.result["learning_steps"].append(total_steps)
self.result["return"].append(performance_return)
self.result["learning_time"].append(self.elapsed_time)
self.result["num_features"].append(
self.agent.representation.features_num)
self.result["steps"].append(performance_steps)
self.result["terminated"].append(performance_term)
self.result["learning_episode"].append(episode_number)
self.result["discounted_return"].append(performance_discounted_return)
# reset start time such that performanceRuns don't count
self.start_time = clock() - elapsedTime
if total_steps > 0:
remaining = hhmmss(elapsedTime * (self.max_steps - total_steps) /
total_steps)
else:
remaining = "?"
self.logger.info(
self.performance_log_template.format(
total_steps=total_steps,
elapsed=hhmmss(elapsedTime),
remaining=remaining,
totreturn=performance_return,
steps=performance_steps,
num_feat=self.agent.representation.features_num))
np.random.set_state(random_state)
def solve(self):
"""Solve the domain MDP."""
self.start_time = clock() # Used to track the total time for solving
self.bellmanUpdates = 0
converged = False
PI_iteration = 0
# The policy is maintained as separate copy of the representation.
# This way as the representation is updated the policy remains intact
policy = eGreedy(deepcopy(self.representation),
epsilon=0,
forcedDeterministicAmongBestActions=True)
while self.hasTime() and not converged:
self.trajectoryBasedPolicyEvaluation(policy)
# Policy Improvement (Updating the representation of the value
# function will automatically improve the policy
PI_iteration += 1
# Theta can increase in size if the representation is expanded hence padding the weight vector with zeros
paddedTheta = padZeros(policy.representation.weight_vec,
len(self.representation.weight_vec))
# Calculate the change in the weight_vec as L2-norm
delta_weight_vec = np.linalg.norm(paddedTheta -
self.representation.weight_vec)
converged = delta_weight_vec < self.convergence_threshold
# Update the underlying value function of the policy
policy.representation = deepcopy(
self.representation) # self.representation
performance_return, performance_steps, performance_term, performance_discounted_return = self.performanceRun(
)
self.logger.info(
'PI #%d [%s]: BellmanUpdates=%d, ||delta-weight_vec||=%0.4f, Return=%0.3f, steps=%d, features=%d'
% (PI_iteration, hhmmss(deltaT(self.start_time)),
self.bellmanUpdates, delta_weight_vec, performance_return,
performance_steps, self.representation.features_num))
if self.show:
self.domain.show(a, representation=self.representation, s=s)
# store stats
self.result["bellman_updates"].append(self.bellmanUpdates)
self.result["return"].append(performance_return)
self.result["planning_time"].append(deltaT(self.start_time))
self.result["num_features"].append(
self.representation.features_num)
self.result["steps"].append(performance_steps)
self.result["terminated"].append(performance_term)
self.result["discounted_return"].append(
performance_discounted_return)
self.result["policy_improvemnt_iteration"].append(PI_iteration)
if converged:
self.logger.info('Converged!')
super(TrajectoryBasedPolicyIteration, self).solve()
def trajectoryBasedPolicyEvaluation(self, policy):
''' evaluate the current policy by simulating trajectories and update the value function along the
visited states
'''
PE_iteration = 0
evaluation_is_accurate = False
converged_trajectories = 0
while not evaluation_is_accurate and self.hasTime(
) and PE_iteration < self.max_PE_iterations:
# Generate a new episode e-greedy with the current values
max_Bellman_Error = 0
step = 0
s, a, terminal = self.sample_ns_na(policy, start_trajectory=True)
while not terminal and step < self.domain.episodeCap and self.hasTime(
):
new_Q = self.representation.Q_oneStepLookAhead(
s, a, self.ns_samples, policy)
phi_s = self.representation.phi(s, terminal)
phi_s_a = self.representation.phi_sa(s,
terminal,
a,
phi_s=phi_s)
old_Q = np.dot(phi_s_a, self.representation.weight_vec)
bellman_error = new_Q - old_Q
# Update the value function using approximate bellman backup
self.representation.weight_vec += (self.alpha * bellman_error *
phi_s_a)
self.bellmanUpdates += 1
step += 1
max_Bellman_Error = max(max_Bellman_Error, abs(bellman_error))
# Discover features if the representation has the discover method
discover_func = getattr(
self.representation, 'discover', None
) # None is the default value if the discover is not an attribute
if discover_func and callable(discover_func):
self.representation.post_discover(phi_s, bellman_error)
# if discovered:
# print "Features = %d" % self.representation.features_num
s, a, terminal = self.sample_ns_na(policy, a)
# check for convergence of policy evaluation
PE_iteration += 1
if max_Bellman_Error < self.convergence_threshold:
converged_trajectories += 1
else:
converged_trajectories = 0
evaluation_is_accurate = converged_trajectories >= self.MIN_CONVERGED_TRAJECTORIES
self.logger.info(
'PE #%d [%s]: BellmanUpdates=%d, ||Bellman_Error||=%0.4f, Features=%d'
% (PE_iteration, hhmmss(deltaT(
self.start_time)), self.bellmanUpdates, max_Bellman_Error,
self.representation.features_num))
def policyImprovement(self, policy):
''' Given a policy improve it by taking the greedy action in each state based on the value function
Returns the new policy
'''
policyChanges = 0
i = 0
while i < self.representation.agg_states_num and self.hasTime():
s = self.representation.stateID2state(i)
if not self.domain.isTerminal(s) and len(
self.domain.possibleActions(s)):
for a in self.domain.possibleActions(s):
if not self.hasTime():
break
self.BellmanBackup(s, a, self.ns_samples, policy)
if policy.pi(s, False, self.domain.possibleActions(
s=s)) != self.representation.bestAction(
s, False, self.domain.possibleActions(s=s)):
policyChanges += 1
i += 1
# This will cause the policy to be copied over
policy.representation.weight_vec = self.representation.weight_vec.copy(
)
performance_return, performance_steps, performance_term, performance_discounted_return = self.performanceRun(
)
self.logger.info(
'PI #%d [%s]: BellmanUpdates=%d, Policy Change=%d, Return=%0.4f, Steps=%d'
% (self.policy_improvement_iteration,
hhmmss(deltaT(self.start_time)), self.bellmanUpdates,
policyChanges, performance_return, performance_steps))
# store stats
self.result["bellman_updates"].append(self.bellmanUpdates)
self.result["return"].append(performance_return)
self.result["planning_time"].append(deltaT(self.start_time))
self.result["num_features"].append(self.representation.features_num)
self.result["steps"].append(performance_steps)
self.result["terminated"].append(performance_term)
self.result["discounted_return"].append(performance_discounted_return)
self.result["policy_improvement_iteration"].append(
self.policy_improvement_iteration)
return policy, policyChanges
def run(self,
visualize_performance=0,
visualize_learning=False,
visualize_steps=False,
debug_on_sigurg=False):
if debug_on_sigurg:
problems.rlpy.Tools.ipshell.ipdb_on_SIGURG()
self.performance_domain = deepcopy(self.domain)
self.seed_components()
self.result = defaultdict(list)
self.result["seed"] = self.exp_id
total_steps = 0
eps_steps = 0
eps_return = 0
episode_number = 0
# show policy or value function of initial policy
if visualize_learning:
self.domain.showLearning(self.agent.representation)
# Used to bound the number of logs in the file
start_log_time = clock()
# Used to show the total time took the process
self.start_time = clock()
self.elapsed_time = 0
# do a first evaluation to get the quality of the inital policy
self.evaluate(total_steps, episode_number, visualize_performance)
self.total_eval_time = 0.
terminal = True
while total_steps < self.max_steps:
if terminal or eps_steps >= self.domain.episodeCap:
s, terminal, p_actions = self.domain.s0()
a = self.agent.policy.pi(s, terminal, p_actions)
# Visual
if visualize_steps:
self.domain.show(a, self.agent.representation)
# Output the current status if certain amount of time has been
# passed
eps_return = 0
eps_steps = 0
episode_number += 1
# Act,Step
r, ns, terminal, np_actions = self.domain.step(a)
self._gather_transition_statistics(s, a, ns, r, learning=True)
na = self.agent.policy.pi(ns, terminal, np_actions)
total_steps += 1
eps_steps += 1
eps_return += r
# Print Current performance
if (terminal or eps_steps == self.domain.episodeCap
) and deltaT(start_log_time) > self.log_interval:
start_log_time = clock()
elapsedTime = deltaT(self.start_time)
self.logger.info(
self.log_template.format(
total_steps=total_steps,
elapsed=hhmmss(elapsedTime),
remaining=hhmmss(elapsedTime *
(self.max_steps - total_steps) /
total_steps),
totreturn=eps_return,
steps=eps_steps,
num_feat=self.agent.representation.features_num))
# learning
self.agent.learn(s, p_actions, a, r, ns, np_actions, na, terminal)
s, a, p_actions = ns, na, np_actions
# Visual
if visualize_steps:
self.domain.show(a, self.agent.representation)
# Check Performance
if total_steps % (old_div(self.max_steps,
self.num_policy_checks)) == 0:
self.elapsed_time = deltaT(
self.start_time) - self.total_eval_time
# show policy or value function
if visualize_learning:
self.domain.showLearning(self.agent.representation)
self.evaluate(total_steps, episode_number,
visualize_performance)
self.total_eval_time += deltaT(self.start_time) - \
self.elapsed_time - \
self.total_eval_time
start_log_time = clock()
# Visual
if visualize_steps:
self.domain.show(a, self.agent.representation)
self.logger.info("Total Experiment_ql Duration %s" %
(hhmmss(deltaT(self.start_time))))
return self.agent.representation.weight_vec
def run(self,
visualize_performance=0,
visualize_learning=False,
visualize_steps=False,
debug_on_sigurg=False):
"""
Run the experiment and collect statistics / generate the results
:param visualize_performance: (int)
determines whether a visualization of the steps taken in
performance runs are shown. 0 means no visualization is shown.
A value n > 0 means that only the first n performance runs for a
specific policy are shown (i.e., for n < checks_per_policy, not all
performance runs are shown)
:param visualize_learning: (boolean)
show some visualization of the learning status before each
performance evaluation (e.g. Value function)
:param visualize_steps: (boolean)
visualize all steps taken during learning
:param debug_on_sigurg: (boolean)
if true, the ipdb debugger is opened when the python process
receives a SIGURG signal. This allows to enter a debugger at any
time, e.g. to view data interactively or actual debugging.
The feature works only in Unix systems. The signal can be sent
with the kill command:
kill -URG pid
where pid is the process id of the python interpreter running this
function.
"""
if debug_on_sigurg:
problems.rlpy.Tools.ipshell.ipdb_on_SIGURG()
self.seed_components()
self.result = defaultdict(list)
self.result["seed"] = self.exp_id
total_steps = 0
eps_steps = 0
eps_return = 0
episode_number = 0
# show policy or value function of initial policy
if visualize_learning:
self.domain.showLearning(self.agent.representation)
# Used to bound the number of logs in the file
start_log_time = clock()
# Used to show the total time took the process
self.start_time = clock()
self.elapsed_time = 0
# do a first evaluation to get the quality of the inital policy
self.evaluate(total_steps, episode_number, visualize_performance)
self.total_eval_time = 0.
terminal = True
while total_steps < self.max_steps:
if terminal or eps_steps >= self.domain.episodeCap:
# print('@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@')
# print('@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@')
# print('@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@')
# print('@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@')
# print('@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@')
s, terminal, p_actions = self.domain.s0()
# print('start train')
a = self.agent.policy.pi(s, terminal, p_actions)
# Visual
if visualize_steps:
self.domain.show(a, self.agent.representation)
# Output the current status if certain amount of time has been
# passed
eps_return = 0
eps_steps = 0
episode_number += 1
# Act,Step
r, ns, terminal, np_actions = self.domain.step(a)
# print('train', r, s, ns, terminal)
self._gather_transition_statistics(s, a, ns, r, learning=True)
na = self.agent.policy.pi(ns, terminal, np_actions)
total_steps += 1
eps_steps += 1
eps_return += r
# Print Current performance
if (terminal or eps_steps == self.domain.episodeCap
) and deltaT(start_log_time) > self.log_interval:
start_log_time = clock()
elapsedTime = deltaT(self.start_time)
self.logger.info(
self.log_template.format(
total_steps=total_steps,
elapsed=hhmmss(elapsedTime),
remaining=hhmmss(elapsedTime *
(self.max_steps - total_steps) /
total_steps),
totreturn=eps_return,
steps=eps_steps,
num_feat=self.agent.representation.features_num))
# learning
self.agent.learn(s, p_actions, a, r, ns, np_actions, na, terminal)
# if ns[-1]!=s[-1]: print(s, a, r, 'collect flag', ns[-1])
# else: print(s, a, r)
# action_num = 4
# flag_num = 2
# gw_size = 70
# state_size = gw_size*(flag_num+1)
# for aaa in range(action_num): # actions
# print('~~~~~~~~~~~~~~~~~~~~~~~~~')
# for fff in range(flag_num+1): # flags
# print(self.agent.eligibility_trace[aaa*state_size+fff*gw_size : aaa*state_size+fff*gw_size+gw_size])
s, a, p_actions = ns, na, np_actions
# Visual
if visualize_steps:
self.domain.show(a, self.agent.representation)
# Check Performance
if total_steps % (old_div(self.max_steps,
self.num_policy_checks)) == 0:
self.elapsed_time = deltaT(
self.start_time) - self.total_eval_time
# show policy or value function
if visualize_learning:
self.domain.showLearning(self.agent.representation)
self.evaluate(total_steps, episode_number,
visualize_performance)
self.total_eval_time += deltaT(self.start_time) - \
self.elapsed_time - \
self.total_eval_time
start_log_time = clock()
# Visual
if visualize_steps:
self.domain.show(a, self.agent.representation)
self.logger.info("Total Experiment Duration %s" %
(hhmmss(deltaT(self.start_time))))
def solve(self):
"""Solve the domain MDP."""
# Used to show the total time took the process
self.start_time = clock()
bellmanUpdates = 0
converged = False
iteration = 0
# Track the number of consequent trajectories with very small observed
# BellmanError
converged_trajectories = 0
while self.hasTime() and not converged:
# Generate a new episode e-greedy with the current values
max_Bellman_Error = 0
step = 0
terminal = False
s, terminal, p_actions = self.domain.s0()
a = self.representation.bestAction(
s, terminal, p_actions
) if np.random.rand() > self.epsilon else randSet(p_actions)
while not terminal and step < self.domain.episodeCap and self.hasTime(
):
new_Q = self.representation.Q_oneStepLookAhead(
s, a, self.ns_samples)
phi_s = self.representation.phi(s, terminal)
phi_s_a = self.representation.phi_sa(s, terminal, a, phi_s)
old_Q = np.dot(phi_s_a, self.representation.weight_vec)
bellman_error = new_Q - old_Q
# print s, old_Q, new_Q, bellman_error
self.representation.weight_vec += self.alpha * bellman_error * phi_s_a
bellmanUpdates += 1
step += 1
# Discover features if the representation has the discover method
discover_func = getattr(
self.representation, 'discover', None
) # None is the default value if the discover is not an attribute
if discover_func and callable(discover_func):
self.representation.discover(phi_s, bellman_error)
max_Bellman_Error = max(max_Bellman_Error, abs(bellman_error))
# Simulate new state and action on trajectory
_, s, terminal, p_actions = self.domain.step(a)
a = self.representation.bestAction(
s, terminal, p_actions
) if np.random.rand() > self.epsilon else randSet(p_actions)
# check for convergence
iteration += 1
if max_Bellman_Error < self.convergence_threshold:
converged_trajectories += 1
else:
converged_trajectories = 0
performance_return, performance_steps, performance_term, performance_discounted_return = self.performanceRun(
)
converged = converged_trajectories >= self.MIN_CONVERGED_TRAJECTORIES
self.logger.info(
'PI #%d [%s]: BellmanUpdates=%d, ||Bellman_Error||=%0.4f, Return=%0.4f, Steps=%d, Features=%d'
% (iteration, hhmmss(deltaT(self.start_time)), bellmanUpdates,
max_Bellman_Error, performance_return, performance_steps,
self.representation.features_num))
if self.show:
self.domain.show(a, representation=self.representation, s=s)
# store stats
self.result["bellman_updates"].append(bellmanUpdates)
self.result["return"].append(performance_return)
self.result["planning_time"].append(deltaT(self.start_time))
self.result["num_features"].append(
self.representation.features_num)
self.result["steps"].append(performance_steps)
self.result["terminated"].append(performance_term)
self.result["discounted_return"].append(
performance_discounted_return)
self.result["iteration"].append(iteration)
if converged:
self.logger.info('Converged!')
super(TrajectoryBasedValueIteration, self).solve()
def solveInMatrixFormat(self):
# while delta_weight_vec > threshold
# 1. Gather data following an e-greedy policy
# 2. Calculate A and b estimates
# 3. calculate new_weight_vec, and delta_weight_vec
# return policy greedy w.r.t last weight_vec
self.policy = eGreedy(self.representation, epsilon=self.epsilon)
# Number of samples to be used for each policy evaluation phase. L1 in
# the Geramifard et. al. FTML 2012 paper
self.samples_num = 1000
self.start_time = clock() # Used to track the total time for solving
samples = 0
converged = False
iteration = 0
while self.hasTime() and not converged:
# 1. Gather samples following an e-greedy policy
S, Actions, NS, R, T = self.collectSamples(self.samples_num)
samples += self.samples_num
# 2. Calculate A and b estimates
a_num = self.domain.actions_num
n = self.representation.features_num
discount_factor = self.domain.discount_factor
self.A = np.zeros((n * a_num, n * a_num))
self.b = np.zeros((n * a_num, 1))
for i in range(self.samples_num):
phi_s_a = self.representation.phi_sa(S[i], T[i],
Actions[i, 0]).reshape(
(-1, 1))
E_phi_ns_na = self.calculate_expected_phi_ns_na(
S[i], Actions[i, 0], self.ns_samples).reshape((-1, 1))
d = phi_s_a - discount_factor * E_phi_ns_na
self.A += np.outer(phi_s_a, d.T)
self.b += phi_s_a * R[i, 0]
# 3. calculate new_weight_vec, and delta_weight_vec
new_weight_vec, solve_time = solveLinear(regularize(self.A),
self.b)
iteration += 1
if solve_time > 1:
self.logger.info(
'#%d: Finished Policy Evaluation. Solve Time = %0.2f(s)' %
(iteration, solve_time))
delta_weight_vec = l_norm(
new_weight_vec - self.representation.weight_vec, np.inf)
converged = delta_weight_vec < self.convergence_threshold
self.representation.weight_vec = new_weight_vec
performance_return, performance_steps, performance_term, performance_discounted_return = self.performanceRun(
)
self.logger.info(
'#%d [%s]: Samples=%d, ||weight-Change||=%0.4f, Return = %0.4f'
% (iteration, hhmmss(deltaT(self.start_time)), samples,
delta_weight_vec, performance_return))
if self.show:
self.domain.show(S[-1], Actions[-1], self.representation)
# store stats
self.result["samples"].append(samples)
self.result["return"].append(performance_return)
self.result["planning_time"].append(deltaT(self.start_time))
self.result["num_features"].append(
self.representation.features_num)
self.result["steps"].append(performance_steps)
self.result["terminated"].append(performance_term)
self.result["discounted_return"].append(
performance_discounted_return)
self.result["iteration"].append(iteration)
if converged:
self.logger.info('Converged!')
super(TrajectoryBasedPolicyIteration, self).solve()
def solve(self):
"""Solve the domain MDP."""
self.start_time = clock() # Used to show the total time took the process
bellmanUpdates = 0 # used to track the performance improvement.
converged = False
iteration = 0
# Check for Tabular Representation
if not self.IsTabularRepresentation():
self.logger.error("Value Iteration works only with a tabular representation.")
return 0
no_of_states = self.representation.agg_states_num
while self.hasTime() and not converged:
iteration += 1
# Store the weight vector for comparison
prev_weight_vec = self.representation.weight_vec.copy()
# Sweep The State Space
for i in range(no_of_states):
s = self.representation.stateID2state(i)
# Sweep through possible actions
for a in self.domain.possibleActions(s):
# Check for available planning time
if not self.hasTime(): break
self.BellmanBackup(s, a, ns_samples=self.ns_samples)
bellmanUpdates += 1
# Create Log
if bellmanUpdates % self.log_interval == 0:
performance_return, _, _, _ = self.performanceRun()
self.logger.info(
'[%s]: BellmanUpdates=%d, Return=%0.4f' %
(hhmmss(deltaT(self.start_time)), bellmanUpdates, performance_return))
# check for convergence
weight_vec_change = l_norm(prev_weight_vec - self.representation.weight_vec, np.inf)
converged = weight_vec_change < self.convergence_threshold
# log the stats
performance_return, performance_steps, performance_term, performance_discounted_return = self.performanceRun()
self.logger.info(
'PI #%d [%s]: BellmanUpdates=%d, ||delta-weight_vec||=%0.4f, Return=%0.4f, Steps=%d' % (iteration,
hhmmss(deltaT(self.start_time)),
bellmanUpdates,
weight_vec_change,
performance_return,
performance_steps))
# Show the domain and value function
if self.show:
self.domain.show(a, s=s, representation=self.representation)
# store stats
self.result["bellman_updates"].append(bellmanUpdates)
self.result["return"].append(performance_return)
self.result["planning_time"].append(deltaT(self.start_time))
self.result["num_features"].append(self.representation.features_num)
self.result["steps"].append(performance_steps)
self.result["terminated"].append(performance_term)
self.result["discounted_return"].append(performance_discounted_return)
self.result["iteration"].append(iteration)
if converged: self.logger.info('Converged!')
super(ValueIteration, self).solve()