class PosteriorBNNSampling(BanditAlgorithm):
"""Posterior Sampling algorithm based on a Bayesian neural network."""
def __init__(self, name, hparams, bnn_model='RMSProp'):
"""Creates a PosteriorBNNSampling object based on a specific optimizer.
The algorithm has two basic tools: an Approx BNN and a Contextual Dataset.
The Bayesian Network keeps the posterior based on the optimizer iterations.
Args:
name: Name of the algorithm.
hparams: Hyper-parameters of the algorithm.
bnn_model: Type of BNN. By default RMSProp (point estimate).
"""
self.name = name
self.hparams = hparams
self.optimizer_n = hparams.optimizer
self.training_freq = hparams.training_freq
self.training_epochs = hparams.training_epochs
self.t = 0
self.data_h = ContextualDataset(hparams.context_dim, hparams.num_actions,
hparams.buffer_s)
# to be extended with more BNNs (BB alpha-div, GPs, SGFS, constSGD...)
bnn_name = '{}-bnn'.format(name)
if bnn_model == 'Variational':
self.bnn = VariationalNeuralBanditModel(hparams, bnn_name)
elif bnn_model == 'AlphaDiv':
self.bnn = BBAlphaDivergence(hparams, bnn_name)
elif bnn_model == 'Variational_BF':
self.bnn = BfVariationalNeuralBanditModel(hparams, bnn_name)
elif bnn_model == 'GP':
self.bnn = MultitaskGP(hparams)
else:
self.bnn = NeuralBanditModel(self.optimizer_n, hparams, bnn_name)
def action(self, context):
"""Selects action for context based on Thompson Sampling using the BNN."""
if self.t < self.hparams.num_actions * self.hparams.initial_pulls:
# round robin until each action has been taken "initial_pulls" times
return self.t % self.hparams.num_actions
with self.bnn.graph.as_default():
c = context.reshape((1, self.hparams.context_dim))
output = self.bnn.sess.run(self.bnn.y_pred, feed_dict={self.bnn.x: c})
return np.argmax(output)
def update(self, context, action, reward):
"""Updates data buffer, and re-trains the BNN every training_freq steps."""
self.t += 1
self.data_h.add(context, action, reward)
if self.t % self.training_freq == 0:
if self.hparams.reset_lr:
self.bnn.assign_lr()
self.bnn.train(self.data_h, self.training_epochs)
class PosteriorBNNSampling(BanditAlgorithm):
"""Posterior Sampling algorithm based on a Bayesian neural network."""
def __init__(self, name, hparams, bnn_model='RMSProp'):
"""Creates a PosteriorBNNSampling object based on a specific optimizer.
The algorithm has two basic tools: an Approx BNN and a Contextual Dataset.
The Bayesian Network keeps the posterior based on the optimizer iterations.
Args:
name: Name of the algorithm.
hparams: Hyper-parameters of the algorithm.
bnn_model: Type of BNN. By default RMSProp (point estimate).
"""
self.name = name
self.hparams = hparams
self.optimizer_n = hparams.optimizer
self.training_freq = hparams.training_freq
self.training_epochs = hparams.training_epochs
self.t = 0
self.data_h = ContextualDataset(hparams.context_dim,
hparams.num_actions, hparams.buffer_s)
# to be extended with more BNNs (BB alpha-div, GPs, SGFS, constSGD...)
bnn_name = '{}-bnn'.format(name)
if bnn_model == 'Variational':
self.bnn = VariationalNeuralBanditModel(hparams, bnn_name)
elif bnn_model == 'AlphaDiv':
self.bnn = BBAlphaDivergence(hparams, bnn_name)
elif bnn_model == 'Variational_BF':
self.bnn = BfVariationalNeuralBanditModel(hparams, bnn_name)
elif bnn_model == 'GP':
self.bnn = MultitaskGP(hparams)
else:
self.bnn = NeuralBanditModel(self.optimizer_n, hparams, bnn_name)
def action(self, context):
"""Selects action for context based on Thompson Sampling using the BNN."""
if self.t < self.hparams.num_actions * self.hparams.initial_pulls:
# round robin until each action has been taken "initial_pulls" times
return self.t % self.hparams.num_actions
with self.bnn.graph.as_default():
c = context.reshape((1, self.hparams.context_dim))
output = self.bnn.sess.run(self.bnn.y_pred,
feed_dict={self.bnn.x: c})
return np.argmax(output)
def update(self, context, action, reward):
"""Updates data buffer, and re-trains the BNN every training_freq steps."""
self.t += 1
self.data_h.add(context, action, reward)
if self.t % self.training_freq == 0:
if self.hparams.reset_lr:
self.bnn.assign_lr()
self.bnn.train(self.data_h, self.training_epochs)
class NeuralLinearPosteriorSampling(BanditAlgorithm):
"""Full Bayesian linear regression on the last layer of a deep neural net."""
def __init__(self, name, hparams, optimizer='RMS'):
self.name = name
self.hparams = hparams
self.latent_dim = self.hparams.layer_sizes[-1]
# Gaussian prior for each beta_i
self._lambda_prior = self.hparams.lambda_prior
self.mu = [
np.zeros(self.latent_dim)
for _ in range(self.hparams.num_actions)
]
self.cov = [(1.0 / self.lambda_prior) * np.eye(self.latent_dim)
for _ in range(self.hparams.num_actions)]
self.precision = [
self.lambda_prior * np.eye(self.latent_dim)
for _ in range(self.hparams.num_actions)
]
# Inverse Gamma prior for each sigma2_i
self._a0 = self.hparams.a0
self._b0 = self.hparams.b0
self.a = [self._a0 for _ in range(self.hparams.num_actions)]
self.b = [self._b0 for _ in range(self.hparams.num_actions)]
# Regression and NN Update Frequency
self.update_freq_lr = hparams.training_freq
self.update_freq_nn = hparams.training_freq_network
self.t = 0
self.optimizer_n = optimizer
self.num_epochs = hparams.training_epochs
self.data_h = ContextualDataset(hparams.context_dim,
hparams.num_actions,
intercept=False)
self.latent_h = ContextualDataset(self.latent_dim,
hparams.num_actions,
intercept=False)
self.bnn = NeuralBanditModel(optimizer, hparams, '{}-bnn'.format(name))
def action(self, context):
"""Samples beta's from posterior, and chooses best action accordingly."""
# Round robin until each action has been selected "initial_pulls" times
if self.t < self.hparams.num_actions * self.hparams.initial_pulls:
return self.t % self.hparams.num_actions
# Sample sigma2, and beta conditional on sigma2
sigma2_s = [
self.b[i] * invgamma.rvs(self.a[i])
for i in range(self.hparams.num_actions)
]
try:
beta_s = [
np.random.multivariate_normal(self.mu[i], sigma2_s[i] * self.cov[i])
for i in range(self.hparams.num_actions)
]
except np.linalg.LinAlgError as e:
# Sampling could fail if covariance is not positive definite
print('Exception when sampling for {}.'.format(self.name))
print('Details: {} | {}.'.format(e.message, e.args))
d = self.latent_dim
beta_s = [
np.random.multivariate_normal(np.zeros((d)), np.eye(d))
for i in range(self.hparams.num_actions)
]
# Compute last-layer representation for the current context
with self.bnn.graph.as_default():
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn, feed_dict={self.bnn.x: c})
# Apply Thompson Sampling to last-layer representation
vals = [
np.dot(beta_s[i], z_context.T) for i in range(self.hparams.num_actions)
]
return np.argmax(vals)
def update(self, context, action, reward):
"""Updates the posterior using linear bayesian regression formula."""
self.t += 1
self.data_h.add(context, action, reward)
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn, feed_dict={self.bnn.x: c})
self.latent_h.add(z_context, action, reward)
# Retrain the network on the original data (data_h)
if self.t % self.update_freq_nn == 0:
if self.hparams.reset_lr:
self.bnn.assign_lr()
self.bnn.train(self.data_h, self.num_epochs)
# Update the latent representation of every datapoint collected so far
new_z = self.bnn.sess.run(self.bnn.nn,
feed_dict={self.bnn.x: self.data_h.contexts})
self.latent_h.replace_data(contexts=new_z)
# Update the Bayesian Linear Regression
if self.t % self.update_freq_lr == 0:
# Find all the actions to update
actions_to_update = self.latent_h.actions[:-self.update_freq_lr]
for action_v in np.unique(actions_to_update):
# Update action posterior with formulas: \beta | z,y ~ N(mu_q, cov_q)
z, y = self.latent_h.get_data(action_v)
# The algorithm could be improved with sequential formulas (cheaper)
s = np.dot(z.T, z)
# Some terms are removed as we assume prior mu_0 = 0.
precision_a = s + self.lambda_prior * np.eye(self.latent_dim)
cov_a = np.linalg.inv(precision_a)
mu_a = np.dot(cov_a, np.dot(z.T, y))
# Inverse Gamma posterior update
a_post = self.a0 + z.shape[0] / 2.0
b_upd = 0.5 * np.dot(y.T, y)
b_upd -= 0.5 * np.dot(mu_a.T, np.dot(precision_a, mu_a))
b_post = self.b0 + b_upd
# Store new posterior distributions
self.mu[action_v] = mu_a
self.cov[action_v] = cov_a
self.precision[action_v] = precision_a
self.a[action_v] = a_post
self.b[action_v] = b_post
@property
def a0(self):
return self._a0
@property
def b0(self):
return self._b0
@property
def lambda_prior(self):
return self._lambda_prior
class NeuralUCBSampling(BanditAlgorithm):
"""UCB Sampling algorithm based on a neural network."""
def __init__(self, name, hparams, bnn_model='RMSProp', optimizer='RMS'):
"""Creates a PosteriorBNNSampling object based on a specific optimizer.
The algorithm has two basic tools: an Approx BNN and a Contextual Dataset.
The Bayesian Network keeps the posterior based on the optimizer iterations.
Args:
name: Name of the algorithm.
hparams: Hyper-parameters of the algorithm.
bnn_model: Type of BNN. By default RMSProp (point estimate).
"""
self.name = name
self.hparams = hparams
self.optimizer_n = hparams.optimizer
self.training_freq = hparams.training_freq
self.training_epochs = hparams.training_epochs
self.t = 0
self.gamma = 0
self.bonus = np.zeros(hparams.num_actions)
self.C1 = 0.001
self.C2 = 0.001
self.C3 = 0.00001
self.data_h = ContextualDataset(hparams.context_dim,
hparams.num_actions, hparams.buffer_s)
# to be extended with more BNNs (BB alpha-div, GPs, SGFS, constSGD...)
bnn_name = '{}-ucb'.format(name)
self.bnn = NeuralBanditModel(self.optimizer_n, hparams, bnn_name)
self.p = (hparams.context_dim + 1) * (hparams.layer_sizes[0]) + (
hparams.layer_sizes[0] + 1) * (hparams.layer_sizes[0]) * (
len(hparams.layer_sizes) - 1) + (hparams.layer_sizes[0] +
1) * hparams.num_actions
self.Zinv = (1 / hparams.lamb) * np.eye(self.p)
self.detZ = hparams.lamb**self.p
def action(self, context):
"""Selects action for context based on UCB using the NN."""
if self.t < self.hparams.num_actions * self.hparams.initial_pulls:
# round robin until each action has been taken "initial_pulls" times
return self.t % self.hparams.num_actions
with self.bnn.graph.as_default():
c = context.reshape((1, self.hparams.context_dim))
output = self.bnn.sess.run(self.bnn.y_pred,
feed_dict={self.bnn.x: c})
### Add confidence bound to outbut²
listTensorGradients = self.bnn.sess.run(self.bnn.gradAction,
feed_dict={self.bnn.x: c})
bonus = []
for act in range(self.hparams.num_actions):
grads = np.array([])
for el in listTensorGradients[act]:
grads = np.concatenate((grads, el.flatten()))
bonus.append(self.gamma * np.sqrt(
grads.dot(self.Zinv.dot(grads)) /
self.hparams.layer_sizes[0]))
output += np.array(bonus)
print("Bonus of the actions", bonus)
print("Gamma", self.gamma)
return np.argmax(output)
def update(self, context, action, reward):
"""Updates data buffer, and re-trains the BNN every training_freq steps."""
self.t += 1
self.data_h.add(context, action, reward)
if self.t % self.training_freq == 0:
if self.hparams.reset_lr:
self.bnn.assign_lr()
self.bnn.train(self.data_h, self.training_epochs)
tensorGradients = self.bnn.sess.run(
self.bnn.gradAction[action],
feed_dict={self.bnn.x: context.reshape(1, -1)})
grads = np.array([])
for el in tensorGradients:
grads = np.concatenate((grads, el.flatten()))
outer = np.outer(grads, grads) / self.hparams.layer_sizes[0]
self.detZ *= 1 + grads.dot(
self.Zinv.dot(grads)) / self.hparams.layer_sizes[0]
self.Zinv -= self.Zinv.dot(outer.dot(self.Zinv)) / (
1 +
(grads.T.dot(self.Zinv.dot(grads)) / self.hparams.layer_sizes[0]))
el1 = np.sqrt(1 + self.C1 * ((self.hparams.layer_sizes[0])**(-1 / 6)) *
np.sqrt(np.log(self.hparams.layer_sizes[0])) *
(len(self.hparams.layer_sizes)**4) * (self.t**(7 / 6)) *
(self.hparams.lamb**(-7 / 6)))
el2 = self.hparams.mu * np.sqrt(
-np.log(self.detZ / (self.hparams.lamb**self.p)) + self.C2 *
((self.hparams.layer_sizes[0])**
(-1 / 6)) * np.sqrt(np.log(self.hparams.layer_sizes[0])) *
(len(self.hparams.layer_sizes)**4) * (self.t**(5 / 3)) *
(self.hparams.lamb**
(-1 / 6)) - 2 * np.log(self.hparams.delta)) + np.sqrt(
self.hparams.lamb) * self.hparams.S
el3 = self.C3 * (
(1 - self.hparams.mu * self.hparams.layer_sizes[0] *
self.hparams.lamb)**
(self.training_epochs) * np.sqrt(self.t / self.hparams.lamb) +
((self.hparams.layer_sizes[0])**
(-1 / 6)) * np.sqrt(np.log(self.hparams.layer_sizes[0])) *
(len(self.hparams.layer_sizes)**(7 / 2)) * (self.t**(5 / 3)) *
(self.hparams.lamb**(-5 / 3)) *
(1 + np.sqrt(self.t / self.hparams.lamb)))
print("Profile Elements", el1, el2, el3)
self.gamma = el1 * el2 + el3
class NeuralLinearPosteriorSamplingFiniteMemory(BanditAlgorithm):
"""Full Bayesian linear regression on the last layer of a deep neural net."""
def __init__(self, name, hparams, optimizer='RMS'):
self.name = name
self.hparams = hparams
self.latent_dim = self.hparams.layer_sizes[-1]
# Gaussian prior for each beta_i
self._lambda_prior = self.hparams.lambda_prior
self.mu = [
np.zeros(self.latent_dim) for _ in range(self.hparams.num_actions)
]
self.cov = [(1.0 / self.lambda_prior) * np.eye(self.latent_dim)
for _ in range(self.hparams.num_actions)]
self.precision = [
self.lambda_prior * np.eye(self.latent_dim)
for _ in range(self.hparams.num_actions)
]
self.mu_prior_flag = self.hparams.mu_prior_flag
self.sigma_prior_flag = self.hparams.sigma_prior_flag
self.precision_prior = self.precision[:]
self.mu_prior = np.zeros((self.latent_dim, self.hparams.num_actions))
# Inverse Gamma prior for each sigma2_i
self._a0 = self.hparams.a0
self._b0 = self.hparams.b0
self.a = [self._a0 for _ in range(self.hparams.num_actions)]
self.b = [self._b0 for _ in range(self.hparams.num_actions)]
# Regression and NN Update Frequency
self.update_freq_lr = hparams.training_freq
self.update_freq_nn = hparams.training_freq_network
self.t = 0
self.optimizer_n = optimizer
self.num_epochs = hparams.training_epochs
self.data_h = ContextualDataset(hparams.context_dim,
hparams.num_actions,
intercept=False,
buffer_s=hparams.mem)
self.latent_h = ContextualDataset(self.latent_dim,
hparams.num_actions,
intercept=False,
buffer_s=hparams.mem)
self.bnn = NeuralBanditModel(optimizer, hparams, '{}-bnn'.format(name))
def action(self, context):
"""Samples beta's from posterior, and chooses best action accordingly."""
# Round robin until each action has been selected "initial_pulls" times
if self.t < self.hparams.num_actions * self.hparams.initial_pulls:
return self.t % self.hparams.num_actions
# Sample sigma2, and beta conditional on sigma2
sigma2_s = [
self.b[i] * invgamma.rvs(self.a[i])
for i in range(self.hparams.num_actions)
]
try:
beta_s = [
np.random.multivariate_normal(self.mu[i],
sigma2_s[i] * self.cov[i])
for i in range(self.hparams.num_actions)
]
except np.linalg.LinAlgError as e:
# Sampling could fail if covariance is not positive definite
print('Exception when sampling for {}.'.format(self.name))
print('Details: {} | {}.'.format(e.message, e.args))
d = self.latent_dim
beta_s = [
np.random.multivariate_normal(np.zeros((d)), np.eye(d))
for i in range(self.hparams.num_actions)
]
# Compute last-layer representation for the current context
with self.bnn.graph.as_default():
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn,
feed_dict={self.bnn.x: c})
# Apply Thompson Sampling to last-layer representation
vals = [
np.dot(beta_s[i], z_context.T)
for i in range(self.hparams.num_actions)
]
return np.argmax(vals)
def calc_precision_prior(self, contexts):
precisions_return = []
n, m = contexts.shape
prior = (0.01) * np.eye(self.latent_dim)
if self.cov is not None:
for action, precision in enumerate(self.cov):
ind = np.array(
[i for i in range(n) if self.data_h.actions[i] == action])
if len(ind) > 0:
"""compute confidence scores for old data"""
d = []
for c in self.latent_h.contexts[ind, :]:
d.append(np.dot(np.dot(c, precision), c.T))
"""compute new data correlations"""
phi = []
for c in contexts[ind, :]:
phi.append(np.outer(c, c))
X = cvx.Variable((m, m), PSD=True)
# Form objective.
obj = cvx.Minimize(
sum([(cvx.trace(X * phi[i]) - d[i])**2
for i in xrange(len(d))]))
prob = cvx.Problem(obj)
prob.solve()
if X.value is None:
precisions_return.append(np.linalg.inv(prior))
else:
precisions_return.append(np.linalg.inv(X.value +
prior))
else:
precisions_return.append(np.linalg.inv(prior))
return precisions_return
def update(self, context, action, reward):
"""Updates the posterior using linear bayesian regression formula."""
self.t += 1
self.data_h.add(context, action, reward)
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn, feed_dict={self.bnn.x: c})
self.latent_h.add(z_context, action, reward)
# Retrain the network on the original data (data_h)
if self.t % self.update_freq_nn == 0:
if self.hparams.reset_lr:
self.bnn.assign_lr()
self.bnn.train(self.data_h, self.num_epochs)
# Update the latent representation of every datapoint collected so far
new_z = self.bnn.sess.run(
self.bnn.nn, feed_dict={self.bnn.x: self.data_h.contexts})
# Update the confidence prior using feature uncertainty matching
if self.sigma_prior_flag == 1:
self.precision_prior = self.calc_precision_prior(
contexts=new_z)
self.latent_h.replace_data(contexts=new_z)
# Update the mean prior using the weights of the NN
if self.mu_prior_flag == 1:
self.mu_prior = self.bnn.get_mu_prior()
# Update the Bayesian Linear Regression
if self.t % self.update_freq_lr == 0:
# Find all the actions to update
actions_to_update = self.latent_h.actions[:-self.update_freq_lr]
for action_v in np.unique(actions_to_update):
# Update action posterior with formulas: \beta | z,y ~ N(mu_q, cov_q)
z, y = self.latent_h.get_data(action_v)
# The algorithm could be improved with sequential formulas (cheaper)
s = np.dot(z.T, z)
# Get priors
sigma0 = self.precision_prior[action_v]
mu_0 = self.mu_prior[:, action_v]
# Calc mean and precision using bayesian linear regression
precision_a = s + sigma0
cov_a = np.linalg.inv(precision_a)
mu_a = np.dot(cov_a, (np.dot(z.T, y) + np.dot(sigma0, mu_0)))
# Inverse Gamma posterior update
a_post = self.a0 + z.shape[0] / 2.0
b_upd = 0.5 * np.dot(y.T, y)
b_upd += 0.5 * np.dot(mu_0.T, np.dot(sigma0, mu_0))
b_upd -= 0.5 * np.dot(mu_a.T, np.dot(precision_a, mu_a))
b_post = self.b0 + b_upd
# Store new posterior distributions
self.mu[action_v] = mu_a
self.cov[action_v] = cov_a
#self.precision[action_v] = precision_a
self.a[action_v] = a_post
self.b[action_v] = b_post
@property
def a0(self):
return self._a0
@property
def b0(self):
return self._b0
@property
def lambda_prior(self):
return self._lambda_prior
class NeuralLinearPosteriorSampling(BanditAlgorithm):
"""Full Bayesian linear regression on the last layer of a deep neural net."""
def __init__(self, name, hparams, optimizer='RMS'):
self.name = name
self.hparams = hparams
self.latent_dim = self.hparams.layer_sizes[-1]
# Gaussian prior for each beta_i
self._lambda_prior = self.hparams.lambda_prior
self.mu = [
np.zeros(self.latent_dim)
for _ in range(self.hparams.num_actions)
]
self.cov = [(1.0 / self.lambda_prior) * np.eye(self.latent_dim)
for _ in range(self.hparams.num_actions)]
self.precision = [
self.lambda_prior * np.eye(self.latent_dim)
for _ in range(self.hparams.num_actions)
]
# Inverse Gamma prior for each sigma2_i
self._a0 = self.hparams.a0
self._b0 = self.hparams.b0
self.a = [self._a0 for _ in range(self.hparams.num_actions)]
self.b = [self._b0 for _ in range(self.hparams.num_actions)]
# Regression and NN Update Frequency
self.update_freq_lr = hparams.training_freq
self.update_freq_nn = hparams.training_freq_network
self.t = 0
self.optimizer_n = optimizer
self.num_epochs = hparams.training_epochs
self.data_h = ContextualDataset(hparams.context_dim,
hparams.num_actions,
intercept=False)
self.latent_h = ContextualDataset(self.latent_dim,
hparams.num_actions,
intercept=False)
self.bnn = NeuralBanditModel(optimizer, hparams, '{}-bnn'.format(name))
def action(self, context):
"""Samples beta's from posterior, and chooses best action accordingly."""
# Round robin until each action has been selected "initial_pulls" times
if self.t < self.hparams.num_actions * self.hparams.initial_pulls:
return self.t % self.hparams.num_actions
# Sample sigma2, and beta conditional on sigma2
sigma2_s = [
self.b[i] * invgamma.rvs(self.a[i])
for i in range(self.hparams.num_actions)
]
try:
beta_s = [
np.random.multivariate_normal(self.mu[i], sigma2_s[i] * self.cov[i])
for i in range(self.hparams.num_actions)
]
except np.linalg.LinAlgError as e:
# Sampling could fail if covariance is not positive definite
print('Exception when sampling for {}.'.format(self.name))
print('Details: {} | {}.'.format(e.message, e.args))
d = self.latent_dim
beta_s = [
np.random.multivariate_normal(np.zeros((d)), np.eye(d))
for i in range(self.hparams.num_actions)
]
# Compute last-layer representation for the current context
with self.bnn.graph.as_default():
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn, feed_dict={self.bnn.x: c})
# Apply Thompson Sampling to last-layer representation
vals = [
np.dot(beta_s[i], z_context.T) for i in range(self.hparams.num_actions)
]
return np.argmax(vals)
def update(self, context, action, reward):
"""Updates the posterior using linear bayesian regression formula."""
self.t += 1
self.data_h.add(context, action, reward)
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn, feed_dict={self.bnn.x: c})
self.latent_h.add(z_context, action, reward)
# Retrain the network on the original data (data_h)
if self.t % self.update_freq_nn == 0:
if self.hparams.reset_lr:
self.bnn.assign_lr()
self.bnn.train(self.data_h, self.num_epochs)
# Update the latent representation of every datapoint collected so far
new_z = self.bnn.sess.run(self.bnn.nn,
feed_dict={self.bnn.x: self.data_h.contexts})
self.latent_h.replace_data(contexts=new_z)
# Update the Bayesian Linear Regression
if self.t % self.update_freq_lr == 0:
# Find all the actions to update
actions_to_update = self.latent_h.actions[:-self.update_freq_lr]
for action_v in np.unique(actions_to_update):
# Update action posterior with formulas: \beta | z,y ~ N(mu_q, cov_q)
z, y = self.latent_h.get_data(action_v)
# The algorithm could be improved with sequential formulas (cheaper)
s = np.dot(z.T, z)
# Some terms are removed as we assume prior mu_0 = 0.
precision_a = s + self.lambda_prior * np.eye(self.latent_dim)
cov_a = np.linalg.inv(precision_a)
mu_a = np.dot(cov_a, np.dot(z.T, y))
# print('beta_cov: ', cov_a)
# Inverse Gamma posterior update
a_post = self.a0 + z.shape[0] / 2.0
b_upd = 0.5 * np.dot(y.T, y)
b_upd -= 0.5 * np.dot(mu_a.T, np.dot(precision_a, mu_a))
b_post = self.b0 + b_upd
# Store new posterior distributions
self.mu[action_v] = mu_a
self.cov[action_v] = cov_a
self.precision[action_v] = precision_a
self.a[action_v] = a_post
self.b[action_v] = b_post
@property
def a0(self):
return self._a0
@property
def b0(self):
return self._b0
@property
def lambda_prior(self):
return self._lambda_prior
class NeuralLinearPosteriorSamplingFiniteMemory(BanditAlgorithm):
"""Full Bayesian linear regression on the last layer of a deep neural net."""
def __init__(self, name, hparams, textflag='no', optimizer='RMS'):
self.name = name
self.hparams = hparams
self.latent_dim = self.hparams.layer_sizes[-1]
self.intercept = False
if self.intercept:
self.param_dim = 1 + self.latent_dim
else:
self.param_dim = self.latent_dim
self.EPSILON = 0.00001
# Gaussian prior for each beta_i
self._lambda_prior = self.hparams.lambda_prior
self.before = []
self.after = []
self.mu = [
np.zeros(self.param_dim) for _ in range(self.hparams.num_actions)
]
self.f = [
np.zeros(self.param_dim) for _ in range(self.hparams.num_actions)
]
self.yy = [0 for _ in range(self.hparams.num_actions)]
self.cov = [(1.0 / self.lambda_prior) * np.eye(self.param_dim)
for _ in range(self.hparams.num_actions)]
self.precision = [
self.lambda_prior * np.eye(self.param_dim)
for _ in range(self.hparams.num_actions)
]
self.mu_prior_flag = self.hparams.mu_prior_flag
self.sigma_prior_flag = self.hparams.sigma_prior_flag
self.precision_prior = self.precision[:]
self.mu_prior = np.zeros((self.param_dim, self.hparams.num_actions))
# Inverse Gamma prior for each sigma2_i
self._a0 = self.hparams.a0
self._b0 = self.hparams.b0
self.a = [self._a0 for _ in range(self.hparams.num_actions)]
self.b = [self._b0 for _ in range(self.hparams.num_actions)]
# Regression and NN Update Frequency
self.update_freq_lr = hparams.training_freq
self.update_freq_nn = hparams.training_freq_network
self.t = 0
self.optimizer_n = optimizer
self.num_epochs = hparams.training_epochs
self.data_h = ContextualDataset(hparams.context_dim,
hparams.num_actions,
intercept=False,
buffer_s=hparams.mem)
self.latent_h = ContextualDataset(self.latent_dim,
hparams.num_actions,
intercept=self.intercept,
buffer_s=hparams.mem)
if textflag == 'yes':
self.bnn = TextCNN('adam', self.hparams.num_actions,
self.hparams.batch_size, '{}-bnn'.format(name))
else:
self.bnn = NeuralBanditModel(optimizer, hparams,
'{}-bnn'.format(name))
def action(self, context):
"""Samples beta's from posterior, and chooses best action accordingly."""
# Round robin until each action has been selected "initial_pulls" times
if self.t < self.hparams.num_actions * self.hparams.initial_pulls:
return self.t % self.hparams.num_actions
# Sample sigma2, and beta conditional on sigma2
sigma2_s = [
self.b[i] * invgamma.rvs(self.a[i])
for i in range(self.hparams.num_actions)
]
try:
beta_s = [
np.random.multivariate_normal(self.mu[i],
sigma2_s[i] * self.cov[i])
for i in range(self.hparams.num_actions)
]
except np.linalg.LinAlgError as e:
# Sampling could fail if covariance is not positive definite
d = self.latent_dim
beta_s = [
np.random.multivariate_normal(np.zeros((d)), np.eye(d))
for i in range(self.hparams.num_actions)
]
# Compute last-layer representation for the current context
with self.bnn.graph.as_default():
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn,
feed_dict={self.bnn.x: c})
if self.intercept:
z_context = np.append(z_context, 1.0).reshape(
(1, self.latent_dim + 1))
# Apply Thompson Sampling to last-layer representation
vals = [
np.dot(beta_s[i], z_context.T)
for i in range(self.hparams.num_actions)
]
return np.argmax(vals)
def calc_precision_prior(self, contexts):
precisions_return = []
n, m = contexts.shape
prior = (self.EPSILON) * np.eye(self.param_dim)
if self.cov is not None:
for action, precision in enumerate(self.cov):
ind = np.array(
[i for i in range(n) if self.data_h.actions[i] == action])
if len(ind) > 0:
"""compute confidence scores for old data"""
d = []
for c in self.latent_h.contexts[ind, :]:
d.append(np.dot(np.dot(c, precision), c.T))
"""compute new data correlations"""
phi = []
for c in contexts[ind, :]:
phi.append(np.outer(c, c))
X = cvx.Variable((m, m), PSD=True)
# Form objective.
obj = cvx.Minimize(
sum([(cvx.trace(X * phi[i]) - d[i])**2
for i in xrange(len(d))]))
prob = cvx.Problem(obj)
prob.solve()
if X.value is None:
precisions_return.append(np.linalg.inv(prior))
self.cov[action] = prior
else:
precisions_return.append(np.linalg.inv(X.value +
prior))
self.cov[action] = X.value + prior
else:
precisions_return.append(np.linalg.inv(prior))
self.cov[action] = prior
return (precisions_return)
def update(self, context, action, reward):
"""Updates the posterior using linear bayesian regression formula."""
self.t += 1
self.data_h.add(context, action, reward)
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn, feed_dict={self.bnn.x: c})
self.latent_h.add(z_context, action, reward)
# Retrain the network on the original data (data_h)
if self.t % self.update_freq_nn == 0:
if self.hparams.reset_lr:
self.bnn.assign_lr()
self.bnn.train(self.data_h, self.num_epochs)
# Update the latent representation of every datapoint collected so far
new_z = self.bnn.sess.run(
self.bnn.nn, feed_dict={self.bnn.x: self.data_h.contexts})
self.latent_h.replace_data(contexts=new_z)
i_contexts = None
for context in new_z:
c = np.array(context[:])
if self.intercept:
c = np.append(c, 1.0).reshape((1, self.latent_dim + 1))
if i_contexts is None:
i_contexts = c
else:
i_contexts = np.vstack((i_contexts, c))
# Update the confidence prior using feature uncertainty matching
#self.before.append(self.calc_model_evidence())
if self.sigma_prior_flag == 1:
self.precision_prior = self.calc_precision_prior(
contexts=i_contexts)
# Update the mean prior using the weights of the NN
if self.mu_prior_flag == 1:
weights_p, bias_p = self.bnn.get_mu_prior()
self.mu_prior[:self.latent_dim] = weights_p
self.mu_prior[-1] = bias_p
#self.after.append(self.calc_model_evidence())
#print(self.before)
#print(self.after)
# Update the Bayesian Linear Regression
for action_v in xrange(self.hparams.num_actions):
# Update action posterior with formulas: \beta | z,y ~ N(mu_q, cov_q)
z, y = self.latent_h.get_data(action_v)
# The algorithm could be improved with sequential formulas (cheaper)
self.precision[action_v] = (np.dot(z.T, z) +
self.precision_prior[action_v])
self.f[action_v] = np.dot(z.T, y)
else:
if self.intercept:
z_context = np.append(z_context, 1.0).reshape(
(1, self.latent_dim + 1))
self.precision[action] += np.dot(z_context.T, z_context)
self.cov[action] = np.linalg.inv(self.precision[action])
self.f[action] += (z_context.T * reward)[:, 0]
# Calc mean and precision using bayesian linear regression
self.mu[action] = np.dot(
self.cov[action],
(self.f[action] +
np.dot(self.precision_prior[action], self.mu_prior[:, action])))
# Inverse Gamma posterior update
self.yy[action] += reward**2
self.a[action] += 0.5
b_upd = 0.5 * self.yy[action]
b_upd += 0.5 * np.dot(
self.mu_prior[:, action].T,
np.dot(self.precision_prior[action], self.mu_prior[:, action]))
b_upd -= 0.5 * np.dot(self.mu[action].T,
np.dot(self.precision[action], self.mu[action]))
self.b[action] = self.b0 + b_upd
@property
def a0(self):
return self._a0
@property
def b0(self):
return self._b0
@property
def lambda_prior(self):
return self._lambda_prior
def calc_model_evidence(self):
vval = 0
for action in xrange(self.hparams.num_actions):
sigma0 = self.precision_prior[action]
mu_0 = self.mu_prior[:, action]
z, y = self.latent_h.get_data(action)
n = z.shape[0]
s = np.dot(z.T, z)
s_n = (sigma0 + s)
cov_a = np.linalg.inv(s_n)
mu_a = np.dot(cov_a, (np.dot(z.T, y) + np.dot(sigma0, mu_0)))
a_post = (self.a0 + n / 2.0)
b_upd = 0.5 * np.dot(y.T, y)
b_upd += 0.5 * np.dot(mu_0.T, np.dot(sigma0, mu_0))
b_upd -= 0.5 * np.dot(mu_a.T, np.dot(s_n, mu_a))
b_post = self.b0 + b_upd
val = np.float128(1)
val /= ((np.float128(2.0) * math.pi)**(n / 2.0))
val *= (gamma(a_post) / gamma(self.a0))
val *= np.sqrt(np.linalg.det(sigma0) / np.linalg.det(s_n))
val *= ((self.hparams.b0**self.hparams.a0) / (b_post**a_post))
vval += val
vval /= self.hparams.num_actions
return vval
class NeuralLinearEpsilonGreedy(BanditAlgorithm):
"""Full Bayesian linear regression on the last layer of a deep neural net."""
def __init__(self, name, hparams, textflag='yes', optimizer='RMS'):
self.name = name
self.hparams = hparams
self.epsilon = self.hparams.epsilon
self.latent_dim = self.hparams.layer_sizes[-1]
self.intercept = True
if self.intercept:
self.param_dim = 1 + self.latent_dim
else:
self.param_dim = self.latent_dim
# Gaussian prior for each beta_i
# Regression and NN Update Frequency
self.update_freq_lr = hparams.training_freq
self.update_freq_nn = hparams.training_freq_network
self.t = 0
self.optimizer_n = optimizer
self.num_epochs = hparams.training_epochs
self.data_h = ContextualDataset(hparams.context_dim,
hparams.num_actions,
intercept=False)
self.latent_h = ContextualDataset(self.latent_dim,
hparams.num_actions,
intercept=self.intercept)
if textflag == 'yes':
self.bnn = TextCNN('adam', self.hparams.num_actions,
self.hparams.batch_size, '{}-bnn'.format(name))
else:
self.bnn = NeuralBanditModel(optimizer, hparams,
'{}-bnn'.format(name))
def action(self, context):
"""Samples beta's from posterior, and chooses best action accordingly."""
# Round robin until each action has been selected "initial_pulls" times
if self.t < self.hparams.num_actions * self.hparams.initial_pulls:
return self.t % self.hparams.num_actions
with self.bnn.graph.as_default():
c = context.reshape((1, self.hparams.context_dim))
y = self.bnn.sess.run(self.bnn.y_pred, feed_dict={self.bnn.x: c})
if random.random() > self.epsilon:
return np.argmax(y)
else:
return random.randrange(self.hparams.num_actions)
def update(self, context, action, reward):
"""Updates the posterior using linear bayesian regression formula."""
self.t += 1
self.data_h.add(context, action, reward)
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn, feed_dict={self.bnn.x: c})
self.latent_h.add(z_context, action, reward)
# Retrain the network on the original data (data_h)
if self.t % self.update_freq_nn == 0:
if self.hparams.reset_lr:
self.bnn.assign_lr()
#self.bnn.set_last_layer(self.mu)
self.bnn.train(self.data_h, self.num_epochs)
@property
def a0(self):
return self._a0
@property
def b0(self):
return self._b0
@property
def lambda_prior(self):
return self._lambda_prior
class NeuralGreedy(BanditAlgorithm):
"""Full Bayesian linear regression on the last layer of a deep neural net."""
def __init__(self, name, hparams, optimizer='RMS'):
self.name = name
self.eps = 0.9
self.decay = 0.99 # computed for 10,000 steps
self.hparams = hparams
# Regression and NN Update Frequency
self.update_freq_lr = hparams.training_freq
self.update_freq_nn = hparams.training_freq_network
self.t = 0
self.optimizer_n = optimizer
self.num_epochs = hparams.training_epochs
self.data_h = ContextualDataset(hparams.context_dim,
hparams.num_actions,
intercept=False)
self.bnn = NeuralBanditModel(optimizer, hparams,
'{}-greedy'.format(name))
def action(self, context):
"""Samples beta's from posterior, and chooses best action accordingly."""
# Round robin until each action has been selected "initial_pulls" times
#if self.t < self.hparams.num_actions * self.hparams.initial_pulls:
#return self.t % self.hparams.num_actions ## No need with greedy
if np.random.random() < self.eps:
return np.random.choice(range(self.hparams.num_actions))
else:
with self.bnn.graph.as_default():
c = context.reshape((1, self.hparams.context_dim))
output = self.bnn.sess.run(self.bnn.y_pred,
feed_dict={self.bnn.x: c})
return np.argmax(output)
def update(self, context, action, reward):
"""Updates the posterior using linear bayesian regression formula."""
self.t += 1
self.eps *= self.decay
self.data_h.add(context, action, reward)
c = context.reshape((1, self.hparams.context_dim))
# Retrain the network on the original data (data_h)
if self.t % self.update_freq_nn == 0:
if self.hparams.reset_lr:
self.bnn.assign_lr()
self.bnn.train(self.data_h, self.num_epochs)
@property
def a0(self):
return self._a0
@property
def b0(self):
return self._b0
@property
def lambda_prior(self):
return self._lambda_prior
class NeuralLinUCB(BanditAlgorithm):
def __init__(self, name, hparams, optimizer='RMS'):
self.name = name
self.hparams = hparams
self.n_a = self.hparams.num_actions
self.n_d = self.hparams.layer_sizes[-1]
self.alpha = self.hparams.alpha
self.lam = self.hparams.lam
self.a = np.concatenate(tuple([np.eye(self.n_d)[np.newaxis, :, :] for i in range(self.n_a)]), axis=0) * self.lam
self.inv_a = np.concatenate(tuple([np.eye(self.n_d)[np.newaxis, :, :] for i in range(self.n_a)]),
axis=0) / self.lam
self.b = np.zeros((self.n_a, self.n_d))
self.theta = np.zeros((self.n_a, self.n_d))
# Params for BNN
self.update_freq_nn = hparams.training_freq_network
self.t = 0
self.optimizer_n = optimizer
self.num_epochs = hparams.training_epochs
self.data_h = ContextualDataset(hparams.context_dim,
hparams.num_actions,
bootstrap=getattr(hparams, 'bootstrap', None),
intercept=False)
self.bnn = NeuralBanditModel(optimizer, hparams, '{}-bnn'.format(name))
def action(self, context):
"""
Args:
context: Context for which the action need to be chosen.
Returns:
action: Selected action for the context.
"""
with self.bnn.graph.as_default():
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn, feed_dict={self.bnn.x: c}).flatten()
vals = np.array([
np.dot(self.theta[i], z_context) + self.alpha * np.sqrt(np.dot(z_context, np.dot(self.inv_a[i], z_context)))
for i in range(self.n_a)])
return np.argmax(vals)
def update(self, context, action, reward):
"""Updates action posterior using the linear Bayesian regression formula.
Args:
context: Last observed context.
action: Last observed action.
reward: Last observed reward.
"""
self.t += 1
self.data_h.add(context, action, reward)
if self.t % self.update_freq_nn == 0:
if self.hparams.reset_lr:
self.bnn.assign_lr()
self.bnn.train(self.data_h, self.num_epochs)
new_z = self.bnn.sess.run(self.bnn.nn,
feed_dict={self.bnn.x: self.data_h.contexts})
contexts = new_z
actions = np.array(self.data_h.actions)
rewards = self.data_h.rewards[np.arange(actions.shape[
0]), actions] # strange but data_h.rewards is of shape (n_samples, n_actions) so we select actions pulled by model
self.a = np.dot(contexts.T, contexts) + np.concatenate(
tuple([np.eye(self.n_d)[np.newaxis, :, :] for i in range(self.n_a)]), axis=0) * self.lam
self.b = np.concatenate(tuple(
[np.dot(rewards[actions == action], contexts[actions == action])[np.newaxis, :] for action in
range(self.n_a)]), axis=0)
self.inv_a = np.concatenate(
tuple([np.linalg.inv(self.a[action])[np.newaxis, :, :] for action in range(self.n_a)]), axis=0)
self.theta = np.concatenate(
tuple([np.dot(self.inv_a[action], self.b[action])[np.newaxis, :] for action in range(self.n_a)]),
axis=0)
else:
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn, feed_dict={self.bnn.x: c}).flatten()
self.a[action] = self.a[action] + np.tensordot(z_context, z_context, axes=0)
self.inv_a[action] = np.linalg.inv(self.a[action])
self.b[action] = self.b[action] + reward * z_context
self.theta[action] = np.dot(self.inv_a[action], self.b[action])
class NeuralLinearPosteriorSampling(BanditAlgorithm):
"""Full Bayesian linear regression on the last layer of a deep neural net."""
def __init__(self, name, hparams,textflag ='no', optimizer='RMS'):
self.name = name
self.hparams = hparams
self.latent_dim = self.hparams.layer_sizes[-1]
self.intercept = False
if self.intercept:
self.param_dim=1+self.latent_dim
else:
self.param_dim = self.latent_dim
# Gaussian prior for each beta_i
self._lambda_prior = self.hparams.lambda_prior
self.mu = [
np.zeros(self.param_dim)
for _ in range(self.hparams.num_actions)
]
self.f = [
np.zeros(self.param_dim)
for _ in range(self.hparams.num_actions)
]
self.yy = [0 for _ in range(self.hparams.num_actions)]
self.cov = [(1.0 / self.lambda_prior) * np.eye(self.param_dim)
for _ in range(self.hparams.num_actions)]
self.precision = [
self.lambda_prior * np.eye(self.param_dim)
for _ in range(self.hparams.num_actions)
]
# Inverse Gamma prior for each sigma2_i
self._a0 = self.hparams.a0
self._b0 = self.hparams.b0
self.a = [self._a0 for _ in range(self.hparams.num_actions)]
self.b = [self._b0 for _ in range(self.hparams.num_actions)]
# Regression and NN Update Frequency
self.update_freq_lr = hparams.training_freq
self.update_freq_nn = hparams.training_freq_network
self.t = 0
self.optimizer_n = optimizer
self.num_epochs = hparams.training_epochs
self.data_h = ContextualDataset(hparams.context_dim,
hparams.num_actions,
intercept=False)
self.latent_h = ContextualDataset(self.latent_dim,
hparams.num_actions,
intercept=self.intercept)
if textflag=='yes':
self.bnn = TextCNN('adam', self.hparams.num_actions,self.hparams.batch_size, '{}-bnn'.format(name))
else:
self.bnn = NeuralBanditModel(optimizer, hparams, '{}-bnn'.format(name))
def action(self, context):
"""Samples beta's from posterior, and chooses best action accordingly."""
# Round robin until each action has been selected "initial_pulls" times
if self.t < self.hparams.num_actions * self.hparams.initial_pulls:
return self.t % self.hparams.num_actions
# Sample sigma2, and beta conditional on sigma2
sigma2_s = [
self.b[i] * invgamma.rvs(self.a[i])
for i in range(self.hparams.num_actions)
]
try:
beta_s = [
np.random.multivariate_normal(self.mu[i], sigma2_s[i] * self.cov[i])
for i in range(self.hparams.num_actions)
]
except np.linalg.LinAlgError as e:
# Sampling could fail if covariance is not positive definite
d = self.param_dim
beta_s = [
np.random.multivariate_normal(np.zeros((d)), np.eye(d))
for i in range(self.hparams.num_actions)
]
# Compute last-layer representation for the current context
with self.bnn.graph.as_default():
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn, feed_dict={self.bnn.x: c})
if self.intercept:
z_context = np.append(z_context, 1.0).reshape((1, self.latent_dim + 1))
# Apply Thompson Sampling to last-layer representation
vals = [
np.dot(beta_s[i], z_context.T) for i in range(self.hparams.num_actions)
]
return np.argmax(vals)
def update(self, context, action, reward):
"""Updates the posterior using linear bayesian regression formula."""
self.t += 1
self.data_h.add(context, action, reward)
c = context.reshape((1, self.hparams.context_dim))
z_context = self.bnn.sess.run(self.bnn.nn, feed_dict={self.bnn.x: c})
self.latent_h.add(z_context, action, reward)
# Retrain the network on the original data (data_h)
if self.t % self.update_freq_nn == 0:
if self.hparams.reset_lr:
self.bnn.assign_lr()
#self.bnn.set_last_layer(self.mu)
self.bnn.train(self.data_h, self.num_epochs)
# Update the latent representation of every datapoint collected so far
new_z = self.bnn.sess.run(self.bnn.nn,
feed_dict={self.bnn.x: self.data_h.contexts})
self.latent_h.replace_data(contexts=new_z)
for action_v in range(self.hparams.num_actions):
# Update action posterior with formulas: \beta | z,y ~ N(mu_q, cov_q)
z, y = self.latent_h.get_data(action_v)
# The algorithm could be improved with sequential formulas (cheaper)
self.precision[action_v] = (np.dot(z.T, z)+self.lambda_prior * np.eye(self.param_dim)) #the new PHI_0
self.f[action_v] = np.dot(z.T, y)
else:
if self.intercept:
z_context = np.append(z_context, 1.0).reshape((1, self.latent_dim + 1))
self.precision[action] += np.dot(z_context.T, z_context)
self.f[action] += (z_context.T * reward)[:, 0]
self.yy[action] += reward ** 2
self.cov[action] = np.linalg.inv(self.precision[action])
self.mu[action] = np.dot(self.cov[action], self.f[action])
# Inverse Gamma posterior update
self.a[action] += 0.5
b_upd = 0.5 * (self.yy[action] - np.dot(self.mu[action].T, np.dot(self.precision[action], self.mu[action])))
self.b[action] = self.b0 + b_upd
#print(self.calc_model_evidence())
@property
def a0(self):
return self._a0
@property
def b0(self):
return self._b0
@property
def lambda_prior(self):
return self._lambda_prior
def calc_model_evidence(self):
vval = 0
mp.mp.dps = 50
for action in range(self.hparams.num_actions):
# val=1
# aa = self.a[action]
# for i in range(int(self.a[action]-self.a0)):
# aa-=1
# val*=aa
# val/=(2.0*math.pi)
# val/=self.b[action]
# val*=gamma(aa)
# val/=(self.b[action]**aa)
# val *= np.sqrt(np.linalg.det(self.lambda_prior * np.eye(self.hparams.context_dim + 1)) / np.linalg.det(self.precision[action]))
# val *= (self.b0 ** self.a0)
# val/= gamma(self.a0)
# vval += val
#val= 1/float((2.0 * math.pi) ** (self.a[action]-self.a0))
#val*= (float(gamma(self.a[action]))/float(gamma(self.a0)))
#val*= np.sqrt(float(np.linalg.det(self.lambda_prior * np.eye(self.hparams.context_dim + 1)))/float(np.linalg.det(self.precision[action])))
#val*= (float(self.b0**self.a0)/float(self.b[action]**self.a[action]))
val= mp.mpf(mp.fmul(mp.fneg(mp.log(mp.fmul(2.0 , mp.pi))) , mp.fsub(self.a[action],self.a0)))
val+= mp.loggamma(self.a[action])
val-= mp.loggamma(self.a0)
val+= 0.5*mp.log(np.linalg.det(self.lambda_prior * np.eye(self.hparams.context_dim + 1)))
val -= 0.5*mp.log(np.linalg.det(self.precision[action]))
val+= mp.fmul(self.a0,mp.log(self.b0))
val-= mp.fmul(self.a[action],mp.log(self.b[action]))
vval+=mp.exp(val)
vval/=float(self.hparams.num_actions)
return vval