def update(self, x: np.matrix, chosen_arm: int,
reward: Union[int, float]) -> None:
"""Update the reward and parameter information about earch arm.
Parameters
----------
x : array-like, shape = (n_features, )
A test sample.
chosen_arm: int
The chosen arm.
reward: int, float
The observed reward value from the chosen arm.
"""
x = _check_x_input(x)
self.data_size += 1
self.counts[chosen_arm] += 1
self.rewards += reward
self._A_inv[chosen_arm] -= \
self._A_inv[chosen_arm] @ x @ x.T @ self._A_inv[chosen_arm] / (1 + x.T @ self._A_inv[chosen_arm] @ x) # d * d
self._b[:, chosen_arm] += np.ravel(x) * reward # d * 1
if self.data_size % self.batch_size == 0:
self.A_inv, self.b = np.copy(self._A_inv), np.copy(
self._b) # d * d, d * 1
def pull(self,
chosen_arm: int,
x: Optional[np.ndarray] = None) -> Union[int, float]:
"""Pull arms.
chosen_arm: int
The chosen arm.
x : array-like, shape = (n_features, ), optional(default=None)
A test sample.
"""
if self.contextual:
x, e = _check_x_input(x), np.random.normal(loc=0, scale=self.noise)
mu = np.ravel(x.T @ self.params)
reward, regret, self.best_arm = \
np.random.binomial(n=1, p=sigmoid(mu[chosen_arm] + e)), \
np.max(mu) - mu[chosen_arm], np.argmax(mu)
else:
reward, regret = \
np.random.binomial(n=1, p=self.mu[chosen_arm]), self.mu_max - self.mu[chosen_arm]
self.rewards += reward
self.regrets += regret
return reward
def select_arm(self, x: np.ndarray) -> int:
"""Select arms according to the policy for new data.
Parameters
----------
x : array-like, shape = (n_features, )
A test sample.
Returns
-------
result: int
The selected arm.
"""
if True in (self.counts < self.warmup):
result = np.argmax(np.array(self.counts < self.warmup, dtype=int))
else:
x = _check_x_input(x)
self.theta_hat = np.concatenate([
self.A_inv[i] @ np.expand_dims(self.b[:, i], axis=1)
for i in np.arange(self.n_arms)
],
axis=1) # user_dim * n_arms
sigma_hat = np.concatenate([
np.sqrt(x.T @ self.A_inv[i] @ x)
for i in np.arange(self.n_arms)
],
axis=1) # 1 * n_arms
result = np.argmax(x.T @ self.theta_hat + self.alpha * sigma_hat)
return result
def update(self, x: np.ndarray, chosen_arm: int, reward: float) -> None:
"""Update the reward and parameter information about earch arm.
Parameters
----------
x : array-like, shape = (n_features, )
A test sample.
chosen_arm: int
The chosen arm.
reward: int, float
The observed reward value from the chosen arm.
"""
x = _check_x_input(x)
self.counts[chosen_arm] += 1
self.rewards += reward
self.data_stock[chosen_arm].append(x) # (user_dim + arm_dim) * 1
self.reward_stock[chosen_arm].append(reward)
self.data_size += 1
if self.data_size % self.batch_size == 0:
for i in np.arange(self.n_iter):
self.theta_hat[:, chosen_arm], self.hessian_inv[chosen_arm] = \
self._update_theta_hat(chosen_arm, self.theta_hat[:, chosen_arm])
def select_arm(self, x: np.ndarray) -> int:
"""Select arms according to the policy for new data.
Parameters
----------
x : array-like, shape = (n_features, )
A test sample.
Returns
-------
result: int
The selected arm.
"""
if True in (self.counts < self.warmup):
result = np.argmax(np.array(self.counts < self.warmup, dtype=int))
else:
x = _check_x_input(x)
if self.data_size % self.sample_batch == 0:
self.theta_tilde = np.concatenate([
np.expand_dims(np.random.multivariate_normal(
self.theta_hat[:, i], self.hessian_inv[i]),
axis=1) for i in np.arange(self.n_arms)
],
axis=1)
result = np.argmax(x.T @ self.theta_tilde)
return result
def select_arm(self, x: np.ndarray) -> int:
"""Select arms according to the policy for new data.
Parameters
----------
x : array-like, shape = (n_features, )
A test sample.
Returns
-------
result: int
The selected arm.
"""
if True in (self.counts < self.warmup):
result = np.argmax(np.array(self.counts < self.warmup, dtype=int))
else:
z, x = _check_x_input(x[:self.z_dim]), _check_x_input(
x[self.z_dim:])
self.beta = np.linalg.inv(self.A_zero) @ self.b_zero # k * 1
self.theta_hat = np.concatenate(
[(self.A_inv[i] @ (np.expand_dims(self.b[:, i], axis=1) -
self.B[i] @ self.beta))
for i in np.arange(self.n_arms)],
axis=1)
s1 = z.T @ np.linalg.inv(self.A_zero) @ z
s2 = -2 * np.concatenate([
z.T @ np.linalg.inv(self.A_zero) @ self.B[i].T @ self.A_inv[i]
@ x for i in np.arange(self.n_arms)
],
axis=1)
s3 = np.concatenate(
[x.T @ self.A_inv[i] @ x for i in np.arange(self.n_arms)],
axis=1)
s4 = np.concatenate([
x.T @ self.A_inv[i] @ self.B[i] @ np.linalg.inv(self.A_zero)
@ self.B[i].T @ self.A_inv[i] @ x
for i in np.arange(self.n_arms)
],
axis=1)
sigma_hat = s1 + s2 + s3 + s4
result = np.argmax(z.T @ self.beta + x.T @ self.theta_hat +
self.alpha * sigma_hat)
return result
def update(self, x: np.ndarray, chosen_arm: int, reward: float) -> None:
"""Update the reward and parameter information about earch arm.
Parameters
----------
x : array-like, shape = (n_features, )
A test sample.
chosen_arm: int
The chosen arm.
reward: int, float
The observed reward value from the chosen arm.
"""
z, x = _check_x_input(x[:self.z_dim]), _check_x_input(x[self.z_dim:])
self.data_size += 1
self.counts[chosen_arm] += 1
self.rewards += reward
self._A_zero += self._B[chosen_arm].T @ self._A_inv[
chosen_arm] @ self._B[chosen_arm]
self._b_zero += self._B[chosen_arm].T @ self._A_inv[
chosen_arm] @ self._b[chosen_arm]
self._A_inv[chosen_arm] -= self._A_inv[
chosen_arm] @ x @ x.T @ self._A_inv[chosen_arm] / (
1 + x.T @ self._A_inv[chosen_arm] @ x)
self._B[chosen_arm] += x @ z.T
self._b[:, chosen_arm] += np.ravel(x) * reward
self._A_zero += z @ z.T - self._B[chosen_arm].T @ self._A_inv[
chosen_arm] @ self._B[chosen_arm]
self._b_zero += z * reward - self._B[chosen_arm].T @ self._A_inv[
chosen_arm] @ np.expand_dims(self._b[:, chosen_arm], axis=1)
if self.data_size % self.batch_size == 0:
self.A_zero, self.b_zero = np.copy(self._A_zero), np.copy(
self._b_zero)
self.A_inv, self.B, self.b = np.copy(self._A_inv), np.copy(
self._B), np.copy(self._b)