class MLP(Policy):
def __init__(self, is_train=False):
root_dir = os.path.dirname(
os.path.dirname(
os.path.dirname(os.path.dirname(os.path.abspath(__file__)))))
self.is_train = is_train
with open(
os.path.join(os.path.dirname(os.path.abspath(__file__)),
'config.json'), 'r') as f:
cfg = json.load(f)
voc_file = os.path.join(root_dir, 'data/camrest/sys_da_voc.txt')
voc_opp_file = os.path.join(root_dir, 'data/camrest/usr_da_voc.txt')
self.vector = CamrestVector(voc_file, voc_opp_file)
self.policy = MultiDiscretePolicy(self.vector.state_dim, cfg['h_dim'],
self.vector.da_dim).to(device=DEVICE)
self.load(cfg['load'])
def predict(self, state):
"""
Predict an system action given state.
Args:
state (dict): Dialog state. Please refer to util/state.py
Returns:
action : System act, with the form of (act_type, {slot_name_1: value_1, slot_name_2, value_2, ...})
"""
s_vec = torch.Tensor(self.vector.state_vectorize(state))
a = self.policy.select_action(s_vec.to(device=DEVICE)).cpu()
action = self.vector.action_devectorize(a.numpy())
return action
def init_session(self):
"""
Restore after one session
"""
pass
def load(self, filename):
policy_mdl = os.path.join(os.path.dirname(os.path.abspath(__file__)),
filename + '_mle.pol.mdl')
if os.path.exists(policy_mdl):
self.policy.load_state_dict(torch.load(policy_mdl))
print('<<dialog policy>> loaded checkpoint from file: {}'.format(
policy_mdl))
class PG(Policy):
def __init__(self, is_train=False, dataset='Multiwoz'):
with open(os.path.join(os.path.dirname(os.path.abspath(__file__)), 'config.json'), 'r') as f:
cfg = json.load(f)
self.save_dir = os.path.join(os.path.dirname(os.path.abspath(__file__)), cfg['save_dir'])
self.save_per_epoch = cfg['save_per_epoch']
self.update_round = cfg['update_round']
self.optim_batchsz = cfg['batchsz']
self.gamma = cfg['gamma']
self.is_train = is_train
if is_train:
init_logging_handler(cfg['log_dir'])
if dataset == 'Multiwoz':
voc_file = os.path.join(root_dir, 'data/multiwoz/sys_da_voc.txt')
voc_opp_file = os.path.join(root_dir, 'data/multiwoz/usr_da_voc.txt')
self.vector = MultiWozVector(voc_file, voc_opp_file)
self.policy = MultiDiscretePolicy(self.vector.state_dim, cfg['h_dim'], self.vector.da_dim).to(device=DEVICE)
# self.policy = MultiDiscretePolicy(self.vector.state_dim, cfg['h_dim'], self.vector.da_dim).to(device=DEVICE)
if is_train:
self.policy_optim = optim.RMSprop(self.policy.parameters(), lr=cfg['lr'])
def predict(self, state):
"""
Predict an system action given state.
Args:
state (dict): Dialog state. Please refer to util/state.py
Returns:
action : System act, with the form of (act_type, {slot_name_1: value_1, slot_name_2, value_2, ...})
"""
s_vec = torch.Tensor(self.vector.state_vectorize(state))
a = self.policy.select_action(s_vec.to(device=DEVICE), self.is_train).cpu()
action = self.vector.action_devectorize(a.numpy())
return action
def init_session(self):
"""
Restore after one session
"""
pass
def est_return(self, r, mask):
"""
we save a trajectory in continuous space and it reaches the ending of current trajectory when mask=0.
:param r: reward, Tensor, [b]
:param mask: indicates ending for 0 otherwise 1, Tensor, [b]
:return: V-target(s), Tensor
"""
batchsz = r.size(0)
# v_target is worked out by Bellman equation.
v_target = torch.Tensor(batchsz).to(device=DEVICE)
prev_v_target = 0
for t in reversed(range(batchsz)):
# mask here indicates a end of trajectory
# this value will be treated as the target value of value network.
# mask = 0 means the immediate reward is the real V(s) since it's end of trajectory.
# formula: V(s_t) = r_t + gamma * V(s_t+1)
v_target[t] = r[t] + self.gamma * prev_v_target * mask[t]
# update previous
prev_v_target = v_target[t]
return v_target
def update(self, epoch, batchsz, s, a, r, mask):
v_target = self.est_return(r, mask)
for i in range(self.update_round):
# 1. shuffle current batch
perm = torch.randperm(batchsz)
# shuffle the variable for mutliple optimize
v_target_shuf, s_shuf, a_shuf = v_target[perm], s[perm], a[perm]
# 2. get mini-batch for optimizing
optim_chunk_num = int(np.ceil(batchsz / self.optim_batchsz))
# chunk the optim_batch for total batch
v_target_shuf, s_shuf, a_shuf = torch.chunk(v_target_shuf, optim_chunk_num), \
torch.chunk(s_shuf, optim_chunk_num), \
torch.chunk(a_shuf, optim_chunk_num)
# 3. iterate all mini-batch to optimize
policy_loss = 0.
for v_target_b, s_b, a_b in zip(v_target_shuf, s_shuf, a_shuf):
# print('optim:', batchsz, v_target_b.size(), A_sa_b.size(), s_b.size(), a_b.size(), log_pi_old_sa_b.size())
# update policy network by clipping
self.policy_optim.zero_grad()
# [b, 1]
log_pi_sa = self.policy.get_log_prob(s_b, a_b)
# ratio = exp(log_Pi(a|s) - log_Pi_old(a|s)) = Pi(a|s) / Pi_old(a|s)
# we use log_pi for stability of numerical operation
# [b, 1] => [b]
# this is element-wise comparing.
# we add negative symbol to convert gradient ascent to gradient descent
surrogate = - (log_pi_sa * v_target_b).mean()
policy_loss += surrogate.item()
# backprop
surrogate.backward()
# gradient clipping, for stability
torch.nn.utils.clip_grad_norm(self.policy.parameters(), 10)
# self.lock.acquire() # retain lock to update weights
self.policy_optim.step()
# self.lock.release() # release lock
policy_loss /= optim_chunk_num
logging.debug('<<dialog policy pg>> epoch {}, iteration {}, policy, loss {}'.format(epoch, i, policy_loss))
if (epoch + 1) % self.save_per_epoch == 0:
self.save(self.save_dir, epoch)
def save(self, directory, epoch):
if not os.path.exists(directory):
os.makedirs(directory)
torch.save(self.policy.state_dict(), directory + '/' + str(epoch) + '_pg.pol.mdl')
logging.info('<<dialog policy>> epoch {}: saved network to mdl'.format(epoch))
def load(self, filename):
policy_mdl = os.path.join(os.path.dirname(os.path.abspath(__file__)), filename + '_pg.pol.mdl')
if os.path.exists(policy_mdl):
self.policy.load_state_dict(torch.load(policy_mdl))
print('<<dialog policy>> loaded checkpoint from file: {}'.format(policy_mdl))
class MLE_Trainer():
def __init__(self, manager, cfg):
self.data_train = manager.create_dataset('train', cfg['batchsz'])
self.data_valid = manager.create_dataset('val', cfg['batchsz'])
self.data_test = manager.create_dataset('test', cfg['batchsz'])
self.save_dir = cfg['save_dir']
self.print_per_batch = cfg['print_per_batch']
self.save_per_epoch = cfg['save_per_epoch']
voc_file = os.path.join(root_dir, 'data/crosswoz/sys_da_voc.json')
voc_opp_file = os.path.join(root_dir, 'data/crosswoz/usr_da_voc.json')
vector = CrossWozVector(voc_file, voc_opp_file)
self.policy = MultiDiscretePolicy(vector.state_dim, cfg['h_dim'],
vector.sys_da_dim).to(device=DEVICE)
self.policy.eval()
self.policy_optim = torch.optim.Adam(self.policy.parameters(),
lr=cfg['lr'])
self.multi_entropy_loss = nn.MultiLabelSoftMarginLoss()
def policy_loop(self, data):
s, target_a = to_device(data)
a_weights = self.policy(s)
loss_a = self.multi_entropy_loss(a_weights, target_a)
return loss_a
def imitating(self, epoch):
"""
pretrain the policy by simple imitation learning (behavioral cloning)
"""
self.policy.train()
a_loss = 0.
for i, data in enumerate(self.data_train):
self.policy_optim.zero_grad()
loss_a = self.policy_loop(data)
a_loss += loss_a.item()
loss_a.backward()
self.policy_optim.step()
if (i + 1) % self.print_per_batch == 0:
a_loss /= self.print_per_batch
logging.debug(
'<<dialog policy>> epoch {}, iter {}, loss_a:{}'.format(
epoch, i, a_loss))
a_loss = 0.
if (epoch + 1) % self.save_per_epoch == 0:
self.save(self.save_dir, epoch)
self.policy.eval()
def imit_test(self, epoch, best):
"""
provide an unbiased evaluation of the policy fit on the training dataset
"""
a_loss = 0.
for i, data in enumerate(self.data_valid):
loss_a = self.policy_loop(data)
a_loss += loss_a.item()
a_loss /= len(self.data_valid)
logging.debug(
'<<dialog policy>> validation, epoch {}, loss_a:{}'.format(
epoch, a_loss))
if a_loss < best:
logging.info('<<dialog policy>> best model saved')
best = a_loss
self.save(self.save_dir, 'best')
a_loss = 0.
for i, data in enumerate(self.data_test):
loss_a = self.policy_loop(data)
a_loss += loss_a.item()
a_loss /= len(self.data_test)
logging.debug('<<dialog policy>> test, epoch {}, loss_a:{}'.format(
epoch, a_loss))
return best
def test(self):
def f1(a, target):
TP, FP, FN = 0, 0, 0
real = target.nonzero().tolist()
predict = a.nonzero().tolist()
# print(real)
# print(predict)
# print()
for item in real:
if item in predict:
TP += 1
else:
FN += 1
for item in predict:
if item not in real:
FP += 1
return TP, FP, FN
a_TP, a_FP, a_FN = 0, 0, 0
for i, data in enumerate(self.data_test):
s, target_a = to_device(data)
a_weights = self.policy(s)
a = a_weights.ge(0)
# TODO: fix batch F1
TP, FP, FN = f1(a, target_a)
a_TP += TP
a_FP += FP
a_FN += FN
prec = a_TP / (a_TP + a_FP)
rec = a_TP / (a_TP + a_FN)
F1 = 2 * prec * rec / (prec + rec)
print(a_TP, a_FP, a_FN, F1)
def save(self, directory, epoch):
if not os.path.exists(directory):
os.makedirs(directory)
torch.save(self.policy.state_dict(),
directory + '/' + str(epoch) + '_mle.pol.mdl')
logging.info(
'<<dialog policy>> epoch {}: saved network to mdl'.format(epoch))
def load(self, filename='save/best'):
policy_mdl = os.path.join(os.path.dirname(os.path.abspath(__file__)),
filename + '_mle.pol.mdl')
if os.path.exists(policy_mdl):
self.policy.load_state_dict(torch.load(policy_mdl))
class MLE(Policy):
def __init__(
self,
archive_file=DEFAULT_ARCHIVE_FILE,
model_file='https://tatk-data.s3-ap-northeast-1.amazonaws.com/mle_policy_camrest.zip'
):
root_dir = os.path.dirname(
os.path.dirname(
os.path.dirname(
os.path.dirname(os.path.dirname(
os.path.abspath(__file__))))))
with open(
os.path.join(os.path.dirname(os.path.abspath(__file__)),
'config.json'), 'r') as f:
cfg = json.load(f)
voc_file = os.path.join(root_dir, 'data/camrest/sys_da_voc.txt')
voc_opp_file = os.path.join(root_dir, 'data/camrest/usr_da_voc.txt')
self.vector = CamrestVector(voc_file, voc_opp_file)
self.policy = MultiDiscretePolicy(self.vector.state_dim, cfg['h_dim'],
self.vector.da_dim).to(device=DEVICE)
if not os.path.isfile(archive_file):
if not model_file:
raise Exception("No model for MLE Policy is specified!")
archive_file = cached_path(model_file)
model_dir = os.path.join(os.path.dirname(os.path.abspath(__file__)),
'save')
if not os.path.exists(model_dir):
os.mkdir(model_dir)
if not os.path.exists(os.path.join(model_dir, 'best_mle.pol.mdl')):
archive = zipfile.ZipFile(archive_file, 'r')
archive.extractall(model_dir)
self.load(cfg['load'])
def predict(self, state):
"""
Predict an system action given state.
Args:
state (dict): Dialog state. Please refer to util/state.py
Returns:
action : System act, with the form of (act_type, {slot_name_1: value_1, slot_name_2, value_2, ...})
"""
s_vec = torch.Tensor(self.vector.state_vectorize(state))
a = self.policy.select_action(s_vec.to(device=DEVICE)).cpu()
action = self.vector.action_devectorize(a.numpy())
return action
def init_session(self):
"""
Restore after one session
"""
pass
def load(self, filename):
policy_mdl = os.path.join(os.path.dirname(os.path.abspath(__file__)),
filename + '_mle.pol.mdl')
if os.path.exists(policy_mdl):
self.policy.load_state_dict(torch.load(policy_mdl))
print('<<dialog policy>> loaded checkpoint from file: {}'.format(
policy_mdl))
class PPO(Policy):
def __init__(self, is_train=False, dataset='Multiwoz'):
with open(os.path.join(os.path.dirname(os.path.abspath(__file__)), 'config.json'), 'r') as f:
cfg = json.load(f)
self.save_dir = os.path.join(os.path.dirname(os.path.abspath(__file__)), cfg['save_dir'])
self.save_per_epoch = cfg['save_per_epoch']
self.update_round = cfg['update_round']
self.optim_batchsz = cfg['batchsz']
self.gamma = cfg['gamma']
self.epsilon = cfg['epsilon']
self.tau = cfg['tau']
self.is_train = is_train
if is_train:
init_logging_handler(os.path.join(os.path.dirname(os.path.abspath(__file__)), cfg['log_dir']))
# construct policy and value network
if dataset == 'Multiwoz':
voc_file = os.path.join(root_dir, 'data/multiwoz/sys_da_voc.txt')
voc_opp_file = os.path.join(root_dir, 'data/multiwoz/usr_da_voc.txt')
self.vector = MultiWozVector(voc_file, voc_opp_file)
self.policy = MultiDiscretePolicy(self.vector.state_dim, cfg['h_dim'], self.vector.da_dim).to(device=DEVICE)
self.value = Value(self.vector.state_dim, cfg['hv_dim']).to(device=DEVICE)
if is_train:
self.policy_optim = optim.RMSprop(self.policy.parameters(), lr=cfg['lr'])
self.value_optim = optim.Adam(self.value.parameters(), lr=cfg['lr'])
def predict(self, state):
"""
Predict an system action given state.
Args:
state (dict): Dialog state. Please refer to util/state.py
Returns:
action : System act, with the form of (act_type, {slot_name_1: value_1, slot_name_2, value_2, ...})
"""
s_vec = torch.Tensor(self.vector.state_vectorize(state))
a = self.policy.select_action(s_vec.to(device=DEVICE), self.is_train).cpu()
return self.vector.action_devectorize(a.numpy())
def init_session(self):
"""
Restore after one session
"""
pass
def est_adv(self, r, v, mask):
"""
we save a trajectory in continuous space and it reaches the ending of current trajectory when mask=0.
:param r: reward, Tensor, [b]
:param v: estimated value, Tensor, [b]
:param mask: indicates ending for 0 otherwise 1, Tensor, [b]
:return: A(s, a), V-target(s), both Tensor
"""
batchsz = v.size(0)
# v_target is worked out by Bellman equation.
v_target = torch.Tensor(batchsz).to(device=DEVICE)
delta = torch.Tensor(batchsz).to(device=DEVICE)
A_sa = torch.Tensor(batchsz).to(device=DEVICE)
prev_v_target = 0
prev_v = 0
prev_A_sa = 0
for t in reversed(range(batchsz)):
# mask here indicates a end of trajectory
# this value will be treated as the target value of value network.
# mask = 0 means the immediate reward is the real V(s) since it's end of trajectory.
# formula: V(s_t) = r_t + gamma * V(s_t+1)
v_target[t] = r[t] + self.gamma * prev_v_target * mask[t]
# please refer to : https://arxiv.org/abs/1506.02438
# for generalized adavantage estimation
# formula: delta(s_t) = r_t + gamma * V(s_t+1) - V(s_t)
delta[t] = r[t] + self.gamma * prev_v * mask[t] - v[t]
# formula: A(s, a) = delta(s_t) + gamma * lamda * A(s_t+1, a_t+1)
# here use symbol tau as lambda, but original paper uses symbol lambda.
A_sa[t] = delta[t] + self.gamma * self.tau * prev_A_sa * mask[t]
# update previous
prev_v_target = v_target[t]
prev_v = v[t]
prev_A_sa = A_sa[t]
# normalize A_sa
A_sa = (A_sa - A_sa.mean()) / A_sa.std()
return A_sa, v_target
def update(self, epoch, batchsz, s, a, r, mask):
# get estimated V(s) and PI_old(s, a)
# actually, PI_old(s, a) can be saved when interacting with env, so as to save the time of one forward elapsed
# v: [b, 1] => [b]
v = self.value(s).squeeze(-1).detach()
log_pi_old_sa = self.policy.get_log_prob(s, a).detach()
# estimate advantage and v_target according to GAE and Bellman Equation
A_sa, v_target = self.est_adv(r, v, mask)
for i in range(self.update_round):
# 1. shuffle current batch
perm = torch.randperm(batchsz)
# shuffle the variable for mutliple optimize
v_target_shuf, A_sa_shuf, s_shuf, a_shuf, log_pi_old_sa_shuf = v_target[perm], A_sa[perm], s[perm], a[perm], \
log_pi_old_sa[perm]
# 2. get mini-batch for optimizing
optim_chunk_num = int(np.ceil(batchsz / self.optim_batchsz))
# chunk the optim_batch for total batch
v_target_shuf, A_sa_shuf, s_shuf, a_shuf, log_pi_old_sa_shuf = torch.chunk(v_target_shuf, optim_chunk_num), \
torch.chunk(A_sa_shuf, optim_chunk_num), \
torch.chunk(s_shuf, optim_chunk_num), \
torch.chunk(a_shuf, optim_chunk_num), \
torch.chunk(log_pi_old_sa_shuf,
optim_chunk_num)
# 3. iterate all mini-batch to optimize
policy_loss, value_loss = 0., 0.
for v_target_b, A_sa_b, s_b, a_b, log_pi_old_sa_b in zip(v_target_shuf, A_sa_shuf, s_shuf, a_shuf,
log_pi_old_sa_shuf):
# print('optim:', batchsz, v_target_b.size(), A_sa_b.size(), s_b.size(), a_b.size(), log_pi_old_sa_b.size())
# 1. update value network
self.value_optim.zero_grad()
v_b = self.value(s_b).squeeze(-1)
loss = (v_b - v_target_b).pow(2).mean()
value_loss += loss.item()
# backprop
loss.backward()
# nn.utils.clip_grad_norm(self.value.parameters(), 4)
self.value_optim.step()
# 2. update policy network by clipping
self.policy_optim.zero_grad()
# [b, 1]
log_pi_sa = self.policy.get_log_prob(s_b, a_b)
# ratio = exp(log_Pi(a|s) - log_Pi_old(a|s)) = Pi(a|s) / Pi_old(a|s)
# we use log_pi for stability of numerical operation
# [b, 1] => [b]
ratio = (log_pi_sa - log_pi_old_sa_b).exp().squeeze(-1)
surrogate1 = ratio * A_sa_b
surrogate2 = torch.clamp(ratio, 1 - self.epsilon, 1 + self.epsilon) * A_sa_b
# this is element-wise comparing.
# we add negative symbol to convert gradient ascent to gradient descent
surrogate = - torch.min(surrogate1, surrogate2).mean()
policy_loss += surrogate.item()
# backprop
surrogate.backward()
# gradient clipping, for stability
torch.nn.utils.clip_grad_norm(self.policy.parameters(), 10)
# self.lock.acquire() # retain lock to update weights
self.policy_optim.step()
# self.lock.release() # release lock
value_loss /= optim_chunk_num
policy_loss /= optim_chunk_num
logging.debug('<<dialog policy ppo>> epoch {}, iteration {}, value, loss {}'.format(epoch, i, value_loss))
logging.debug('<<dialog policy ppo>> epoch {}, iteration {}, policy, loss {}'.format(epoch, i, policy_loss))
if (epoch+1) % self.save_per_epoch == 0:
self.save(self.save_dir, epoch)
def save(self, directory, epoch):
if not os.path.exists(directory):
os.makedirs(directory)
torch.save(self.value.state_dict(), directory + '/' + str(epoch) + '_ppo.val.mdl')
torch.save(self.policy.state_dict(), directory + '/' + str(epoch) + '_ppo.pol.mdl')
logging.info('<<dialog policy>> epoch {}: saved network to mdl'.format(epoch))
def load(self, filename):
value_mdl = os.path.join(os.path.dirname(os.path.abspath(__file__)), filename + '_ppo.val.mdl')
if os.path.exists(value_mdl):
self.value.load_state_dict(torch.load(value_mdl))
print('<<dialog policy>> loaded checkpoint from file: {}'.format(value_mdl))
policy_mdl = os.path.join(os.path.dirname(os.path.abspath(__file__)), filename + '_ppo.pol.mdl')
if os.path.exists(policy_mdl):
self.policy.load_state_dict(torch.load(policy_mdl))
print('<<dialog policy>> loaded checkpoint from file: {}'.format(policy_mdl))
class MLE_Trainer():
def __init__(self, manager, cfg):
self.data_train = manager.create_dataset('train', cfg['batchsz'])
self.data_valid = manager.create_dataset('val', cfg['batchsz'])
self.data_test = manager.create_dataset('test', cfg['batchsz'])
self.save_dir = cfg['save_dir']
self.print_per_batch = cfg['print_per_batch']
self.save_per_epoch = cfg['save_per_epoch']
voc_file = os.path.join(root_dir, 'data/multiwoz/sys_da_voc.txt')
voc_opp_file = os.path.join(root_dir, 'data/multiwoz/usr_da_voc.txt')
vector = MultiWozVector(voc_file, voc_opp_file)
self.policy = MultiDiscretePolicy(vector.state_dim, cfg['h_dim'],
vector.da_dim).to(device=DEVICE)
self.policy.eval()
self.policy_optim = torch.optim.Adam(self.policy.parameters(),
lr=cfg['lr'])
self.multi_entropy_loss = nn.MultiLabelSoftMarginLoss()
def policy_loop(self, data):
s, target_a = to_device(data)
a_weights = self.policy(s)
loss_a = self.multi_entropy_loss(a_weights, target_a)
return loss_a
def imitating(self, epoch):
"""
pretrain the policy by simple imitation learning (behavioral cloning)
"""
self.policy.train()
a_loss = 0.
for i, data in enumerate(self.data_train):
self.policy_optim.zero_grad()
loss_a = self.policy_loop(data)
a_loss += loss_a.item()
loss_a.backward()
self.policy_optim.step()
if (i + 1) % self.print_per_batch == 0:
a_loss /= self.print_per_batch
logging.debug(
'<<dialog policy>> epoch {}, iter {}, loss_a:{}'.format(
epoch, i, a_loss))
a_loss = 0.
if (epoch + 1) % self.save_per_epoch == 0:
self.save(self.save_dir, epoch)
self.policy.eval()
def imit_test(self, epoch, best):
"""
provide an unbiased evaluation of the policy fit on the training dataset
"""
a_loss = 0.
for i, data in enumerate(self.data_valid):
loss_a = self.policy_loop(data)
a_loss += loss_a.item()
a_loss /= len(self.data_valid)
logging.debug(
'<<dialog policy>> validation, epoch {}, loss_a:{}'.format(
epoch, a_loss))
if a_loss < best:
logging.info('<<dialog policy>> best model saved')
best = a_loss
self.save(self.save_dir, 'best')
a_loss = 0.
for i, data in enumerate(self.data_test):
loss_a = self.policy_loop(data)
a_loss += loss_a.item()
a_loss /= len(self.data_test)
logging.debug('<<dialog policy>> test, epoch {}, loss_a:{}'.format(
epoch, a_loss))
return best
def save(self, directory, epoch):
if not os.path.exists(directory):
os.makedirs(directory)
torch.save(self.policy.state_dict(),
directory + '/' + str(epoch) + '_mle.pol.mdl')
logging.info(
'<<dialog policy>> epoch {}: saved network to mdl'.format(epoch))
def load(self, filename):
policy_mdl = filename + '_mle.pol.mdl'
if os.path.exists(policy_mdl):
self.policy.load_state_dict(torch.load(policy_mdl))
logging.info(
'<<dialog policy>> loaded checkpoint from file: {}'.format(
policy_mdl))
best_pkl = filename + '.pkl'
if os.path.exists(best_pkl):
with open(best_pkl, 'rb') as f:
best = pickle.load(f)
else:
best = float('inf')
return best