def kl(self, other):
        """
        Args:
            other: object of CategoricalDistribution

        Returns:
            kl: A float32 tensor with shape [BATCH_SIZE]
        """
        assert isinstance(other, CategoricalDistribution)

        logits = self.logits - layers.reduce_max(self.logits, dim=1)
        other_logits = other.logits - layers.reduce_max(other.logits, dim=1)

        e_logits = layers.exp(logits)
        other_e_logits = layers.exp(other_logits)

        z = layers.reduce_sum(e_logits, dim=1)
        other_z = layers.reduce_sum(other_e_logits, dim=1)

        prob = e_logits / z
        kl = layers.reduce_sum(
            prob *
            (logits - layers.log(z) - other_logits + layers.log(other_z)),
            dim=1)
        return kl
    def logp(self, actions, eps=1e-6):
        """
        Args:
            actions: An int64 tensor with shape [BATCH_SIZE]
            eps: A small float constant that avoids underflows when computing the log probability

        Returns:
            actions_log_prob: A float32 tensor with shape [BATCH_SIZE]
        """
        assert len(actions.shape) == 1

        logits = self.logits - layers.reduce_max(self.logits, dim=1)
        e_logits = layers.exp(logits)
        z = layers.reduce_sum(e_logits, dim=1)
        prob = e_logits / z

        actions = layers.unsqueeze(actions, axes=[1])
        actions_onehot = layers.one_hot(actions, prob.shape[1])
        actions_onehot = layers.cast(actions_onehot, dtype='float32')
        actions_prob = layers.reduce_sum(prob * actions_onehot, dim=1)

        actions_prob = actions_prob + eps
        actions_log_prob = layers.log(actions_prob)

        return actions_log_prob
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    def learn(self,
              obs,
              action,
              reward,
              next_obs,
              terminal,
              learning_rate=None):
        """ update value model self.model with DQN algorithm
        """
        # Support the modification of learning_rate
        if learning_rate is None:
            assert isinstance(
                self.lr,
                float), "Please set the learning rate of DQN in initializaion."
            learning_rate = self.lr

        pred_value = self.model.value(obs)
        next_pred_value = self.target_model.value(next_obs)
        best_v = layers.reduce_max(next_pred_value, dim=1)
        best_v.stop_gradient = True
        target = reward + (
            1.0 - layers.cast(terminal, dtype='float32')) * self.gamma * best_v

        action_onehot = layers.one_hot(action, self.act_dim)
        action_onehot = layers.cast(action_onehot, dtype='float32')
        pred_action_value = layers.reduce_sum(
            layers.elementwise_mul(action_onehot, pred_value), dim=1)
        cost = layers.square_error_cost(pred_action_value, target)
        cost = layers.reduce_mean(cost)
        optimizer = fluid.optimizer.Adam(
            learning_rate=learning_rate, epsilon=1e-3)
        optimizer.minimize(cost)
        return cost
    def entropy(self):
        """
        Returns:
            entropy: A float32 tensor with shape [BATCH_SIZE] of entropy of self policy distribution.
        """
        logits = self.logits - layers.reduce_max(self.logits, dim=1)
        e_logits = layers.exp(logits)
        z = layers.reduce_sum(e_logits, dim=1)
        prob = e_logits / z
        entropy = -1.0 * layers.reduce_sum(prob * (logits - layers.log(z)),
                                           dim=1)

        return entropy
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    def cal_bellman_residual(self, obs, action, reward, next_obs, terminal):
        """ use self.model to get squared Bellman residual with fed data
        """
        pred_value = self.model.value(obs)
        next_pred_value = self.target_model.value(next_obs)
        best_v = layers.reduce_max(next_pred_value, dim=1)
        best_v.stop_gradient = True
        target = reward + (
            1.0 - layers.cast(terminal, dtype='float32')) * self.gamma * best_v

        action_onehot = layers.one_hot(action, self.act_dim)
        action_onehot = layers.cast(action_onehot, dtype='float32')
        pred_action_value = layers.reduce_sum(
            layers.elementwise_mul(action_onehot, pred_value), dim=1)
        cost = layers.square_error_cost(pred_action_value, target)
        cost = layers.reduce_mean(cost)
        return cost
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    def learn(self, obs, action, reward, next_obs, terminal, sample_weight):
        """ update value model self.model with DQN algorithm
        """

        pred_value = self.model.value(obs)
        next_pred_value = self.target_model.value(next_obs)
        best_v = layers.reduce_max(next_pred_value, dim=1)
        best_v.stop_gradient = True
        target = reward + (
            1.0 - layers.cast(terminal, dtype='float32')) * self.gamma * best_v

        action_onehot = layers.one_hot(action, self.act_dim)
        action_onehot = layers.cast(action_onehot, dtype='float32')
        pred_action_value = layers.reduce_sum(action_onehot * pred_value,
                                              dim=1)
        delta = layers.abs(target - pred_action_value)
        cost = sample_weight * layers.square_error_cost(
            pred_action_value, target)
        cost = layers.reduce_mean(cost)
        optimizer = fluid.optimizer.Adam(learning_rate=self.lr, epsilon=1e-3)
        optimizer.minimize(cost)
        return cost, delta  # `delta` is the TD-error