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Models, Preprocessors, and Action Distributions

The following diagram provides a conceptual overview of data flow between different components in RLlib. We start with an Environment, which - given an action - produces an observation. The observation is preprocessed by a Preprocessor and Filter (e.g. for running mean normalization) before being sent to a neural network Model. The model output is in turn interpreted by an ActionDistribution to determine the next action.

image

The components highlighted in green can be replaced with custom user-defined implementations, as described in the next sections. The purple components are RLlib internal, which means they can only be modified by changing the algorithm source code.

Default Behaviors

Built-in Preprocessors

RLlib tries to pick one of its built-in preprocessors based on the environment's observation space. Thereby, the following simple rules apply:

  • Discrete observations are one-hot encoded, e.g. Discrete(3) and value=1 -> [0, 1, 0].
  • MultiDiscrete observations are encoded by one-hot encoding each discrete element and then concatenating the respective one-hot encoded vectors. e.g. MultiDiscrete([3, 4]) and value=[1, 3] -> [0 1 0 0 0 0 1] because the first 1 is encoded as [0 1 0] and the second 3 is encoded as [0 0 0 1]; these two vectors are then concatenated to [0 1 0 0 0 0 1].
  • Tuple and Dict observations are flattened, thereby, Discrete and MultiDiscrete sub-spaces are handled as described above. Also, the original dict/tuple observations are still available inside a) the Model via the input dict's "obs" key (the flattened observations are in "obs_flat"), as well as b) the Policy via the following line of code (e.g. put this into your loss function to access the original observations: dict_or_tuple_obs = restore_original_dimensions(input_dict["obs"], self.obs_space, "tf|torch")

For Atari observation spaces, RLlib defaults to using the DeepMind preprocessors (preprocessor_pref=deepmind). However, if the Algorithm's config key preprocessor_pref is set to "rllib", the following mappings apply for Atari-type observation spaces:

  • Images of shape (210, 160, 3) are downscaled to dim x dim, where dim is a model config key (see default Model config below). Also, you can set grayscale=True for reducing the color channel to 1, or zero_mean=True for producing -1.0 to 1.0 values (instead of 0.0 to 1.0 values by default).
  • Atari RAM observations (1D space of shape (128, )) are zero-averaged (values between -1.0 and 1.0).

In all other cases, no preprocessor will be used and the raw observations from the environment will be sent directly into your model.

Default Model Config Settings

In the following paragraphs, we will first describe RLlib's default behavior for automatically constructing models (if you don't setup a custom one), then dive into how you can customize your models by changing these settings or writing your own model classes.

By default, RLlib will use the following config settings for your models. These include options for the FullyConnectedNetworks (fcnet_hiddens and fcnet_activation), VisionNetworks (conv_filters and conv_activation), auto-RNN wrapping, auto-Attention (GTrXL) wrapping, and some special options for Atari environments:

../../../rllib/models/catalog.py

The dict above (or an overriding sub-set) is handed to the Algorithm via the model key within the main config dict like so:

algo_config = {
    # All model-related settings go into this sub-dict.
    "model": {
        # By default, the MODEL_DEFAULTS dict above will be used.

        # Change individual keys in that dict by overriding them, e.g.
        "fcnet_hiddens": [512, 512, 512],
        "fcnet_activation": "relu",
    },

    # ... other Algorithm config keys, e.g. "lr" ...
    "lr": 0.00001,
}

Built-in Models

After preprocessing (if applicable) the raw environment outputs, the processed observations are fed through the policy's model. In case, no custom model is specified (see further below on how to customize models), RLlib will pick a default model based on simple heuristics:

  • A vision network (TF or Torch) for observations that have a shape of length larger than 2, for example, (84 x 84 x 3).
  • A fully connected network (TF or Torch) for everything else.

These default model types can further be configured via the model config key inside your Algorithm config (as discussed above). Available settings are listed above and also documented in the model catalog file.

Note that for the vision network case, you'll probably have to configure conv_filters, if your environment observations have custom sizes. For example, "model": {"dim": 42, "conv_filters": [[16, [4, 4], 2], [32, [4, 4], 2], [512, [11, 11], 1]]} for 42x42 observations. Thereby, always make sure that the last Conv2D output has an output shape of [B, 1, 1, X] ([B, X, 1, 1] for PyTorch), where B=batch and X=last Conv2D layer's number of filters, so that RLlib can flatten it. An informative error will be thrown if this is not the case.

Built-in auto-LSTM, and auto-Attention Wrappers

In addition, if you set "use_lstm": True or "use_attention": True in your model config, your model's output will be further processed by an LSTM cell (TF or Torch), or an attention (GTrXL) network (TF or Torch), respectively. More generally, RLlib supports the use of recurrent/attention models for all its policy-gradient algorithms (A3C, PPO, PG, IMPALA), and the necessary sequence processing support is built into its policy evaluation utilities.

See above for which additional config keys to use to configure in more detail these two auto-wrappers (e.g. you can specify the size of the LSTM layer by lstm_cell_size or the attention dim by attention_dim).

For fully customized RNN/LSTM/Attention-Net setups see the Recurrent Models and Attention Networks/Transformers sections below.

Note

It is not possible to use both auto-wrappers (lstm and attention) at the same time. Doing so will create an error.

Customizing Preprocessors and Models

Custom Preprocessors and Environment Filters

Warning

Custom preprocessors have been fully deprecated, since they sometimes conflict with the built-in preprocessors for handling complex observation spaces. Please use wrapper classes around your environment instead of preprocessors. Note that the built-in default Preprocessors described above will still be used and won't be deprecated.

Instead of using the deprecated custom Preprocessors, you should use gym.Wrappers to preprocess your environment's output (observations and rewards), but also your Model's computed actions before sending them back to the environment.

For example, for manipulating your env's observations or rewards, do:

import gymnasium as gym
from ray.rllib.utils.numpy import one_hot

class OneHotEnv(gym.core.ObservationWrapper):
    # Override `observation` to custom process the original observation
    # coming from the env.
    def observation(self, observation):
        # E.g. one-hotting a float obs [0.0, 5.0[.
        return one_hot(observation, depth=5)


class ClipRewardEnv(gym.core.RewardWrapper):
    def __init__(self, env, min_, max_):
        super().__init__(env)
        self.min = min_
        self.max = max_

    # Override `reward` to custom process the original reward coming
    # from the env.
    def reward(self, reward):
        # E.g. simple clipping between min and max.
        return np.clip(reward, self.min, self.max)

Custom Models: Implementing your own Forward Logic

If you would like to provide your own model logic (instead of using RLlib's built-in defaults), you can sub-class either TFModelV2 (for TensorFlow) or TorchModelV2 (for PyTorch) and then register and specify your sub-class in the config as follows:

Custom TensorFlow Models

Custom TensorFlow models should subclass TFModelV2 and implement the __init__() and forward() methods. forward() takes a dict of tensor inputs (mapping str to Tensor types), whose keys and values depend on the view requirements of the model. Normally, this input dict contains only the current observation obs and an is_training boolean flag, as well as an optional list of RNN states. forward() should return the model output (of size self.num_outputs) and - if applicable - a new list of internal states (in case of RNNs or attention nets). You can also override extra methods of the model such as value_function to implement a custom value branch.

Additional supervised/self-supervised losses can be added via the TFModelV2.custom_loss method:

ray.rllib.models.tf.tf_modelv2.TFModelV2

Once implemented, your TF model can then be registered and used in place of a built-in default one:

import ray
import ray.rllib.algorithms.ppo as ppo
from ray.rllib.models import ModelCatalog
from ray.rllib.models.tf.tf_modelv2 import TFModelV2

class MyModelClass(TFModelV2):
    def __init__(self, obs_space, action_space, num_outputs, model_config, name): ...
    def forward(self, input_dict, state, seq_lens): ...
    def value_function(self): ...

ModelCatalog.register_custom_model("my_tf_model", MyModelClass)

ray.init()
algo = ppo.PPO(env="CartPole-v1", config={
    "model": {
        "custom_model": "my_tf_model",
        # Extra kwargs to be passed to your model's c'tor.
        "custom_model_config": {},
    },
})

See the keras model example for a full example of a TF custom model.

More examples and explanations on how to implement custom Tuple/Dict processing models (also check out this test case here), custom RNNs, custom model APIs (on top of default models) follow further below.

Custom PyTorch Models

Similarly, you can create and register custom PyTorch models by subclassing TorchModelV2 and implement the __init__() and forward() methods. forward() takes a dict of tensor inputs (mapping str to PyTorch tensor types), whose keys and values depend on the view requirements of the model. Usually, the dict contains only the current observation obs and an is_training boolean flag, as well as an optional list of RNN states. forward() should return the model output (of size self.num_outputs) and - if applicable - a new list of internal states (in case of RNNs or attention nets). You can also override extra methods of the model such as value_function to implement a custom value branch.

Additional supervised/self-supervised losses can be added via the TorchModelV2.custom_loss method:

See these examples of fully connected, convolutional, and recurrent torch models.

ray.rllib.models.torch.torch_modelv2.TorchModelV2

Once implemented, your PyTorch model can then be registered and used in place of a built-in model:

import torch.nn as nn

import ray
from ray.rllib.algorithms import ppo
from ray.rllib.models import ModelCatalog
from ray.rllib.models.torch.torch_modelv2 import TorchModelV2

class CustomTorchModel(TorchModelV2):
    def __init__(self, obs_space, action_space, num_outputs, model_config, name): ...
    def forward(self, input_dict, state, seq_lens): ...
    def value_function(self): ...

ModelCatalog.register_custom_model("my_torch_model", CustomTorchModel)

ray.init()
algo = ppo.PPO(env="CartPole-v1", config={
    "framework": "torch",
    "model": {
        "custom_model": "my_torch_model",
        # Extra kwargs to be passed to your model's c'tor.
        "custom_model_config": {},
    },
})

See the torch model examples for various examples on how to build a custom PyTorch model (including recurrent ones).

More examples and explanations on how to implement custom Tuple/Dict processing models (also check out this test case here), custom RNNs, custom model APIs (on top of default models) follow further below.

Wrapping a Custom Model (TF and PyTorch) with an LSTM- or Attention Net

You can also use a custom (TF or PyTorch) model with our auto-wrappers for LSTMs (use_lstm=True) or Attention networks (use_attention=True). For example, if you would like to wrap some non-default model logic with an LSTM, simply do:

../../../rllib/examples/lstm_auto_wrapping.py

Implementing custom Recurrent Networks

Instead of using the use_lstm: True option, it may be preferable to use a custom recurrent model. This provides more control over postprocessing the LSTM's output and can also allow the use of multiple LSTM cells to process different portions of the input. For an RNN model it is recommended to subclass RecurrentNetwork (either the TF or PyTorch versions) and then implement __init__(), get_initial_state(), and forward_rnn().

ray.rllib.models.tf.recurrent_net.RecurrentNetwork

__init__

get_initial_state

forward_rnn

Note that the inputs arg entering forward_rnn is already a time-ranked single tensor (not an input_dict!) with shape (B x T x ...). If you further want to customize and need more direct access to the complete (non time-ranked) input_dict, you can also override your Model's forward method directly (as you would do with a non-RNN ModelV2). In that case, though, you are responsible for changing your inputs and add the time rank to the incoming data (usually you just have to reshape).

You can check out the rnn_model.py models as examples to implement your own (either TF or Torch).

Implementing custom Attention Networks

Similar to the RNN case described above, you could also implement your own attention-based networks, instead of using the use_attention: True flag in your model config.

Check out RLlib's GTrXL (Attention Net) implementations (for TF and PyTorch) to get a better idea on how to write your own models of this type. These are the models we use as wrappers when use_attention=True.

You can run this example script to run these nets within some of our algorithms. There is also a test case, which confirms their learning capabilities in PPO and IMPALA.

Batch Normalization

You can use tf.layers.batch_normalization(x, training=input_dict["is_training"]) to add batch norm layers to your custom model (see a code example here). RLlib will automatically run the update ops for the batch norm layers during optimization (see tf_policy.py and multi_gpu_learner_thread.py for the exact handling of these updates).

In case RLlib does not properly detect the update ops for your custom model, you can override the update_ops() method to return the list of ops to run for updates.

Custom Model APIs (on Top of Default- or Custom Models)

So far we talked about a) the default models that are built into RLlib and are being provided automatically if you don't specify anything in your Algorithm's config and b) custom Models through which you can define any arbitrary forward passes.

Another typical situation in which you would have to customize a model would be to add a new API that your algorithm needs in order to learn, for example a Q-value calculating head on top of your policy model. In order to expand a Model's API, simply define and implement a new method (e.g. get_q_values()) in your TF- or TorchModelV2 sub-class.

You can now wrap this new API either around RLlib's default models or around your custom (forward()-overriding) model classes. Here are two examples that illustrate how to do this:

The Q-head API: Adding a dueling layer on top of a default RLlib model.

The following code adds a get_q_values() method to the automatically chosen default Model (e.g. a FullyConnectedNetwork if the observation space is a 1D Box or Discrete):

../../../rllib/examples/models/custom_model_api.py

Now, for your algorithm that needs to have this model API to work properly (e.g. DQN), you use this following code to construct the complete final Model using the ModelCatalog.get_model_v2 factory function (code here):

../../../rllib/examples/custom_model_api.py

With the model object constructed above, you can get the underlying intermediate output (before the dueling head) by calling my_dueling_model directly (out = my_dueling_model([input_dict])), and then passing out into your custom get_q_values method: q_values = my_dueling_model.get_q_values(out).

The single Q-value API for SAC.

Our DQN model from above takes an observation and outputs one Q-value per (discrete) action. Continuous SAC - on the other hand - uses Models that calculate one Q-value only for a single (continuous) action, given an observation and that particular action.

Let's take a look at how we would construct this API and wrap it around a custom model:

../../../rllib/examples/models/custom_model_api.py

Now, for your algorithm that needs to have this model API to work properly (e.g. SAC), you use this following code to construct the complete final Model using the ModelCatalog.get_model_v2 factory function (code here):

../../../rllib/examples/custom_model_api.py

With the model object constructed above, you can get the underlying intermediate output (before the q-head) by calling my_cont_action_q_model directly (out = my_cont_action_q_model([input_dict])), and then passing out and some action into your custom get_single_q_value method: q_value = my_cont_action_q_model.get_signle_q_value(out, action).

More examples for Building Custom Models

A multi-input capable model for Tuple observation spaces (for PPO)

RLlib's default preprocessor for Tuple and Dict spaces is to flatten incoming observations into one flat 1D array, and then pick a fully connected network (by default) to process this flattened vector. This is usually ok, if you have only 1D Box or Discrete/MultiDiscrete sub-spaces in your observations.

However, what if you had a complex observation space with one or more image components in it (besides 1D Boxes and discrete spaces). You would probably want to preprocess each of the image components using some convolutional network, and then concatenate their outputs with the remaining non-image (flat) inputs (the 1D Box and discrete/one-hot components).

Take a look at this model example that does exactly that:

../../../rllib/models/tf/complex_input_net.py

Using the Trajectory View API: Passing in the last n actions (or rewards or observations) as inputs to a custom Model

It is sometimes helpful for learning not only to look at the current observation in order to calculate the next action, but also at the past n observations. In other cases, you may want to provide the most recent rewards or actions to the model as well (like our LSTM wrapper does if you specify: use_lstm=True and lstm_use_prev_action/reward=True). All this may even be useful when not working with partially observable environments (PO-MDPs) and/or RNN/Attention models, as for example in classic Atari runs, where we usually use framestacking of the last four observed images.

The trajectory view API allows your models to specify these more complex "view requirements".

Here is a simple (non-RNN/Attention) example of a Model that takes as input the last 3 observations (very similar to the recommended "framestacking" for learning in Atari environments):

../../../rllib/examples/models/trajectory_view_utilizing_models.py

A PyTorch version of the above model is also given in the same file.

Custom Action Distributions

Similar to custom models and preprocessors, you can also specify a custom action distribution class as follows. The action dist class is passed a reference to the model, which you can use to access model.model_config or other attributes of the model. This is commonly used to implement autoregressive action outputs.

import ray
import ray.rllib.algorithms.ppo as ppo
from ray.rllib.models import ModelCatalog
from ray.rllib.models.preprocessors import Preprocessor

class MyActionDist(ActionDistribution):
    @staticmethod
    def required_model_output_shape(action_space, model_config):
        return 7  # controls model output feature vector size

    def __init__(self, inputs, model):
        super(MyActionDist, self).__init__(inputs, model)
        assert model.num_outputs == 7

    def sample(self): ...
    def logp(self, actions): ...
    def entropy(self): ...

ModelCatalog.register_custom_action_dist("my_dist", MyActionDist)

ray.init()
algo = ppo.PPO(env="CartPole-v1", config={
    "model": {
        "custom_action_dist": "my_dist",
    },
})

Supervised Model Losses

You can mix supervised losses into any RLlib algorithm through custom models. For example, you can add an imitation learning loss on expert experiences, or a self-supervised autoencoder loss within the model. These losses can be defined over either policy evaluation inputs, or data read from offline storage.

TensorFlow: To add a supervised loss to a custom TF model, you need to override the custom_loss() method. This method takes in the existing policy loss for the algorithm, which you can add your own supervised loss to before returning. For debugging, you can also return a dictionary of scalar tensors in the metrics() method. Here is a runnable example of adding an imitation loss to CartPole training that is defined over a offline dataset.

PyTorch: There is no explicit API for adding losses to custom torch models. However, you can modify the loss in the policy definition directly. Like for TF models, offline datasets can be incorporated by creating an input reader and calling reader.next() in the loss forward pass.

Self-Supervised Model Losses

You can also use the custom_loss() API to add in self-supervised losses such as VAE reconstruction loss and L2-regularization.

Variable-length / Complex Observation Spaces

RLlib supports complex and variable-length observation spaces, including gym.spaces.Tuple, gym.spaces.Dict, and rllib.utils.spaces.Repeated. The handling of these spaces is transparent to the user. RLlib internally will insert preprocessors to insert padding for repeated elements, flatten complex observations into a fixed-size vector during transit, and unpack the vector into the structured tensor before sending it to the model. The flattened observation is available to the model as input_dict["obs_flat"], and the unpacked observation as input_dict["obs"].

To enable batching of struct observations, RLlib unpacks them in a StructTensor-like format. In summary, repeated fields are "pushed down" and become the outer dimensions of tensor batches, as illustrated in this figure from the StructTensor RFC.

image

For further information about complex observation spaces, see:

Variable-length / Parametric Action Spaces

Custom models can be used to work with environments where (1) the set of valid actions varies per step, and/or (2) the number of valid actions is very large. The general idea is that the meaning of actions can be completely conditioned on the observation, i.e., the a in Q(s, a) becomes just a token in [0, MAX_AVAIL_ACTIONS) that only has meaning in the context of s. This works with algorithms in the DQN and policy-gradient families and can be implemented as follows:

  1. The environment should return a mask and/or list of valid action embeddings as part of the observation for each step. To enable batching, the number of actions can be allowed to vary from 1 to some max number:
class MyParamActionEnv(gym.Env):
    def __init__(self, max_avail_actions):
        self.action_space = Discrete(max_avail_actions)
        self.observation_space = Dict({
            "action_mask": Box(0, 1, shape=(max_avail_actions, )),
            "avail_actions": Box(-1, 1, shape=(max_avail_actions, action_embedding_sz)),
            "real_obs": ...,
        })
  1. A custom model can be defined that can interpret the action_mask and avail_actions portions of the observation. Here the model computes the action logits via the dot product of some network output and each action embedding. Invalid actions can be masked out of the softmax by scaling the probability to zero:
class ParametricActionsModel(TFModelV2):
    def __init__(self,
                 obs_space,
                 action_space,
                 num_outputs,
                 model_config,
                 name,
                 true_obs_shape=(4,),
                 action_embed_size=2):
        super(ParametricActionsModel, self).__init__(
            obs_space, action_space, num_outputs, model_config, name)
        self.action_embed_model = FullyConnectedNetwork(...)

    def forward(self, input_dict, state, seq_lens):
        # Extract the available actions tensor from the observation.
        avail_actions = input_dict["obs"]["avail_actions"]
        action_mask = input_dict["obs"]["action_mask"]

        # Compute the predicted action embedding
        action_embed, _ = self.action_embed_model({
            "obs": input_dict["obs"]["cart"]
        })

        # Expand the model output to [BATCH, 1, EMBED_SIZE]. Note that the
        # avail actions tensor is of shape [BATCH, MAX_ACTIONS, EMBED_SIZE].
        intent_vector = tf.expand_dims(action_embed, 1)

        # Batch dot product => shape of logits is [BATCH, MAX_ACTIONS].
        action_logits = tf.reduce_sum(avail_actions * intent_vector, axis=2)

        # Mask out invalid actions (use tf.float32.min for stability)
        inf_mask = tf.maximum(tf.log(action_mask), tf.float32.min)
        return action_logits + inf_mask, state

Depending on your use case it may make sense to use just the masking_, just action embeddings_, or both_. For a runnable example of "just action embeddings" in code, check out examples/parametric_actions_cartpole.py.

Note that since masking introduces tf.float32.min values into the model output, this technique might not work with all algorithm options. For example, algorithms might crash if they incorrectly process the tf.float32.min values. The cartpole example has working configurations for DQN (must set hiddens=[]), PPO (must disable running mean and set model.vf_share_layers=True), and several other algorithms. Not all algorithms support parametric actions; see the algorithm overview.

Autoregressive Action Distributions

In an action space with multiple components (e.g., Tuple(a1, a2)), you might want a2 to be conditioned on the sampled value of a1, i.e., a2_sampled ~ P(a2 | a1_sampled, obs). Normally, a1 and a2 would be sampled independently, reducing the expressivity of the policy.

To do this, you need both a custom model that implements the autoregressive pattern, and a custom action distribution class that leverages that model. The autoregressive_action_dist.py example shows how this can be implemented for a simple binary action space. For a more complex space, a more efficient architecture such as a MADE is recommended. Note that sampling a N-part action requires N forward passes through the model, however computing the log probability of an action can be done in one pass:

class BinaryAutoregressiveOutput(ActionDistribution):
    """Action distribution P(a1, a2) = P(a1) * P(a2 | a1)"""

    @staticmethod
    def required_model_output_shape(self, model_config):
        return 16  # controls model output feature vector size

    def sample(self):
        # first, sample a1
        a1_dist = self._a1_distribution()
        a1 = a1_dist.sample()

        # sample a2 conditioned on a1
        a2_dist = self._a2_distribution(a1)
        a2 = a2_dist.sample()

        # return the action tuple
        return TupleActions([a1, a2])

    def logp(self, actions):
        a1, a2 = actions[:, 0], actions[:, 1]
        a1_vec = tf.expand_dims(tf.cast(a1, tf.float32), 1)
        a1_logits, a2_logits = self.model.action_model([self.inputs, a1_vec])
        return (Categorical(a1_logits, None).logp(a1) + Categorical(
            a2_logits, None).logp(a2))

    def _a1_distribution(self):
        BATCH = tf.shape(self.inputs)[0]
        a1_logits, _ = self.model.action_model(
            [self.inputs, tf.zeros((BATCH, 1))])
        a1_dist = Categorical(a1_logits, None)
        return a1_dist

    def _a2_distribution(self, a1):
        a1_vec = tf.expand_dims(tf.cast(a1, tf.float32), 1)
        _, a2_logits = self.model.action_model([self.inputs, a1_vec])
        a2_dist = Categorical(a2_logits, None)
        return a2_dist

class AutoregressiveActionsModel(TFModelV2):
    """Implements the `.action_model` branch required above."""

    def __init__(self, obs_space, action_space, num_outputs, model_config,
                 name):
        super(AutoregressiveActionsModel, self).__init__(
            obs_space, action_space, num_outputs, model_config, name)
        if action_space != Tuple([Discrete(2), Discrete(2)]):
            raise ValueError(
                "This model only supports the [2, 2] action space")

        # Inputs
        obs_input = tf.keras.layers.Input(
            shape=obs_space.shape, name="obs_input")
        a1_input = tf.keras.layers.Input(shape=(1, ), name="a1_input")
        ctx_input = tf.keras.layers.Input(
            shape=(num_outputs, ), name="ctx_input")

        # Output of the model (normally 'logits', but for an autoregressive
        # dist this is more like a context/feature layer encoding the obs)
        context = tf.keras.layers.Dense(
            num_outputs,
            name="hidden",
            activation=tf.nn.tanh,
            kernel_initializer=normc_initializer(1.0))(obs_input)

        # P(a1 | obs)
        a1_logits = tf.keras.layers.Dense(
            2,
            name="a1_logits",
            activation=None,
            kernel_initializer=normc_initializer(0.01))(ctx_input)

        # P(a2 | a1)
        # --note: typically you'd want to implement P(a2 | a1, obs) as follows:
        # a2_context = tf.keras.layers.Concatenate(axis=1)(
        #     [ctx_input, a1_input])
        a2_context = a1_input
        a2_hidden = tf.keras.layers.Dense(
            16,
            name="a2_hidden",
            activation=tf.nn.tanh,
            kernel_initializer=normc_initializer(1.0))(a2_context)
        a2_logits = tf.keras.layers.Dense(
            2,
            name="a2_logits",
            activation=None,
            kernel_initializer=normc_initializer(0.01))(a2_hidden)

        # Base layers
        self.base_model = tf.keras.Model(obs_input, context)
        self.register_variables(self.base_model.variables)
        self.base_model.summary()

        # Autoregressive action sampler
        self.action_model = tf.keras.Model([ctx_input, a1_input],
                                           [a1_logits, a2_logits])
        self.action_model.summary()
        self.register_variables(self.action_model.variables)

Note

Not all algorithms support autoregressive action distributions; see the algorithm overview table for more information.