gumbel_muzero.py

import copy
from typing import List, Dict, Any, Tuple, Union

import numpy as np
import torch
import torch.optim as optim
from ding.model import model_wrap
from ding.torch_utils import to_tensor
from ding.utils import POLICY_REGISTRY
from torch.nn import L1Loss, KLDivLoss

from lzero.mcts import GumbelMuZeroMCTSCtree as MCTSCtree
from lzero.mcts import MuZeroMCTSPtree as MCTSPtree
from lzero.model import ImageTransforms
from lzero.policy import scalar_transform, InverseScalarTransform, cross_entropy_loss, phi_transform, \
    DiscreteSupport, to_torch_float_tensor, mz_network_output_unpack, select_action, negative_cosine_similarity, \
    prepare_obs, \
    configure_optimizers
from lzero.policy.muzero import MuZeroPolicy


@POLICY_REGISTRY.register('gumbel_muzero')
class GumbelMuZeroPolicy(MuZeroPolicy):
    """
    Overview:
        The policy class for Gumbel MuZero proposed in the paper https://openreview.net/forum?id=bERaNdoegnO.
    """

    # The default_config for Gumbel MuZero policy.
    config = dict(
        model=dict(
            # (str) The model type. For 1-dimensional vector obs, we use mlp model. For the image obs, we use conv model.
            model_type='conv',  # options={'mlp', 'conv'}
            # (bool) If True, the action space of the environment is continuous, otherwise discrete.
            continuous_action_space=False,
            # (tuple) The stacked obs shape.
            # observation_shape=(1, 96, 96),  # if frame_stack_num=1
            observation_shape=(4, 96, 96),  # if frame_stack_num=4
            # (bool) Whether to use the self-supervised learning loss.
            self_supervised_learning_loss=False,
            # (bool) Whether to use discrete support to represent categorical distribution for value/reward/value_prefix.
            categorical_distribution=True,
            # (int) The image channel in image observation.
            image_channel=1,
            # (int) The number of frames to stack together.
            frame_stack_num=1,
            # (int) The number of res blocks in MuZero model.
            num_res_blocks=1,
            # (int) The number of channels of hidden states in MuZero model.
            num_channels=64,
            # (int) The scale of supports used in categorical distribution.
            # This variable is only effective when ``categorical_distribution=True``.
            support_scale=300,
            # (bool) whether to learn bias in the last linear layer in value and policy head.
            bias=True,
            # (str) The type of action encoding. Options are ['one_hot', 'not_one_hot']. Default to 'one_hot'.
            discrete_action_encoding_type='one_hot',
            # (bool) whether to use res connection in dynamics.
            res_connection_in_dynamics=True,
            # (str) The type of normalization in MuZero model. Options are ['BN', 'LN']. Default to 'LN'.
            norm_type='BN',
        ),
        # ****** common ******
        # (bool) Whether to use multi-gpu training.
        multi_gpu=False,
        # (bool) Whether to enable the sampled-based algorithm (e.g. Sampled EfficientZero)
        # this variable is used in ``collector``.
        sampled_algo=False,
        # (bool) Whether to enable the gumbel-based algorithm (e.g. Gumbel Muzero).
        gumbel_algo=True,
        # (bool) Whether to use C++ MCTS in policy. If False, use Python implementation.
        mcts_ctree=True,
        # (bool) Whether to use cuda for network.
        cuda=True,
        # (int) The number of environments used in collecting data.
        collector_env_num=8,
        # (int) The number of environments used in evaluating policy.
        evaluator_env_num=3,
        # (str) The type of environment. Options is ['not_board_games', 'board_games'].
        env_type='not_board_games',
        # (str) The type of action space. Options are ['fixed_action_space', 'varied_action_space'].
        action_type='fixed_action_space',
        # (str) The type of battle mode. Options is ['play_with_bot_mode', 'self_play_mode'].
        battle_mode='play_with_bot_mode',
        # (bool) Whether to monitor extra statistics in tensorboard.
        monitor_extra_statistics=True,
        # (int) The transition number of one ``GameSegment``.
        game_segment_length=200,
        # (bool): Indicates whether to perform an offline evaluation of the checkpoint (ckpt).
        # If set to True, the checkpoint will be evaluated after the training process is complete.
        # IMPORTANT: Setting eval_offline to True requires configuring the saving of checkpoints to align with the evaluation frequency.
        # This is done by setting the parameter learn.learner.hook.save_ckpt_after_iter to the same value as eval_freq in the train_muzero.py automatically.
        eval_offline=False,

        # ****** observation ******
        # (bool) Whether to transform image to string to save memory.
        transform2string=False,
        # (bool) Whether to use gray scale image.
        gray_scale=False,
        # (bool) Whether to use data augmentation.
        use_augmentation=False,
        # (list) The style of augmentation.
        augmentation=['shift', 'intensity'],

        # ******* learn ******
        # (bool) Whether to ignore the done flag in the training data. Typically, this value is set to False.
        # However, for some environments with a fixed episode length, to ensure the accuracy of Q-value calculations,
        # we should set it to True to avoid the influence of the done flag.
        ignore_done=False,
        # (int) How many updates(iterations) to train after collector's one collection.
        # Bigger "update_per_collect" means bigger off-policy.
        # collect data -> update policy-> collect data -> ...
        # For different env, we have different episode_length,
        # If we set update_per_collect=None, we will set update_per_collect = collected_transitions_num * cfg.policy.model_update_ratio automatically.
        update_per_collect=None,
        # (float) The ratio of the collected data used for training. Only effective when ``update_per_collect`` is not None.
        model_update_ratio=0.1,
        # (int) Minibatch size for one gradient descent.
        batch_size=256,
        # (str) Optimizer for training policy network. ['SGD' or 'Adam']
        optim_type='SGD',
        # (float) Learning rate for training policy network. Ininitial lr for manually decay schedule.
        learning_rate=0.2,
        # (int) Frequency of target network update.
        target_update_freq=100,
        # (float) Weight decay for training policy network.
        weight_decay=1e-4,
        # (float) One-order Momentum in optimizer, which stabilizes the training process (gradient direction).
        momentum=0.9,
        # (float) The maximum constraint value of gradient norm clipping.
        grad_clip_value=10,
        # (int) The number of episode in each collecting stage.
        n_episode=8,
        # (int) the number of simulations in MCTS.
        num_simulations=50,
        # (int) the max considred number in Gumbel MuZero MCTS simulation.
        max_num_considered_actions=4,
        # (float) Discount factor (gamma) for returns.
        discount_factor=0.997,
        # (int) The number of step for calculating target q_value.
        td_steps=5,
        # (int) The number of unroll steps in dynamics network.
        num_unroll_steps=5,
        # (float) The weight of reward loss.
        reward_loss_weight=1,
        # (float) The weight of value loss.
        value_loss_weight=0.25,
        # (float) The weight of policy loss.
        policy_loss_weight=1,
        # (float) The weight of ssl (self-supervised learning) loss.
        ssl_loss_weight=0,
        # (bool) Whether to use piecewise constant learning rate decay.
        # i.e. lr: 0.2 -> 0.02 -> 0.002
        lr_piecewise_constant_decay=True,
        # (int) The number of final training iterations to control lr decay, which is only used for manually decay.
        threshold_training_steps_for_final_lr=int(5e4),
        # (bool) Whether to use manually decayed temperature.
        manual_temperature_decay=False,
        # (int) The number of final training iterations to control temperature, which is only used for manually decay.
        threshold_training_steps_for_final_temperature=int(1e5),
        # (float) The fixed temperature value for MCTS action selection, which is used to control the exploration.
        # The larger the value, the more exploration. This value is only used when manual_temperature_decay=False.
        fixed_temperature_value=0.25,
        # (bool) Whether to add noise to roots during reanalyze process.
        reanalyze_noise=False,

        # ****** Priority ******
        # (bool) Whether to use priority when sampling training data from the buffer.
        use_priority=True,
        # (float) The degree of prioritization to use. A value of 0 means no prioritization,
        # while a value of 1 means full prioritization.
        priority_prob_alpha=0.6,
        # (float) The degree of correction to use. A value of 0 means no correction,
        # while a value of 1 means full correction.
        priority_prob_beta=0.4,

        # ****** UCB ******
        # (float) The alpha value used in the Dirichlet distribution for exploration at the root node of search tree.
        root_dirichlet_alpha=0.3,
        # (float) The noise weight at the root node of the search tree.
        root_noise_weight=0.25,

        # ****** Explore by random collect ******
        # (int) The number of episodes to collect data randomly before training.
        random_collect_episode_num=0,

        # ****** Explore by eps greedy ******
        eps=dict(
            # (bool) Whether to use eps greedy exploration in collecting data.
            eps_greedy_exploration_in_collect=False,
            # (str) The type of decaying epsilon. Options are 'linear', 'exp'.
            type='linear',
            # (float) The start value of eps.
            start=1.,
            # (float) The end value of eps.
            end=0.05,
            # (int) The decay steps from start to end eps.
            decay=int(1e5),
        ),
    )

    def default_model(self) -> Tuple[str, List[str]]:
        """
        Overview:
            Return this algorithm default model setting for demonstration.
        Returns:
            - model_info (:obj:`Tuple[str, List[str]]`): model name and model import_names.
                - model_type (:obj:`str`): The model type used in this algorithm, which is registered in ModelRegistry.
                - import_names (:obj:`List[str]`): The model class path list used in this algorithm.
        .. note::
            The user can define and use customized network model but must obey the same interface definition indicated \
            by import_names path. For MuZero, ``lzero.model.muzero_model.MuZeroModel``
        """
        if self._cfg.model.model_type == "conv":
            return 'MuZeroModel', ['lzero.model.muzero_model']
        elif self._cfg.model.model_type == "mlp":
            return 'MuZeroModelMLP', ['lzero.model.muzero_model_mlp']
        else:
            raise ValueError("model type {} is not supported".format(self._cfg.model.model_type))

    def _init_learn(self) -> None:
        """
        Overview:
            Learn mode init method. Called by ``self.__init__``. Initialize the learn model, optimizer and MCTS utils.
        """
        assert self._cfg.optim_type in ['SGD', 'Adam', 'AdamW'], self._cfg.optim_type
        # NOTE: in board_games, for fixed lr 0.003, 'Adam' is better than 'SGD'.
        if self._cfg.optim_type == 'SGD':
            self._optimizer = optim.SGD(
                self._model.parameters(),
                lr=self._cfg.learning_rate,
                momentum=self._cfg.momentum,
                weight_decay=self._cfg.weight_decay,
            )
        elif self._cfg.optim_type == 'Adam':
            self._optimizer = optim.Adam(
                self._model.parameters(), lr=self._cfg.learning_rate, weight_decay=self._cfg.weight_decay
            )
        elif self._cfg.optim_type == 'AdamW':
            self._optimizer = configure_optimizers(model=self._model, weight_decay=self._cfg.weight_decay,
                                                   learning_rate=self._cfg.learning_rate, device_type=self._cfg.device)

        if self._cfg.lr_piecewise_constant_decay:
            from torch.optim.lr_scheduler import LambdaLR
            max_step = self._cfg.threshold_training_steps_for_final_lr
            # NOTE: the 1, 0.1, 0.01 is the decay rate, not the lr.
            lr_lambda = lambda step: 1 if step < max_step * 0.5 else (0.1 if step < max_step else 0.01)  # noqa
            self.lr_scheduler = LambdaLR(self._optimizer, lr_lambda=lr_lambda)

        # use model_wrapper for specialized demands of different modes
        self._target_model = copy.deepcopy(self._model)
        self._target_model = model_wrap(
            self._target_model,
            wrapper_name='target',
            update_type='assign',
            update_kwargs={'freq': self._cfg.target_update_freq}
        )
        self._learn_model = self._model

        if self._cfg.use_augmentation:
            self.image_transforms = ImageTransforms(
                self._cfg.augmentation,
                image_shape=(self._cfg.model.observation_shape[1], self._cfg.model.observation_shape[2])
            )
        self.value_support = DiscreteSupport(-self._cfg.model.support_scale, self._cfg.model.support_scale, delta=1)
        self.reward_support = DiscreteSupport(-self._cfg.model.support_scale, self._cfg.model.support_scale, delta=1)
        self.inverse_scalar_transform_handle = InverseScalarTransform(
            self._cfg.model.support_scale, self._cfg.device, self._cfg.model.categorical_distribution
        )
        self.kl_loss = KLDivLoss(reduction='none')

    def _forward_learn(self, data: torch.Tensor) -> Dict[str, Union[float, int]]:
        """
        Overview:
            The forward function for learning policy in learn mode, which is the core of the learning process.
            The data is sampled from replay buffer.
            The loss is calculated by the loss function and the loss is backpropagated to update the model.
        Arguments:
            - data (:obj:`Tuple[torch.Tensor]`): The data sampled from replay buffer, which is a tuple of tensors.
                The first tensor is the current_batch, the second tensor is the target_batch.
        Returns:
            - info_dict (:obj:`Dict[str, Union[float, int]]`): The information dict to be logged, which contains \
                current learning loss and learning statistics.
        """
        self._learn_model.train()
        self._target_model.train()

        current_batch, target_batch = data
        obs_batch_ori, action_batch, improved_policy_batch, mask_batch, indices, weights, make_time = current_batch
        target_reward, target_value, target_policy = target_batch

        obs_batch, obs_target_batch = prepare_obs(obs_batch_ori, self._cfg)

        # do augmentations
        if self._cfg.use_augmentation:
            obs_batch = self.image_transforms.transform(obs_batch)
            if self._cfg.model.self_supervised_learning_loss:
                obs_target_batch = self.image_transforms.transform(obs_target_batch)

        # shape: (batch_size, num_unroll_steps, action_dim)
        # NOTE: .long(), in discrete action space.
        action_batch = torch.from_numpy(action_batch).to(self._cfg.device).unsqueeze(-1).long()
        data_list = [
            mask_batch,
            target_reward.astype('float32'),
            target_value.astype('float32'), target_policy, weights
        ]
        [mask_batch, target_reward, target_value, target_policy,
         weights] = to_torch_float_tensor(data_list, self._cfg.device)

        target_reward = target_reward.view(self._cfg.batch_size, -1)
        target_value = target_value.view(self._cfg.batch_size, -1)

        assert obs_batch.size(0) == self._cfg.batch_size == target_reward.size(0)

        # ``scalar_transform`` to transform the original value to the scaled value,
        # i.e. h(.) function in paper https://arxiv.org/pdf/1805.11593.pdf.
        transformed_target_reward = scalar_transform(target_reward)
        transformed_target_value = scalar_transform(target_value)

        # transform a scalar to its categorical_distribution. After this transformation, each scalar is
        # represented as the linear combination of its two adjacent supports.
        target_reward_categorical = phi_transform(self.reward_support, transformed_target_reward)
        target_value_categorical = phi_transform(self.value_support, transformed_target_value)

        # ==============================================================
        # the core initial_inference in Gumbel MuZero policy.
        # ==============================================================
        network_output = self._learn_model.initial_inference(obs_batch)

        # value_prefix shape: (batch_size, 10), the ``value_prefix`` at the first step is zero padding.
        latent_state, reward, value, policy_logits = mz_network_output_unpack(network_output)

        # transform the scaled value or its categorical representation to its original value,
        # i.e. h^(-1)(.) function in paper https://arxiv.org/pdf/1805.11593.pdf.
        original_value = self.inverse_scalar_transform_handle(value)

        # Note: The following lines are just for debugging.
        predicted_rewards = []
        if self._cfg.monitor_extra_statistics:
            predicted_values, predicted_policies = original_value.detach().cpu(), torch.softmax(
                policy_logits, dim=1
            ).detach().cpu()

        # calculate the new priorities for each transition.
        value_priority = L1Loss(reduction='none')(original_value.squeeze(-1), target_value[:, 0])
        value_priority = value_priority.data.cpu().numpy() + 1e-6

        # ==============================================================
        # calculate policy and value loss for the first step.
        # ==============================================================
        # ==============================================================
        # The core difference between GumbelMuZero and MuZero
        # ==============================================================
        # In Gumbel MuZero, the policy loss is defined as the KL loss between current policy and improved policy calculated in MCTS.
        policy_loss = self.kl_loss(torch.log(torch.softmax(policy_logits, dim=1)),
                                   torch.from_numpy(improved_policy_batch[:, 0]).to(self._cfg.device).detach().float())
        policy_loss = policy_loss.mean(dim=-1) * mask_batch[:, 0]
        # Output the entropy for experimental observation.

        prob = torch.softmax(policy_logits, dim=-1)
        policy_entropy = -(prob * prob.log()).sum(-1)

        value_loss = cross_entropy_loss(value, target_value_categorical[:, 0])

        reward_loss = torch.zeros(self._cfg.batch_size, device=self._cfg.device)
        consistency_loss = torch.zeros(self._cfg.batch_size, device=self._cfg.device)

        # ==============================================================
        # the core recurrent_inference in Gumbel MuZero policy.
        # ==============================================================
        for step_k in range(self._cfg.num_unroll_steps):
            # unroll with the dynamics function: predict the next ``latent_state``, ``reward``,
            # given current ``latent_state`` and ``action``.
            # And then predict policy_logits and value with the prediction function.
            network_output = self._learn_model.recurrent_inference(latent_state, action_batch[:, step_k])
            latent_state, reward, value, policy_logits = mz_network_output_unpack(network_output)

            # transform the scaled value or its categorical representation to its original value,
            # i.e. h^(-1)(.) function in paper https://arxiv.org/pdf/1805.11593.pdf.
            original_value = self.inverse_scalar_transform_handle(value)

            if self._cfg.model.self_supervised_learning_loss:
                # ==============================================================
                # calculate consistency loss for the next ``num_unroll_steps`` unroll steps.
                # ==============================================================
                if self._cfg.ssl_loss_weight > 0:
                    # obtain the oracle latent states from representation function.
                    beg_index, end_index = self._get_target_obs_index_in_step_k(step_k)
                    network_output = self._learn_model.initial_inference(obs_target_batch[:, beg_index:end_index])

                    latent_state = to_tensor(latent_state)
                    representation_state = to_tensor(network_output.latent_state)

                    # NOTE: no grad for the representation_state branch
                    dynamic_proj = self._learn_model.project(latent_state, with_grad=True)
                    observation_proj = self._learn_model.project(representation_state, with_grad=False)
                    temp_loss = negative_cosine_similarity(dynamic_proj, observation_proj) * mask_batch[:, step_k]
                    consistency_loss += temp_loss

            # NOTE: the target policy, target_value_categorical, target_reward_categorical is calculated in
            # game buffer now.
            # ==============================================================
            # calculate policy loss for the next ``num_unroll_steps`` unroll steps.
            # NOTE: the +=.
            # ==============================================================
            policy_loss += self.kl_loss(torch.log(torch.softmax(policy_logits, dim=1)),
                                        torch.from_numpy(improved_policy_batch[:, step_k + 1]).to(
                                            self._cfg.device).detach().float()).mean(dim=-1) * mask_batch[:, step_k + 1]
            value_loss += cross_entropy_loss(value, target_value_categorical[:, step_k + 1])
            reward_loss += cross_entropy_loss(reward, target_reward_categorical[:, step_k])

            prob = torch.softmax(policy_logits, dim=-1)
            policy_entropy += (prob * prob.log()).sum(-1)

            if self._cfg.monitor_extra_statistics:
                original_rewards = self.inverse_scalar_transform_handle(reward)
                original_rewards_cpu = original_rewards.detach().cpu()

                predicted_values = torch.cat(
                    (predicted_values, self.inverse_scalar_transform_handle(value).detach().cpu())
                )
                predicted_rewards.append(original_rewards_cpu)
                predicted_policies = torch.cat((predicted_policies, torch.softmax(policy_logits, dim=1).detach().cpu()))

        # ==============================================================
        # the core learn model update step.
        # ==============================================================
        # weighted loss with masks (some invalid states which are out of trajectory.)
        loss = (
                self._cfg.ssl_loss_weight * consistency_loss + self._cfg.policy_loss_weight * policy_loss +
                self._cfg.value_loss_weight * value_loss + self._cfg.reward_loss_weight * reward_loss
        )
        weighted_total_loss = (weights * loss).mean()

        gradient_scale = 1 / self._cfg.num_unroll_steps
        weighted_total_loss.register_hook(lambda grad: grad * gradient_scale)
        self._optimizer.zero_grad()
        weighted_total_loss.backward()
        if self._cfg.multi_gpu:
            self.sync_gradients(self._learn_model)
        total_grad_norm_before_clip = torch.nn.utils.clip_grad_norm_(
            self._learn_model.parameters(), self._cfg.grad_clip_value
        )
        self._optimizer.step()
        if self._cfg.lr_piecewise_constant_decay:
            self.lr_scheduler.step()

        # ==============================================================
        # the core target model update step.
        # ==============================================================
        self._target_model.update(self._learn_model.state_dict())

        if self._cfg.monitor_extra_statistics:
            predicted_rewards = torch.stack(predicted_rewards).transpose(1, 0).squeeze(-1)
            predicted_rewards = predicted_rewards.reshape(-1).unsqueeze(-1)

        return {
            'collect_mcts_temperature': self._collect_mcts_temperature,
            'cur_lr': self._optimizer.param_groups[0]['lr'],
            'weighted_total_loss': weighted_total_loss.item(),
            'total_loss': loss.mean().item(),
            'policy_loss': policy_loss.mean().item(),
            'reward_loss': reward_loss.mean().item(),
            'value_loss': value_loss.mean().item(),
            'consistency_loss': consistency_loss.mean().item() / self._cfg.num_unroll_steps,
            'policy_entropy': policy_entropy.mean().item(),

            # ==============================================================
            # priority related
            # ==============================================================
            'value_priority_orig': value_priority,
            'value_priority': value_priority.mean().item(),
            'target_reward': target_reward.detach().cpu().numpy().mean().item(),
            'target_value': target_value.detach().cpu().numpy().mean().item(),
            'transformed_target_reward': transformed_target_reward.detach().cpu().numpy().mean().item(),
            'transformed_target_value': transformed_target_value.detach().cpu().numpy().mean().item(),
            'predicted_rewards': predicted_rewards.detach().cpu().numpy().mean().item(),
            'predicted_values': predicted_values.detach().cpu().numpy().mean().item(),
            'total_grad_norm_before_clip': total_grad_norm_before_clip.item()
        }

    def _init_collect(self) -> None:
        """
        Overview:
            Collect mode init method. Called by ``self.__init__``. Initialize the collect model and MCTS utils.
        """
        self._collect_model = self._model
        if self._cfg.mcts_ctree:
            self._mcts_collect = MCTSCtree(self._cfg)
        else:
            self._mcts_collect = MCTSPtree(self._cfg)
        self._collect_mcts_temperature = 1

    def _forward_collect(
            self,
            data: torch.Tensor,
            action_mask: list = None,
            temperature: float = 1,
            to_play: List = [-1],
            epsilon: float = 0.25,
            ready_env_id: np.array = None,
    ) -> Dict:
        """
        Overview:
            The forward function for collecting data in collect mode. Use model to execute MCTS search.
            Choosing the action through sampling during the collect mode.
        Arguments:
            - data (:obj:`torch.Tensor`): The input data, i.e. the observation.
            - action_mask (:obj:`list`): The action mask, i.e. the action that cannot be selected.
            - temperature (:obj:`float`): The temperature of the policy.
            - to_play (:obj:`int`): The player to play.
            - ready_env_id (:obj:`list`): The id of the env that is ready to collect.
        Shape:
            - data (:obj:`torch.Tensor`):
                - For Atari, :math:`(N, C*S, H, W)`, where N is the number of collect_env, C is the number of channels, \
                    S is the number of stacked frames, H is the height of the image, W is the width of the image.
                - For lunarlander, :math:`(N, O)`, where N is the number of collect_env, O is the observation space size.
            - action_mask: :math:`(N, action_space_size)`, where N is the number of collect_env.
            - temperature: :math:`(1, )`.
            - to_play: :math:`(N, 1)`, where N is the number of collect_env.
            - ready_env_id: None
        Returns:
            - output (:obj:`Dict[int, Any]`): Dict type data, the keys including ``action``, ``distributions``, \
                ``visit_count_distribution_entropy``, ``value``, ``roots_completed_value``, ``improved_policy_probs``, \
                ``pred_value``, ``policy_logits``.
        """
        self._collect_model.eval()
        self._collect_mcts_temperature = temperature
        self.collect_epsilon = epsilon
        active_collect_env_num = data.shape[0]
        with torch.no_grad():
            # data shape [B, S x C, W, H], e.g. {Tensor:(B, 12, 96, 96)}
            network_output = self._collect_model.initial_inference(data)
            latent_state_roots, reward_roots, pred_values, policy_logits = mz_network_output_unpack(network_output)

            pred_values = self.inverse_scalar_transform_handle(pred_values).detach().cpu().numpy()
            latent_state_roots = latent_state_roots.detach().cpu().numpy()
            policy_logits = policy_logits.detach().cpu().numpy().tolist()

            legal_actions = [[i for i, x in enumerate(action_mask[j]) if x == 1] for j in range(active_collect_env_num)]
            # the only difference between collect and eval is the dirichlet noise
            noises = [
                np.random.dirichlet([self._cfg.root_dirichlet_alpha] * int(sum(action_mask[j]))
                                    ).astype(np.float32).tolist() for j in range(active_collect_env_num)
            ]
            if self._cfg.mcts_ctree:
                # cpp mcts_tree
                roots = MCTSCtree.roots(active_collect_env_num, legal_actions)
            else:
                # python mcts_tree
                roots = MCTSPtree.roots(active_collect_env_num, legal_actions)

            roots.prepare(self._cfg.root_noise_weight, noises, reward_roots, list(pred_values), policy_logits, to_play)
            self._mcts_collect.search(roots, self._collect_model, latent_state_roots, to_play)

            # list of list, shape: ``{list: batch_size} -> {list: action_space_size}``
            roots_visit_count_distributions = roots.get_distributions()
            roots_values = roots.get_values()  # shape: {list: batch_size}
            roots_completed_values = roots.get_children_values(self._cfg.discount_factor,
                                                               self._cfg.model.action_space_size)

            # ==============================================================
            # The core difference between GumbelMuZero and MuZero
            # ==============================================================
            # Gumbel MuZero selects the action according to the improved policy
            roots_improved_policy_probs = roots.get_policies(self._cfg.discount_factor,
                                                             self._cfg.model.action_space_size)  # new policy constructed with completed Q in gumbel muzero
            roots_improved_policy_probs = np.array(roots_improved_policy_probs)

            data_id = [i for i in range(active_collect_env_num)]
            output = {i: None for i in data_id}

            if ready_env_id is None:
                ready_env_id = np.arange(active_collect_env_num)

            for i, env_id in enumerate(ready_env_id):
                distributions, value, improved_policy_probs = roots_visit_count_distributions[i], roots_values[i], \
                roots_improved_policy_probs[i]

                roots_completed_value = roots_completed_values[i]
                # NOTE: Only legal actions possess visit counts, so the ``action_index_in_legal_action_set`` represents
                # the index within the legal action set, rather than the index in the entire action set.
                action_index_in_legal_action_set, visit_count_distribution_entropy = select_action(
                    distributions, temperature=self._collect_mcts_temperature, deterministic=False
                )
                # NOTE: Convert the ``action_index_in_legal_action_set`` to the corresponding ``action`` in the
                # entire action set.
                valid_value = np.where(action_mask[i] == 1.0, improved_policy_probs, 0.0)
                action = np.argmax([v for v in valid_value])
                roots_completed_value = np.where(action_mask[i] == 1.0, roots_completed_value, 0.0)

                output[env_id] = {
                    'action': action,
                    'visit_count_distributions': distributions,
                    'visit_count_distribution_entropy': visit_count_distribution_entropy,
                    'searched_value': value,
                    'roots_completed_value': roots_completed_value,
                    'improved_policy_probs': improved_policy_probs,
                    'predicted_value': pred_values[i],
                    'predicted_policy_logits': policy_logits[i],
                }

        return output

    def _init_eval(self) -> None:
        """
        Overview:
            Evaluate mode init method. Called by ``self.__init__``. Initialize the eval model and MCTS utils.
        """
        self._eval_model = self._model
        if self._cfg.mcts_ctree:
            self._mcts_eval = MCTSCtree(self._cfg)
        else:
            self._mcts_eval = MCTSPtree(self._cfg)

    def _forward_eval(self, data: torch.Tensor, action_mask: list, to_play: int = -1,
                      ready_env_id: np.array = None, ) -> Dict:
        """
        Overview:
            The forward function for evaluating the current policy in eval mode. Use model to execute MCTS search.
            Choosing the action with the highest value (argmax) rather than sampling during the eval mode.
        Arguments:
            - data (:obj:`torch.Tensor`): The input data, i.e. the observation.
            - action_mask (:obj:`list`): The action mask, i.e. the action that cannot be selected.
            - to_play (:obj:`int`): The player to play.
            - ready_env_id (:obj:`list`): The id of the env that is ready to collect.
        Shape:
            - data (:obj:`torch.Tensor`):
                - For Atari, :math:`(N, C*S, H, W)`, where N is the number of collect_env, C is the number of channels, \
                    S is the number of stacked frames, H is the height of the image, W is the width of the image.
                - For lunarlander, :math:`(N, O)`, where N is the number of collect_env, O is the observation space size.
            - action_mask: :math:`(N, action_space_size)`, where N is the number of collect_env.
            - to_play: :math:`(N, 1)`, where N is the number of collect_env.
            - ready_env_id: None
        Returns:
            - output (:obj:`Dict[int, Any]`): Dict type data, the keys including ``action``, ``distributions``, \
                ``visit_count_distribution_entropy``, ``value``, ``pred_value``, ``policy_logits``.
        """
        self._eval_model.eval()
        active_eval_env_num = data.shape[0]
        with torch.no_grad():
            # data shape [B, S x C, W, H], e.g. {Tensor:(B, 12, 96, 96)}
            network_output = self._collect_model.initial_inference(data)
            latent_state_roots, reward_roots, pred_values, policy_logits = mz_network_output_unpack(network_output)

            if not self._eval_model.training:
                # if not in training, obtain the scalars of the value/reward
                pred_values = self.inverse_scalar_transform_handle(pred_values).detach().cpu().numpy()  # shape（B, 1）
                latent_state_roots = latent_state_roots.detach().cpu().numpy()
                policy_logits = policy_logits.detach().cpu().numpy().tolist()  # list shape（B, A）

            legal_actions = [[i for i, x in enumerate(action_mask[j]) if x == 1] for j in range(active_eval_env_num)]
            if self._cfg.mcts_ctree:
                # cpp mcts_tree
                roots = MCTSCtree.roots(active_eval_env_num, legal_actions)
            else:
                # python mcts_tree
                roots = MCTSPtree.roots(active_eval_env_num, legal_actions)
            roots.prepare_no_noise(reward_roots, list(pred_values), policy_logits, to_play)
            self._mcts_eval.search(roots, self._eval_model, latent_state_roots, to_play)

            # list of list, shape: ``{list: batch_size} -> {list: action_space_size}``
            roots_visit_count_distributions = roots.get_distributions()
            roots_values = roots.get_values()  # shape: {list: batch_size}

            # ==============================================================
            # The core difference between GumbelMuZero and MuZero
            # ==============================================================
            # Gumbel MuZero selects the action according to the improved policy
            roots_improved_policy_probs = roots.get_policies(self._cfg.discount_factor,
                                                             self._cfg.model.action_space_size)  # new policy constructed with completed Q in gumbel muzero
            roots_improved_policy_probs = np.array(roots_improved_policy_probs)

            data_id = [i for i in range(active_eval_env_num)]
            output = {i: None for i in data_id}

            if ready_env_id is None:
                ready_env_id = np.arange(active_eval_env_num)

            for i, env_id in enumerate(ready_env_id):
                distributions, value, improved_policy_probs = roots_visit_count_distributions[i], roots_values[i], \
                roots_improved_policy_probs[i]
                # NOTE: Only legal actions possess visit counts, so the ``action_index_in_legal_action_set`` represents
                # the index within the legal action set, rather than the index in the entire action set.
                #  Setting deterministic=True implies choosing the action with the highest value (argmax) rather than
                # sampling during the evaluation phase.
                action_index_in_legal_action_set, visit_count_distribution_entropy = select_action(
                    distributions, temperature=1, deterministic=True
                )
                # NOTE: Convert the ``action_index_in_legal_action_set`` to the corresponding ``action`` in the
                # entire action set.
                # action = np.where(action_mask[i] == 1.0)[0][action_index_in_legal_action_set]

                valid_value = np.where(action_mask[i] == 1.0, improved_policy_probs, 0.0)
                action = np.argmax([v for v in valid_value])

                output[env_id] = {
                    'action': action,
                    'visit_count_distributions': distributions,
                    'visit_count_distribution_entropy': visit_count_distribution_entropy,
                    'searched_value': value,
                    'predicted_value': pred_values[i],
                    'predicted_policy_logits': policy_logits[i],
                }

        return output

    def _monitor_vars_learn(self) -> List[str]:
        """
        Overview:
            Register the variables to be monitored in learn mode. The registered variables will be logged in
            tensorboard according to the return value ``_forward_learn``.
        """
        return [
            'collect_mcts_temperature',
            'cur_lr',
            'weighted_total_loss',
            'total_loss',
            'policy_loss',
            'reward_loss',
            'value_loss',
            'consistency_loss',
            'policy_entropy',
            'value_priority',
            'target_reward',
            'target_value',
            'predicted_rewards',
            'predicted_values',
            'transformed_target_reward',
            'transformed_target_value',
            'total_grad_norm_before_clip',
        ]

    def _state_dict_learn(self) -> Dict[str, Any]:
        """
        Overview:
            Return the state_dict of learn mode, usually including model, target_model and optimizer.
        Returns:
            - state_dict (:obj:`Dict[str, Any]`): The dict of current policy learn state, for saving and restoring.
        """
        return {
            'model': self._learn_model.state_dict(),
            'target_model': self._target_model.state_dict(),
            'optimizer': self._optimizer.state_dict(),
        }

    def _load_state_dict_learn(self, state_dict: Dict[str, Any]) -> None:
        """
        Overview:
            Load the state_dict variable into policy learn mode.
        Arguments:
            - state_dict (:obj:`Dict[str, Any]`): The dict of policy learn state saved before.
        """
        self._learn_model.load_state_dict(state_dict['model'])
        self._target_model.load_state_dict(state_dict['target_model'])
        self._optimizer.load_state_dict(state_dict['optimizer'])

    def _process_transition(self, obs, policy_output, timestep):
        # be compatible with DI-engine Policy class
        pass

    def _get_train_sample(self, data):
        # be compatible with DI-engine Policy class
        pass