agent1 = agents[i]
agent2 = agents[j]
if i == j:
cov_mat[i][j] = variances[agents[i]]
elif (i != j) and (agent1 == agent2):
cov_mat[i][j] = intra_covs[agent1 + agent2]
cov_mat[j][i] = intra_covs[agent1 + agent2]
else:
cov_mat[i][j] = inter_covs[''.join(sorted(agent1 + agent2))]
cov_mat[j][i] = inter_covs[''.join(sorted(agent1 + agent2))]
cov_mat = np.dot(np.matrix(cov_mat), np.matrix(cov_mat).T)
print(cov_mat)
means = [V for i in range(num_agents)]
draw = multi_norm(means, cov_mat)
cov_mat = cov_mat.tolist()
variances = {
"A": cov_mat[0][0],
"B": cov_mat[len(cov_mat) - 1][len(cov_mat) - 1]
}
intra_covs = {
"AA": cov_mat[0][1],
"BB": cov_mat[len(cov_mat) - 1][len(cov_mat) - 2]
}
inter_covs = {
"AB": cov_mat[type_populations["A"] - 1][type_populations["A"] + 1]
from numpy.random import multivariate_normal as multi_norm cov = [[0.9, 0.7, 0.4], [0.7, 0.8, 0.3], [0.4, 0.3, 0.7]] means = [0, 0, 0] print(multi_norm(means, cov))
def smc2(actions, rewards, idx_blocks, choices, subj_idx, show_progress,
apply_rep, apply_weber, beta_softmax, temperature,
observational_noise):
assert (2 not in actions)
assert (0 in actions)
assert (1 in actions)
assert (apply_rep == 0 or apply_rep == 1)
assert (apply_weber == 0 or apply_weber == 1)
# Extract parameters from task description
actions = np.asarray(actions, dtype=np.intc)
rewards = np.ascontiguousarray(rewards)
idx_blocks = np.asarray(idx_blocks, dtype=np.intc)
N_samples = 1000
n_theta = 1000
coefficient = .5
T = actions.shape[0]
prev_action = -1
upp_bound_eta = 10.
if apply_rep:
n_param = 5
else:
n_param = 4
if apply_weber == 1:
upp_bound_eps = 1.
else:
upp_bound_eps = .5
# samples
samples = np.random.rand(n_theta, n_param)
if beta_softmax > 0:
temperature = False
samples[:, 2] = beta_softmax
sample_beta = False
upp_bound_beta = beta_softmax
else:
if temperature:
upp_bound_beta = np.sqrt(6) / (np.pi * 5)
else:
upp_bound_beta = 2.
samples[:, 2] = np.random.rand(n_theta) * upp_bound_beta
sample_beta = True
samples[:, 3] = np.random.rand(n_theta) * upp_bound_eps
if apply_rep:
samples[:, 4] = (2 * np.random.rand(n_theta) - 1) * upp_bound_eta
# variable memory
noisy_descendants = np.zeros([n_theta, N_samples, 2])
noisy_ancestors = np.zeros([n_theta, N_samples, 2])
weights_norm = np.zeros([n_theta, N_samples])
log_weights_a = np.zeros([n_theta])
ancestorsIndexes = np.ascontiguousarray(np.zeros(n_theta, dtype=np.intc))
logThetaWeights = np.zeros(n_theta)
logThetalkd = np.zeros(n_theta)
log_lkd = np.zeros(n_theta)
essList = np.zeros(T)
acceptance_list = []
marg_loglkd = 0
#move step variables
ancestors_indexes_p = np.ascontiguousarray(
np.zeros(N_samples, dtype=np.intc))
samples_new = np.zeros([n_theta, n_param])
weights_new = np.zeros([n_theta, N_samples])
states_new = np.zeros([n_theta, N_samples, 2])
logThetalkd_new = np.zeros(n_theta)
state_candidates = np.zeros([N_samples, 2])
state_candidates_a = np.zeros([N_samples, 2])
weights_candidates = np.zeros(N_samples)
# history of samples
noisy_history = np.zeros([T, 2])
if show_progress:
plt.figure(figsize=(15, 9))
plt.suptitle("noisy rl", fontsize=14)
plt.ion()
for t_idx in range(T):
# Print progress
if (t_idx + 1) % 10 == 0:
sys.stdout.write(' ' + str(t_idx + 1))
sys.stdout.flush()
print ' marg_loglkd ' + str(marg_loglkd)
prev_rew = np.ascontiguousarray(rewards[:, max(0, t_idx - 1)])
log_weights_a[:] = logThetaWeights
if t_idx > 0 and choices[t_idx - 1]:
assert (actions[max(0, t_idx - 1)] == prev_action)
smc_c.smc_update_2q_c(log_lkd, logThetalkd, noisy_descendants, noisy_ancestors, weights_norm, logThetaWeights, ancestorsIndexes, samples, \
idx_blocks, choices, prev_action, actions, prev_rew, t_idx, apply_rep, apply_weber, 2, temperature, observational_noise)
# save and update
marg_loglkd += logsumexp(log_weights_a +
log_lkd) - logsumexp(log_weights_a)
normalisedThetaWeights = uf.to_normalized_weights(logThetaWeights)
noisy_history[t_idx] = np.sum((normalisedThetaWeights * np.sum(
np.transpose(weights_norm * noisy_descendants.T), axis=1).T),
axis=1)
# Degeneray criterion
logEss = 2 * uf.log_sum(logThetaWeights) - uf.log_sum(
2 * logThetaWeights)
essList[t_idx] = np.exp(logEss)
# update repetition action
if choices[t_idx] == 1:
prev_action = actions[t_idx]
# Move step
if (essList[t_idx] < coefficient * n_theta):
acceptance_proba = 0
if not sample_beta:
samples_tmp = np.delete(samples, 2, axis=1)
mu_p = np.sum(samples_tmp.T * normalisedThetaWeights, axis=1)
Sigma_p = np.dot(
(samples_tmp - mu_p).T * normalisedThetaWeights,
(samples_tmp - mu_p))
else:
mu_p = np.sum(samples.T * normalisedThetaWeights, axis=1)
Sigma_p = np.dot((samples - mu_p).T * normalisedThetaWeights,
(samples - mu_p))
ancestorsIndexes[:] = uf.stratified_resampling(
normalisedThetaWeights)
for theta_idx in range(n_theta):
idx_traj = ancestorsIndexes[theta_idx]
while True:
sample_cand = np.array(samples[idx_traj])
sample_p = multi_norm(mu_p, Sigma_p)
sample_p_copy = np.array(sample_p)
if (not sample_beta) and apply_rep:
sample_p = np.array([
sample_p[0], sample_p[1], beta_softmax,
sample_p[2], sample_p[3]
])
sample_cand = np.delete(sample_cand, 2)
elif not sample_beta:
sample_p = np.array([
sample_p[0], sample_p[1], beta_softmax, sample_p[2]
])
sample_cand = np.delete(sample_cand, 2)
if apply_rep:
if sample_p[0] > 0 and sample_p[0] < 1 and sample_p[1] > 0 and sample_p[1] < 1. and sample_p[2] > 0 and sample_p[2] <= upp_bound_beta \
and sample_p[3] > 0 and sample_p[3] < upp_bound_eps and sample_p[4] > -upp_bound_eta and sample_p[4] < upp_bound_eta:
break
else:
if sample_p[0] > 0 and sample_p[0] < 1 and sample_p[1] > 0 and sample_p[1] < 1. and sample_p[2] > 0 and sample_p[2] <= upp_bound_beta \
and sample_p[3] > 0 and sample_p[3] < upp_bound_eps:
break
# Launch SMC
logmarglkd_p = smc_c.smc_2q_c(state_candidates, state_candidates_a, weights_candidates, sample_p, ancestors_indexes_p, \
idx_blocks, actions, rewards, choices, t_idx + 1, apply_rep, apply_weber, 2, temperature, observational_noise)
logAlpha = np.minimum(0, logmarglkd_p - logThetalkd[idx_traj] \
+ get_logtruncnorm(sample_cand, mu_p, Sigma_p) - get_logtruncnorm(sample_p_copy, mu_p, Sigma_p) )
# accept or reject
if np.log(np.random.rand()) < logAlpha:
acceptance_proba += 1.
samples_new[theta_idx] = sample_p
weights_new[theta_idx] = weights_candidates
states_new[theta_idx] = state_candidates
logThetalkd_new[theta_idx] = logmarglkd_p
else:
samples_new[theta_idx] = samples[idx_traj]
weights_new[theta_idx] = weights_norm[idx_traj]
states_new[theta_idx] = noisy_descendants[idx_traj]
logThetalkd_new[theta_idx] = logThetalkd[idx_traj]
print('\n')
print('acceptance ratio is ')
print(acceptance_proba / n_theta)
print('\n')
acceptance_list.append(acceptance_proba / n_theta)
weights_norm[:] = weights_new
logThetalkd[:] = logThetalkd_new
logThetaWeights[:] = np.zeros(n_theta)
noisy_descendants[:] = states_new
samples[:] = samples_new
normalisedThetaWeights = uf.to_normalized_weights(logThetaWeights)
if show_progress and t_idx % 10:
plt.subplot(3, 2, 1)
plt.plot(range(t_idx), noisy_history[:t_idx, 0], 'r')
plt.hold(True)
plt.plot(range(t_idx), noisy_history[:t_idx, 1], 'b')
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('Q-value 0 (red), and 1 (blue)')
plt.subplot(3, 2, 4)
plt.plot(range(t_idx), essList[:t_idx], 'b', linewidth=2)
plt.hold(True)
plt.plot(plt.gca().get_xlim(), [n_theta / 2, n_theta / 2],
'b--',
linewidth=2)
plt.axis([0, t_idx - 1, 0, n_theta]) # For speed
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('ess')
if temperature:
mean_beta = np.sum(normalisedThetaWeights *
(1. / samples[:, 2]))
std_beta = np.sqrt(
np.sum(normalisedThetaWeights * (1. / samples[:, 2])**2) -
mean_beta**2)
x = np.linspace(0., 200, 5000)
else:
mean_beta = np.sum(normalisedThetaWeights *
(10**samples[:, 2]))
std_beta = np.sqrt(
np.sum(normalisedThetaWeights * (10**samples[:, 2])**2) -
mean_beta**2)
x = np.linspace(0., 10**upp_bound_beta, 5000)
plt.subplot(3, 2, 3)
plt.plot(x, norm.pdf(x, mean_beta, std_beta), 'g')
plt.hold(True)
plt.plot([mean_beta, mean_beta],
plt.gca().get_ylim(),
'g',
linewidth=2)
plt.hold(False)
plt.xlabel('beta softmax')
plt.ylabel('pdf')
mean_alpha_0 = np.sum(normalisedThetaWeights * samples[:, 0])
std_alpha_0 = np.sqrt(
np.sum(normalisedThetaWeights * samples[:, 0]**2) -
mean_alpha_0**2)
mean_alpha_1 = np.sum(normalisedThetaWeights * samples[:, 1])
std_alpha_1 = np.sqrt(
np.sum(normalisedThetaWeights * samples[:, 1]**2) -
mean_alpha_1**2)
plt.subplot(3, 2, 2)
x = np.linspace(0., 1., 5000)
plt.plot(x, norm.pdf(x, mean_alpha_0, std_alpha_0), 'm')
plt.hold(True)
plt.plot([mean_alpha_0, mean_alpha_0], plt.gca().get_ylim(), 'm')
plt.plot(x, norm.pdf(x, mean_alpha_1, std_alpha_1), 'c')
plt.plot([mean_alpha_1, mean_alpha_1], plt.gca().get_ylim(), 'c')
plt.hold(False)
plt.xlabel('learning rates')
plt.ylabel('pdf')
mean_epsilon = np.sum(normalisedThetaWeights * samples[:, 3])
std_epsilon = np.sqrt(
np.sum(normalisedThetaWeights * samples[:, 3]**2) -
mean_epsilon**2)
plt.subplot(3, 2, 6)
x = np.linspace(0., upp_bound_eps, 5000)
if apply_rep == 1:
mean_rep = np.sum(normalisedThetaWeights * samples[:, 4])
std_rep = np.sqrt(
np.sum(normalisedThetaWeights * samples[:, 4]**2) -
mean_rep**2)
x = np.linspace(-2., 2., 5000)
plt.plot(x, norm.pdf(x, mean_rep, std_rep), 'y')
plt.hold(True)
plt.plot([mean_rep, mean_rep],
plt.gca().get_ylim(),
'y',
linewidth=2)
plt.plot(x, norm.pdf(x, mean_epsilon, std_epsilon), 'g')
plt.hold(True)
plt.plot([mean_epsilon, mean_epsilon],
plt.gca().get_ylim(),
'g',
linewidth=2)
plt.hold(False)
plt.xlabel('epsilon std (green), rep_bias (yellow)')
plt.ylabel('pdf')
plt.draw()
plt.show()
plt.pause(0.05)
return [
samples, noisy_history, acceptance_list, normalisedThetaWeights,
logThetalkd, marg_loglkd
]
def ibis(actions, rewards, choices, idx_blocks, subj_idx, apply_rep_bias,
apply_weber_decision_noise, curiosity_bias, show_progress,
temperature):
assert (2 not in actions)
assert (0 in actions)
assert (1 in actions)
actions = np.asarray(actions, dtype=np.intc)
rewards = np.ascontiguousarray(rewards)
choices = np.asarray(choices, dtype=np.intc)
idx_blocks = np.asarray(idx_blocks, dtype=np.intc)
nb_samples = 1000
T = actions.shape[0]
upp_bound_eta = 10.
# sample initialisation
if (apply_rep_bias or curiosity_bias) and apply_weber_decision_noise == 0:
samples = np.random.rand(nb_samples, 4)
if temperature:
upp_bound_beta = np.sqrt(6) / (np.pi * 5)
else:
upp_bound_beta = 2.
samples[:, 2] = np.random.rand(nb_samples) * upp_bound_beta
samples[:, 3] = upp_bound_eta * (np.random.rand(nb_samples) * 2. - 1.)
elif apply_weber_decision_noise == 0:
samples = np.random.rand(nb_samples, 3)
if temperature:
upp_bound_beta = np.sqrt(6) / (np.pi * 5)
else:
upp_bound_beta = 2.
samples[:, 2] = np.random.rand(nb_samples) * upp_bound_beta
elif apply_weber_decision_noise == 1:
if apply_rep_bias:
samples = np.random.rand(nb_samples, 5)
if temperature:
upp_bound_beta = np.sqrt(6) / (np.pi * 5)
else:
upp_bound_beta = 2.
samples[:,
4] = upp_bound_eta * (np.random.rand(nb_samples) * 2. - 1.)
else:
samples = np.random.rand(nb_samples, 4)
if temperature:
upp_bound_beta = np.sqrt(6) / (np.pi * 5)
else:
upp_bound_beta = 2.
upp_bound_k = 10
samples[:, 2] = np.random.rand(
nb_samples) * upp_bound_beta # bound on the beta
samples[:, 3] = np.random.rand(nb_samples) * upp_bound_k
Q_samples = np.zeros([nb_samples, 2])
prev_action = np.zeros(nb_samples) - 1
# ibis param
esslist = np.zeros(T)
log_weights = np.zeros(nb_samples)
weights_a = np.zeros(nb_samples)
p_loglkd = np.zeros(nb_samples)
loglkd = np.zeros(nb_samples)
marg_loglkd = 0
coefficient = .5
marg_loglkd_l = np.zeros(T)
acceptance_l = []
# move step param
if apply_rep_bias and apply_weber_decision_noise:
move_samples = np.zeros([nb_samples, 5])
elif apply_rep_bias or curiosity_bias:
move_samples = np.zeros([nb_samples, 4])
elif apply_weber_decision_noise:
move_samples = np.zeros([nb_samples, 4])
else:
move_samples = np.zeros([nb_samples, 3])
move_p_loglkd = np.zeros(nb_samples)
Q_samples_move = np.zeros([nb_samples, 2])
prev_action_move = np.zeros(nb_samples)
mean_Q = np.zeros([T, 2])
prediction_err = np.zeros(nb_samples)
prediction_err[:] = -np.inf
prediction_err_move = np.zeros(nb_samples)
if show_progress:
plt.figure(figsize=(15, 9))
plt.suptitle("noiseless rl", fontsize=14)
plt.ion()
# loop
for t_idx in range(T):
if (t_idx + 1) % 10 == 0:
sys.stdout.write(' ' + str(t_idx + 1) + ' ')
print 'marg_loglkd ' + str(marg_loglkd)
if (t_idx + 1) % 100 == 0: print('\n')
assert (len(np.unique(prev_action)) == 1)
# update step
weights_a[:] = log_weights
if idx_blocks[t_idx]:
Q_samples[:] = 0.5
prev_action[:] = -1
# loop over samples
for n_idx in range(nb_samples):
alpha_c = samples[n_idx, 0]
alpha_u = samples[n_idx, 1]
if temperature:
beta = 1. / samples[n_idx, 2]
else:
beta = 10**samples[n_idx, 2]
if apply_rep_bias or curiosity_bias:
eta = samples[n_idx, -1]
if apply_weber_decision_noise:
k_beta = samples[n_idx, 3]
# reweighting
if choices[t_idx] == 1 and prev_action[n_idx] != -1 and (
apply_rep_bias == 1
or curiosity_bias) and apply_weber_decision_noise == 0:
if apply_rep_bias:
value = 1. / (
1. +
np.exp(beta *
(Q_samples[n_idx, 0] - Q_samples[n_idx, 1]) -
np.sign(prev_action[n_idx] - .5) * eta))
loglkd[n_idx] = np.log((value**actions[t_idx]) *
(1 - value)**((1 - actions[t_idx])))
prev_action[n_idx] = actions[t_idx]
elif curiosity_bias:
try:
count_samples = t_idx - 1 - np.where(
actions[:t_idx] != actions[t_idx - 1])[0][-1]
except:
count_samples = t_idx
assert (count_samples > 0)
value = 1. / (1. + np.exp(
beta * (Q_samples[n_idx, 0] - Q_samples[n_idx, 1]) +
np.sign(prev_action[n_idx] - .5) * eta * count_samples)
)
loglkd[n_idx] = np.log((value**actions[t_idx]) *
(1 - value)**((1 - actions[t_idx])))
prev_action[n_idx] = actions[t_idx]
elif choices[t_idx] == 1 and apply_weber_decision_noise == 0:
value = 1. / (
1. + np.exp(beta *
(Q_samples[n_idx, 0] - Q_samples[n_idx, 1])))
loglkd[n_idx] = np.log((value**actions[t_idx]) *
(1 - value)**((1 - actions[t_idx])))
prev_action[n_idx] = actions[t_idx]
elif choices[
t_idx] == 1 and apply_weber_decision_noise == 1 and apply_rep_bias == 0:
beta_modified = beta / (1. + k_beta * prediction_err[n_idx])
value = 1. / (
1. + np.exp(beta_modified *
(Q_samples[n_idx, 0] - Q_samples[n_idx, 1])))
loglkd[n_idx] = np.log((value**actions[t_idx]) *
(1 - value)**((1 - actions[t_idx])))
prev_action[n_idx] = actions[t_idx]
elif choices[
t_idx] == 1 and apply_weber_decision_noise == 1 and apply_rep_bias == 1:
beta_modified = beta / (1. + k_beta * prediction_err[n_idx])
value = 1. / (
1. + np.exp(beta_modified *
(Q_samples[n_idx, 0] - Q_samples[n_idx, 1]) -
np.sign(prev_action[n_idx] - .5) * eta))
loglkd[n_idx] = np.log((value**actions[t_idx]) *
(1 - value)**((1 - actions[t_idx])))
prev_action[n_idx] = actions[t_idx]
else:
value = 1.
loglkd[n_idx] = 0.
if np.isnan(loglkd[n_idx]):
print t_idx
print n_idx
print beta
print value
raise Exception
p_loglkd[n_idx] = p_loglkd[n_idx] + loglkd[n_idx]
log_weights[n_idx] = log_weights[n_idx] + loglkd[n_idx]
# update step
if actions[t_idx] == 0:
prediction_err[n_idx] = np.abs(Q_samples[n_idx, 0] -
rewards[0, t_idx])
Q_samples[n_idx, 0] = (1 - alpha_c) * Q_samples[
n_idx, 0] + alpha_c * rewards[0, t_idx]
if not curiosity_bias:
Q_samples[n_idx, 1] = (1 - alpha_u) * Q_samples[
n_idx, 1] + alpha_u * rewards[1, t_idx]
else:
prediction_err[n_idx] = np.abs(Q_samples[n_idx, 1] -
rewards[1, t_idx])
if not curiosity_bias:
Q_samples[n_idx, 0] = (1 - alpha_u) * Q_samples[
n_idx, 0] + alpha_u * rewards[0, t_idx]
Q_samples[n_idx, 1] = (1 - alpha_c) * Q_samples[
n_idx, 1] + alpha_c * rewards[1, t_idx]
marg_loglkd += logsumexp(weights_a + loglkd) - logsumexp(weights_a)
marg_loglkd_l[t_idx] = marg_loglkd
ess = np.exp(2 * logsumexp(log_weights) - logsumexp(2 * log_weights))
esslist[t_idx] = ess
weights_a[:] = uf.to_normalized_weights(log_weights)
mean_Q[t_idx] = np.sum((Q_samples.T * weights_a).T, axis=0)
# move step
if ess < coefficient * nb_samples:
idxTrajectories = uf.stratified_resampling(weights_a)
mu_p = np.sum(samples.T * weights_a, axis=1)
Sigma_p = np.dot((samples - mu_p).T * weights_a, (samples - mu_p))
nb_acceptance = 0.
for n_idx in range(nb_samples):
idx_traj = idxTrajectories[n_idx]
while True:
sample_p = multi_norm(mu_p, Sigma_p)
if not apply_rep_bias and not apply_weber_decision_noise:
if sample_p[0] > 0 and sample_p[0] < 1 and sample_p[
1] > 0 and sample_p[1] < 1 and sample_p[
2] > 0 and sample_p[2] <= upp_bound_beta:
break
elif not apply_rep_bias and apply_weber_decision_noise:
if sample_p[0] > 0 and sample_p[0] < 1 and sample_p[1] > 0 and sample_p[1] < 1 \
and sample_p[2] > 0 and sample_p[2] <= upp_bound_beta and sample_p[3] > 0 and sample_p[3] <= upp_bound_k:
break
elif apply_rep_bias and not apply_weber_decision_noise:
if sample_p[0] > 0 and sample_p[0] < 1 and sample_p[1] > 0 and sample_p[1] < 1 \
and sample_p[2] > 0 and sample_p[2] <= upp_bound_beta and sample_p[3] > -upp_bound_eta and sample_p[3] < upp_bound_eta:
break
else:
if sample_p[0] > 0 and sample_p[0] < 1 and sample_p[1] > 0 and sample_p[1] < 1 \
and sample_p[2] > 0 and sample_p[2] <= upp_bound_beta and sample_p[3] > 0 and sample_p[3] < upp_bound_k \
and sample_p[-1] > -upp_bound_eta and sample_p[-1] < upp_bound_eta:
break
[loglkd_prop, Q_prop, prev_action_prop, prediction_err_prop
] = get_loglikelihood(sample_p, rewards, actions, choices,
idx_blocks, t_idx + 1, apply_rep_bias,
apply_weber_decision_noise,
curiosity_bias, temperature)
log_ratio = loglkd_prop - p_loglkd[idx_traj] \
+ get_logtruncnorm(samples[idx_traj], mu_p, Sigma_p) - get_logtruncnorm(sample_p, mu_p, Sigma_p)
log_ratio = np.minimum(log_ratio, 0)
if (np.log(np.random.rand()) < log_ratio):
nb_acceptance += 1.
move_samples[n_idx] = sample_p
move_p_loglkd[n_idx] = loglkd_prop
Q_samples_move[n_idx] = Q_prop
prediction_err_move[n_idx] = prediction_err_prop
else:
move_samples[n_idx] = samples[idx_traj]
move_p_loglkd[n_idx] = p_loglkd[idx_traj]
Q_samples_move[n_idx] = Q_samples[idx_traj]
prediction_err_move[n_idx] = prediction_err[idx_traj]
print 'acceptance ratio %s' % str(nb_acceptance / nb_samples)
assert (prev_action_prop == prev_action[0])
acceptance_l.append(nb_acceptance / nb_samples)
# move samples
samples[:] = move_samples
p_loglkd[:] = move_p_loglkd
log_weights[:] = 0.
Q_samples[:] = Q_samples_move
prediction_err[:] = prediction_err_move
if show_progress and t_idx % 10 == 0:
weights_a[:] = uf.to_normalized_weights(log_weights)
plt.subplot(3, 2, 1)
plt.plot(range(t_idx), mean_Q[:t_idx], 'm', linewidth=2)
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('Q values')
if apply_rep_bias == 1:
mean_rep = np.sum(weights_a * samples[:, 3])
std_rep = np.sqrt(
np.sum(weights_a * samples[:, 3]**2) - mean_rep**2)
plt.subplot(3, 2, 2)
x = np.linspace(-2., 2., 5000)
plt.plot(x, norm.pdf(x, mean_rep, std_rep), 'g')
plt.hold(True)
plt.plot([mean_rep, mean_rep],
plt.gca().get_ylim(),
'g',
linewidth=2)
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('rep param')
if temperature:
mean_beta = np.sum(weights_a * 1. / samples[:, 2])
std_beta = np.sqrt(
np.sum(weights_a * ((1. / samples[:, 2])**2)) -
mean_beta**2)
else:
mean_beta = np.sum(weights_a * 10**samples[:, 2])
std_beta = np.sqrt(
np.sum(weights_a * ((10**samples[:, 2])**2)) -
mean_beta**2)
if apply_weber_decision_noise:
mean_k = np.sum(weights_a * samples[:, 3])
std_k = np.sqrt(
np.sum(weights_a * (samples[:, 3]**2)) - mean_k**2)
plt.subplot(3, 2, 3)
x = np.linspace(0.01, 200., 5000)
plt.plot(x, norm.pdf(x, mean_beta, std_beta), 'g', linewidth=2)
plt.hold(True)
plt.plot([mean_beta, mean_beta],
plt.gca().get_ylim(),
'g',
linewidth=2)
plt.hold(False)
plt.xlabel('beta softmax')
plt.ylabel('pdf')
mean_alpha_0 = np.sum(weights_a * samples[:, 0])
std_alpha_0 = np.sqrt(
np.sum(weights_a * (samples[:, 0]**2)) - mean_alpha_0**2)
mean_alpha_1 = np.sum(weights_a * samples[:, 1])
std_alpha_1 = np.sqrt(
np.sum(weights_a * (samples[:, 1]**2)) - mean_alpha_1**2)
plt.subplot(3, 2, 4)
x = np.linspace(0., 1., 5000)
plt.plot(x,
norm.pdf(x, mean_alpha_0, std_alpha_0),
'm',
linewidth=2)
plt.hold(True)
plt.plot([mean_alpha_0, mean_alpha_0],
plt.gca().get_ylim(),
'm',
linewidth=2)
plt.plot(x,
norm.pdf(x, mean_alpha_1, std_alpha_1),
'c',
linewidth=2)
plt.plot([mean_alpha_1, mean_alpha_1],
plt.gca().get_ylim(),
'c',
linewidth=2)
plt.hold(False)
plt.xlabel('learning rate chosen (majenta) an unchosen (cyan)')
plt.ylabel('pdf')
plt.subplot(3, 2, 5)
plt.plot(range(t_idx), esslist[:t_idx], 'b', linewidth=2)
plt.hold(True)
plt.plot(plt.gca().get_xlim(), [nb_samples / 2, nb_samples / 2],
'b--',
linewidth=2)
plt.axis([0, t_idx - 1, 0, nb_samples])
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('ess')
# modified here add the plot for k
plt.subplot(3, 2, 6)
x = np.linspace(0.01, 10., 5000)
plt.plot(x, norm.pdf(x, mean_k, std_k), 'k', linewidth=2)
plt.hold(True)
plt.plot([mean_k, mean_k], plt.gca().get_ylim(), 'k', linewidth=2)
plt.hold(False)
plt.xlabel('scaling parameter for softmax 1/[0 1]')
plt.ylabel('pdf')
plt.draw()
plt.show()
plt.pause(0.05)
return [
samples, mean_Q, esslist, acceptance_l, log_weights, p_loglkd,
marg_loglkd_l
]
px = np.array(list(np.arange(0, 2, 0.02)))
for j in range(0, m):
mj = 2 * j / m
pphi[:, j] = ((px - mj) / s).reshape(100)
phi = 1 / (1 + np.exp(-phi))
pphi = 1 / (1 + np.exp(-pphi))
alpha = 10**(-6)
s0_inv = alpha * np.identity(3)
beta = 1
sn_inv = s0_inv + beta * phi.T.dot(phi)
sn = inv(sn_inv)
mn = sn.dot(beta * phi.T.dot(t[0:N]))
w = multi_norm(np.squeeze(mn), sn, 5)
plt.figure(figsize=(10, 8))
for i in range(5):
pt = pphi.dot(w[i, :])
plt.plot(px, pt, 'r')
plt.plot(x[0:N], t[0:N], 'ok', markerfacecolor='none')
pt_m = pphi.dot(mn)
plt.plot(px, pt_m, color='r')
plt.ylim(-1, 4)
sigma2 = 1 / beta + pphi.dot(sn).dot(pphi.T)
sigma = np.sqrt(sigma2)
sigma = np.diag(sigma)
plt.figure(figsize=(10, 8))
plt.plot(px, pt_m, 'r')
def ibis(actions, rewards, tau, subj_idx, apply_rep_bias, show_progress = True, temperature = True, model_id = 0):
'''
model_id = 0 : 1 alpha, 1 beta
model_id = 1 : n alpha, 1 beta
model_id = 2 : n alpha, n beta
'''
actions = np.asarray(actions, dtype=np.intc)
rewards = np.ascontiguousarray(rewards)
nb_samples = 1000
T = actions.shape[0]
upp_bound_eta = 10.
# sample initialisation
if model_id == 2:
n_alpha = 6
n_beta = 6
tau_unique = np.unique(tau)
x_coor_a = np.array([np.where(tau_unique == t)[0][0] for t in tau])
x_coor_b = np.array([np.where(tau_unique == t)[0][0] for t in tau]) + n_alpha
elif model_id == 1:
n_alpha = 6
n_beta = 1
tau_unique = np.unique(tau)
x_coor_a = np.array([np.where(tau_unique == t)[0][0] for t in tau])
x_coor_b = np.zeros(len(tau), dtype=np.int8) + n_alpha
else:
n_alpha = 1
n_beta = 1
x_coor_a = np.zeros(len(tau), dtype=np.int8)
x_coor_b = np.zeros(len(tau), dtype=np.int8) + n_alpha
n_theta = n_alpha + n_beta
if apply_rep_bias:
n_theta += 1
samples = np.random.rand(nb_samples, n_theta)
if temperature:
upp_bound_beta = .6
else:
upp_bound_beta = 2.
samples[:, n_alpha:(n_beta + n_alpha)] = np.random.rand(nb_samples, n_beta) * upp_bound_beta
if apply_rep_bias:
samples[:, -1] = upp_bound_eta * (np.random.rand(nb_samples) * 2. - 1.)
Q_samples = np.zeros([nb_samples, 2]) + .5
prev_action = np.zeros(nb_samples) - 1
# ibis param
esslist = np.zeros(T)
log_weights = np.zeros(nb_samples)
weights_a = np.zeros(nb_samples)
p_loglkd = np.zeros(nb_samples)
loglkd = np.zeros(nb_samples)
marg_loglkd = 0
coefficient = .5
marg_loglkd_l = np.zeros(T)
acceptance_l = []
# move step param
move_samples = np.zeros([nb_samples, n_theta])
move_p_loglkd = np.zeros(nb_samples)
Q_samples_move = np.zeros([nb_samples, 2])
prev_action_move = np.zeros(nb_samples)
mean_Q = np.zeros([T, 2])
if show_progress : plt.figure(figsize=(15,9)); plt.suptitle("noiseless rl", fontsize=14); plt.ion()
# loop
for t_idx in range(T):
#print t_idx
if (t_idx+1) % 10 == 0 : sys.stdout.write(' ' + str(t_idx+1) + ' '); print 'marg_loglkd ' + str(marg_loglkd);
if (t_idx+1) % 100 == 0: print ('\n')
# epsilon
assert(len(np.unique(prev_action)) == 1)
# update step
weights_a[:] = log_weights
for n_idx in range(nb_samples):
alpha = samples[n_idx, x_coor_a[t_idx]]
if temperature:
beta = 1./samples[n_idx, x_coor_b[t_idx]]
else:
beta = 10**samples[n_idx, x_coor_b[t_idx]]
if apply_rep_bias:
eta = samples[n_idx, -1]
if prev_action[n_idx] != -1 and apply_rep_bias:
value = 1./(1. + np.exp(beta * (Q_samples[n_idx, 0] - Q_samples[n_idx, 1]) - np.sign(prev_action[n_idx] - .5) * eta))
loglkd[n_idx] = np.log(((value)**actions[t_idx]) * (1 - value)**((1 - actions[t_idx])))
prev_action[n_idx] = actions[t_idx]
else:
value = 1./(1. + np.exp(beta * (Q_samples[n_idx, 0] - Q_samples[n_idx, 1])))
loglkd[n_idx] = np.log(((value)**actions[t_idx]) * (1 - value)**((1 - actions[t_idx])))
prev_action[n_idx] = actions[t_idx]
if np.isnan(loglkd[n_idx]):
print t_idx
print n_idx
print beta
print value
raise Exception
p_loglkd[n_idx] = p_loglkd[n_idx] + loglkd[n_idx]
log_weights[n_idx] = log_weights[n_idx] + loglkd[n_idx]
if actions[t_idx] == 0:
Q_samples[n_idx, 0] = (1 - alpha) * Q_samples[n_idx, 0] + alpha * rewards[t_idx]
Q_samples[n_idx, 1] = (1 - alpha) * Q_samples[n_idx, 1] + alpha * (1 - rewards[t_idx])
else:
Q_samples[n_idx, 0] = (1 - alpha) * Q_samples[n_idx, 0] + alpha * (1 - rewards[t_idx])
Q_samples[n_idx, 1] = (1 - alpha) * Q_samples[n_idx, 1] + alpha * rewards[t_idx]
marg_loglkd += logsumexp(weights_a + loglkd) - logsumexp(weights_a)
marg_loglkd_l[t_idx] = marg_loglkd
ess = np.exp(2 * logsumexp(log_weights) - logsumexp(2 * log_weights))
esslist[t_idx] = ess
weights_a[:] = uf.to_normalized_weights(log_weights)
mean_Q[t_idx] = np.sum((Q_samples.T * weights_a).T, axis=0)
# move step
if ess < coefficient * nb_samples:
idxTrajectories = uf.stratified_resampling(weights_a)
mu_p = np.sum(samples.T * weights_a, axis=1)
Sigma_p = np.dot((samples - mu_p).T * weights_a, (samples - mu_p))
nb_acceptance = 0.
for n_idx in range(nb_samples):
idx_traj = idxTrajectories[n_idx]
while True:
sample_p = multi_norm(mu_p, Sigma_p)
if not apply_rep_bias:
if np.all(sample_p[:n_alpha] > 0) and np.all(sample_p[:n_alpha] < 1) and np.all(sample_p[n_alpha:(n_beta + n_alpha)] > 0) and np.all(sample_p[n_alpha:(n_beta + n_alpha)] <= upp_bound_beta):
break
else:
if np.all(sample_p[:n_alpha] > 0) and np.all(sample_p[:n_alpha] < 1) and np.all(sample_p[n_alpha:(n_beta + n_alpha)] > 0) and np.all(sample_p[n_alpha:(n_beta + n_alpha)] <= upp_bound_beta) and sample_p[-1] > -upp_bound_eta and sample_p[-1] < upp_bound_eta:
break
[loglkd_prop, Q_prop, prev_action_prop] = get_loglikelihood(sample_p, x_coor_a, x_coor_b, rewards, actions, t_idx + 1, apply_rep_bias, temperature)
log_ratio = loglkd_prop - p_loglkd[idx_traj] \
+ get_logtruncnorm(samples[idx_traj], mu_p, Sigma_p) - get_logtruncnorm(sample_p, mu_p, Sigma_p)
log_ratio = np.minimum(log_ratio, 0)
if (np.log(np.random.rand()) < log_ratio):
nb_acceptance += 1.
move_samples[n_idx] = sample_p
move_p_loglkd[n_idx] = loglkd_prop
Q_samples_move[n_idx] = Q_prop
else:
move_samples[n_idx] = samples[idx_traj]
move_p_loglkd[n_idx] = p_loglkd[idx_traj]
Q_samples_move[n_idx] = Q_samples[idx_traj]
print 'acceptance ratio %s'%str(nb_acceptance/nb_samples)
assert(prev_action_prop == prev_action[0])
acceptance_l.append(nb_acceptance/nb_samples)
# move samples
samples[:] = move_samples
p_loglkd[:] = move_p_loglkd
log_weights[:] = 0.
Q_samples[:] = Q_samples_move
if show_progress and t_idx%10==0 :
weights_a[:] = uf.to_normalized_weights(log_weights)
plt.subplot(3,2,1)
plt.plot(range(t_idx), mean_Q[:t_idx], 'm', linewidth=2);
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('Q values')
if apply_rep_bias == 1:
mean_rep = np.sum(weights_a * samples[:,2])
std_rep = np.sqrt(np.sum(weights_a * samples[:,2]**2) - mean_rep**2)
plt.subplot(3,2,2)
x = np.linspace(-2.,2.,5000)
plt.plot(x, norm.pdf(x, mean_rep, std_rep), 'g'); plt.hold(True)
plt.plot([mean_rep, mean_rep], plt.gca().get_ylim(),'g', linewidth=2)
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('rep param')
if temperature:
mean_beta = np.sum(weights_a * 1./samples[:, 1])
std_beta = np.sqrt(np.sum(weights_a * ((1./samples[:,1])**2)) - mean_beta**2)
else:
mean_beta = np.sum(weights_a * 10**samples[:, 1])
std_beta = np.sqrt(np.sum(weights_a * ((10**samples[:,1])**2)) - mean_beta**2)
plt.subplot(3,2,3)
x = np.linspace(0.01,200.,5000)
plt.plot(x, norm.pdf(x, mean_beta, std_beta), 'g', linewidth=2); plt.hold(True)
plt.plot([mean_beta, mean_beta], plt.gca().get_ylim(), 'g', linewidth=2)
plt.hold(False)
plt.xlabel('beta softmax')
plt.ylabel('pdf')
mean_alpha_0 = np.sum(weights_a * samples[:, 0])
std_alpha_0 = np.sqrt(np.sum(weights_a * (samples[:, 0]**2)) - mean_alpha_0**2)
plt.subplot(3,2,4)
x = np.linspace(0.,1.,5000)
plt.plot(x, norm.pdf(x, mean_alpha_0, std_alpha_0), 'm', linewidth=2); plt.hold(True)
plt.plot([mean_alpha_0, mean_alpha_0], plt.gca().get_ylim(), 'm', linewidth=2)
plt.hold(False)
plt.xlabel('learning rate (majenta)')
plt.ylabel('pdf')
plt.subplot(3,2,5)
plt.plot(range(t_idx), esslist[:t_idx], 'b', linewidth=2); plt.hold(True)
plt.plot(plt.gca().get_xlim(), [nb_samples/2, nb_samples/2],'b--', linewidth=2)
plt.axis([0, t_idx-1, 0, nb_samples]) # For speed
plt.hold(False)
plt.xlabel('trials')
plt.ylabel('ess')
plt.draw()
plt.show()
plt.pause(0.05)
return [samples, Q_samples, mean_Q, esslist, acceptance_l, log_weights, p_loglkd, marg_loglkd_l]
def ibis(actions, rewards, tau, subj_idx, apply_rep_bias, show_progress = True, temperature = True, n_alpha_model=False):
actions = np.asarray(actions, dtype=np.intc)
rewards = np.ascontiguousarray(rewards)
nb_samples = 1000
T = actions.shape[0]
upp_bound_eta = 10.
nb_acceptance = 0
# sample initialisation
if n_alpha_model:
n_alpha = 6
tau_unique = np.unique(tau)
x_coor = np.array([np.where(tau_unique == t)[0][0] for t in tau])
else:
n_alpha = 1
x_coor = np.zeros(len(tau), dtype=np.int8)
if apply_rep_bias:
samples = np.random.rand(n_alpha + 2)
if temperature:
upp_bound_beta = np.sqrt(6)/(np.pi * 5)
else:
upp_bound_beta = 2.
n_index_beta = n_alpha
samples[n_index_beta] = upp_bound_beta/2.
samples[n_index_beta + 1] = upp_bound_eta * (np.random.rand() * 2. - 1.)
else:
samples = np.zeros(n_alpha + 1) + .5
if temperature:
upp_bound_beta = np.sqrt(6)/(np.pi * 5)
else:
upp_bound_beta = 2.
n_index_beta = n_alpha
samples[-1] = upp_bound_beta/2.
all_samples = np.zeros([nb_samples, len(samples)])
all_samples[0] = samples
lkd = get_loglikelihood(samples, x_coor, rewards, actions, T, apply_rep_bias, temperature)[0]
# loop
for n_idx in range(nb_samples):
Sigma_p = 1e-2 * np.eye(len(samples))
Sigma_p[-1][-1] = 1e-3
while True:
sample_p = multi_norm(samples, Sigma_p)
if not apply_rep_bias:
if np.all(sample_p[:n_alpha] > 0) and np.all(sample_p[:n_alpha] < 1) and sample_p[n_alpha] > 0 and sample_p[n_alpha] <= upp_bound_beta:
break
else:
if np.all(sample_p[:n_alpha] > 0) and np.all(sample_p[:n_alpha] < 1) and sample_p[n_alpha] > 0 and sample_p[n_alpha] <= upp_bound_beta and sample_p[n_alpha + 1] > -upp_bound_eta and sample_p[n_alpha + 1] < upp_bound_eta:
break
[loglkd_prop, Q_prop, prev_action_prop] = get_loglikelihood(sample_p, x_coor, rewards, actions, T, apply_rep_bias, temperature)
log_ratio = loglkd_prop - lkd
log_ratio = np.minimum(log_ratio, 0)
if (np.log(np.random.rand()) < log_ratio):
nb_acceptance += 1.
all_samples[n_idx] = sample_p
lkd = loglkd_prop
samples = sample_p
else:
all_samples[n_idx] = samples
print('acception ratio is {0}'.format(nb_acceptance/nb_samples))
return [samples, Q_samples, mean_Q, esslist, acceptance_l, log_weights, p_loglkd, marg_loglkd_l]