Deep Q-Network (DQN)#

DQN is a model-free, off-policy algorithm that trains a control policies directly from high-dimensional sensory using a deep function approximator to represent the Q-value function

Paper: Playing Atari with Deep Reinforcement Learning

Algorithm#

Algorithm implementation#

Decision making#

act(...)
\(\epsilon \leftarrow \epsilon_{_{final}} + (\epsilon_{_{initial}} - \epsilon_{_{final}}) \; e^{-1 \; \frac{\text{timestep}}{\epsilon_{_{timesteps}}}}\)
\(a \leftarrow \begin{cases} a \in_R A & x < \epsilon \\ \underset{a}{\arg\max} \; Q_\phi(s) & x \geq \epsilon \end{cases} \qquad\) for \(\; x \leftarrow U(0,1)\)

Learning algorithm#

_update(...)
# sample a batch from memory
[\(s, a, r, s', d\)] \(\leftarrow\) states, actions, rewards, next_states, dones of size batch_size
# gradient steps
FOR each gradient step up to gradient_steps DO
# compute target values
\(Q' \leftarrow Q_{\phi_{target}}(s')\)
\(Q_{_{target}} \leftarrow \underset{a}{\max} \; Q' \qquad\) # the only difference with DDQN
\(y \leftarrow r \;+\) discount_factor \(\neg d \; Q_{_{target}}\)
# compute Q-network loss
\(Q \leftarrow Q_\phi(s)[a]\)
\({Loss}_{Q_\phi} \leftarrow \frac{1}{N} \sum_{i=1}^N (Q - y)^2\)
# optimize Q-network
\(\nabla_{\phi} {Loss}_{Q_\phi}\)
# update target network
IF it’s time to update target network THEN
\(\phi_{target} \leftarrow\) polyak \(\phi + (1 \;-\) polyak \() \phi_{target}\)
# update learning rate
IF there is a learning_rate_scheduler THEN
step \(\text{scheduler}_\phi (\text{optimizer}_\phi)\)

Usage#

# import the agent and its default configuration
from skrl.agents.torch.dqn import DQN, DQN_DEFAULT_CONFIG

# instantiate the agent's models
models = {}
models["q_network"] = ...
models["target_q_network"] = ...  # only required during training

# adjust some configuration if necessary
cfg_agent = DQN_DEFAULT_CONFIG.copy()
cfg_agent["<KEY>"] = ...

# instantiate the agent
# (assuming a defined environment <env> and memory <memory>)
agent = DQN(models=models,
            memory=memory,  # only required during training
            cfg=cfg_agent,
            observation_space=env.observation_space,
            action_space=env.action_space,
            device=env.device)

# import the agent and its default configuration
from skrl.agents.jax.dqn import DQN, DQN_DEFAULT_CONFIG

# instantiate the agent's models
models = {}
models["q_network"] = ...
models["target_q_network"] = ...  # only required during training

# adjust some configuration if necessary
cfg_agent = DQN_DEFAULT_CONFIG.copy()
cfg_agent["<KEY>"] = ...

# instantiate the agent
# (assuming a defined environment <env> and memory <memory>)
agent = DQN(models=models,
            memory=memory,  # only required during training
            cfg=cfg_agent,
            observation_space=env.observation_space,
            action_space=env.action_space,
            device=env.device)

Configuration and hyperparameters#

DQN_DEFAULT_CONFIG = {
    "gradient_steps": 1,            # gradient steps
    "batch_size": 64,               # training batch size

    "discount_factor": 0.99,        # discount factor (gamma)
    "polyak": 0.005,                # soft update hyperparameter (tau)

    "learning_rate": 1e-3,          # learning rate
    "learning_rate_scheduler": None,        # learning rate scheduler class (see torch.optim.lr_scheduler)
    "learning_rate_scheduler_kwargs": {},   # learning rate scheduler's kwargs (e.g. {"step_size": 1e-3})

    "state_preprocessor": None,             # state preprocessor class (see skrl.resources.preprocessors)
    "state_preprocessor_kwargs": {},        # state preprocessor's kwargs (e.g. {"size": env.observation_space})

    "random_timesteps": 0,          # random exploration steps
    "learning_starts": 0,           # learning starts after this many steps

    "update_interval": 1,           # agent update interval
    "target_update_interval": 10,   # target network update interval

    "exploration": {
        "initial_epsilon": 1.0,       # initial epsilon for epsilon-greedy exploration
        "final_epsilon": 0.05,        # final epsilon for epsilon-greedy exploration
        "timesteps": 1000,            # timesteps for epsilon-greedy decay
    },

    "rewards_shaper": None,         # rewards shaping function: Callable(reward, timestep, timesteps) -> reward

    "experiment": {
        "directory": "",            # experiment's parent directory
        "experiment_name": "",      # experiment name
        "write_interval": 250,      # TensorBoard writing interval (timesteps)

        "checkpoint_interval": 1000,        # interval for checkpoints (timesteps)
        "store_separately": False,          # whether to store checkpoints separately

        "wandb": False,             # whether to use Weights & Biases
        "wandb_kwargs": {}          # wandb kwargs (see https://docs.wandb.ai/ref/python/init)
    }
}

Spaces#

The implementation supports the following Gym spaces / Gymnasium spaces

Gym/Gymnasium spaces	Observation	Action
Discrete	\(\square\)	\(\blacksquare\)
MultiDiscrete	\(\square\)	\(\square\)
Box	\(\blacksquare\)	\(\square\)
Dict	\(\blacksquare\)	\(\square\)

Models#

The implementation uses 2 deterministic function approximators. These function approximators (models) must be collected in a dictionary and passed to the constructor of the class under the argument models

Notation	Concept	Key	Input shape	Output shape	Type
\(Q_\phi(s, a)\)	Q-network	`"q_network"`	observation	action	Deterministic
\(Q_{\phi_{target}}(s, a)\)	Target Q-network	`"target_q_network"`	observation	action	Deterministic

Features#

Support for advanced features is described in the next table

Feature	Support and remarks
Shared model	-	\(\square\)	\(\square\)
RNN support	-	\(\square\)	\(\square\)

API (PyTorch)#

skrl.agents.torch.dqn.DQN_DEFAULT_CONFIG#: alias of {‘batch_size’: 64, ‘discount_factor’: 0.99, ‘experiment’: {‘checkpoint_interval’: 1000, ‘directory’: ‘’, ‘experiment_name’: ‘’, ‘store_separately’: False, ‘wandb’: False, ‘wandb_kwargs’: {}, ‘write_interval’: 250}, ‘exploration’: {‘final_epsilon’: 0.05, ‘initial_epsilon’: 1.0, ‘timesteps’: 1000}, ‘gradient_steps’: 1, ‘learning_rate’: 0.001, ‘learning_rate_scheduler’: None, ‘learning_rate_scheduler_kwargs’: {}, ‘learning_starts’: 0, ‘polyak’: 0.005, ‘random_timesteps’: 0, ‘rewards_shaper’: None, ‘state_preprocessor’: None, ‘state_preprocessor_kwargs’: {}, ‘target_update_interval’: 10, ‘update_interval’: 1}

Bases: Agent

Deep Q-Network (DQN)

https://arxiv.org/abs/1312.5602

Parameters:

models (dictionary of skrl.models.torch.Model) – Models used by the agent
memory (skrl.memory.torch.Memory, list of skrl.memory.torch.Memory or None) – Memory to storage the transitions. If it is a tuple, the first element will be used for training and for the rest only the environment transitions will be added
observation_space (int, tuple or list of int, gym.Space, gymnasium.Space or None, optional) – Observation/state space or shape (default: None)
action_space (int, tuple or list of int, gym.Space, gymnasium.Space or None, optional) – Action space or shape (default: None)
device (str or torch.device, optional) – Device on which a tensor/array is or will be allocated (default: None). If None, the device will be either "cuda" if available or "cpu"
cfg (dict) – Configuration dictionary

Raises:

KeyError – If the models dictionary is missing a required key

_update(timestep: int, timesteps: int) → None#

Algorithm’s main update step

Parameters:

timestep (int) – Current timestep
timesteps (int) – Number of timesteps

act(states: torch.Tensor, timestep: int, timesteps: int) → torch.Tensor#

Process the environment’s states to make a decision (actions) using the main policy

Parameters:

states (torch.Tensor) – Environment’s states
timestep (int) – Current timestep
timesteps (int) – Number of timesteps

Returns:

Actions

Return type:

torch.Tensor

init(trainer_cfg: Mapping[str, Any] | None = None) → None#: Initialize the agent

post_interaction(timestep: int, timesteps: int) → None#

Callback called after the interaction with the environment

Parameters:

timestep (int) – Current timestep
timesteps (int) – Number of timesteps

pre_interaction(timestep: int, timesteps: int) → None#

Callback called before the interaction with the environment

Parameters:

timestep (int) – Current timestep
timesteps (int) – Number of timesteps

record_transition(states: torch.Tensor, actions: torch.Tensor, rewards: torch.Tensor, next_states: torch.Tensor, terminated: torch.Tensor, truncated: torch.Tensor, infos: Any, timestep: int, timesteps: int) → None#

Record an environment transition in memory

Parameters:

states (torch.Tensor) – Observations/states of the environment used to make the decision
actions (torch.Tensor) – Actions taken by the agent
rewards (torch.Tensor) – Instant rewards achieved by the current actions
next_states (torch.Tensor) – Next observations/states of the environment
terminated (torch.Tensor) – Signals to indicate that episodes have terminated
truncated (torch.Tensor) – Signals to indicate that episodes have been truncated
infos (Any type supported by the environment) – Additional information about the environment
timestep (int) – Current timestep
timesteps (int) – Number of timesteps

API (JAX)#

skrl.agents.jax.dqn.DQN_DEFAULT_CONFIG#: alias of {‘batch_size’: 64, ‘discount_factor’: 0.99, ‘experiment’: {‘checkpoint_interval’: 1000, ‘directory’: ‘’, ‘experiment_name’: ‘’, ‘store_separately’: False, ‘wandb’: False, ‘wandb_kwargs’: {}, ‘write_interval’: 250}, ‘exploration’: {‘final_epsilon’: 0.05, ‘initial_epsilon’: 1.0, ‘timesteps’: 1000}, ‘gradient_steps’: 1, ‘learning_rate’: 0.001, ‘learning_rate_scheduler’: None, ‘learning_rate_scheduler_kwargs’: {}, ‘learning_starts’: 0, ‘polyak’: 0.005, ‘random_timesteps’: 0, ‘rewards_shaper’: None, ‘state_preprocessor’: None, ‘state_preprocessor_kwargs’: {}, ‘target_update_interval’: 10, ‘update_interval’: 1}

Bases: Agent

Deep Q-Network (DQN)

https://arxiv.org/abs/1312.5602

Parameters:

models (dictionary of skrl.models.jax.Model) – Models used by the agent
memory (skrl.memory.jax.Memory, list of skrl.memory.jax.Memory or None) – Memory to storage the transitions. If it is a tuple, the first element will be used for training and for the rest only the environment transitions will be added
observation_space (int, tuple or list of int, gym.Space, gymnasium.Space or None, optional) – Observation/state space or shape (default: None)
action_space (int, tuple or list of int, gym.Space, gymnasium.Space or None, optional) – Action space or shape (default: None)
device (str or jax.Device, optional) – Device on which a tensor/array is or will be allocated (default: None). If None, the device will be either "cuda" if available or "cpu"
cfg (dict) – Configuration dictionary

Raises:

KeyError – If the models dictionary is missing a required key

_update(timestep: int, timesteps: int) → None#

Algorithm’s main update step

Parameters:

timestep (int) – Current timestep
timesteps (int) – Number of timesteps

act(states: ndarray | jax.Array, timestep: int, timesteps: int) → ndarray | jax.Array#

Process the environment’s states to make a decision (actions) using the main policy

Parameters:

states (np.ndarray or jax.Array) – Environment’s states
timestep (int) – Current timestep
timesteps (int) – Number of timesteps

Returns:

Actions

Return type:

np.ndarray or jax.Array

init(trainer_cfg: Mapping[str, Any] | None = None) → None#: Initialize the agent

post_interaction(timestep: int, timesteps: int) → None#

Callback called after the interaction with the environment

Parameters:

timestep (int) – Current timestep
timesteps (int) – Number of timesteps

pre_interaction(timestep: int, timesteps: int) → None#

Callback called before the interaction with the environment

Parameters:

timestep (int) – Current timestep
timesteps (int) – Number of timesteps

Record an environment transition in memory

Parameters:

states (np.ndarray or jax.Array) – Observations/states of the environment used to make the decision
actions (np.ndarray or jax.Array) – Actions taken by the agent
rewards (np.ndarray or jax.Array) – Instant rewards achieved by the current actions
next_states (np.ndarray or jax.Array) – Next observations/states of the environment
terminated (np.ndarray or jax.Array) – Signals to indicate that episodes have terminated
truncated (np.ndarray or jax.Array) – Signals to indicate that episodes have been truncated
infos (Any type supported by the environment) – Additional information about the environment
timestep (int) – Current timestep
timesteps (int) – Number of timesteps