# Cross-Entropy Method (CEM)#

## Algorithm#

### Algorithm implementation#

Main notation/symbols:
- policy function approximator ($$\pi_\theta$$)
- states ($$s$$), actions ($$a$$), rewards ($$r$$), next states ($$s'$$), dones ($$d$$)
- loss ($$L$$)

#### Decision making#

act(...)
$$a \leftarrow \pi_\theta(s)$$

#### Learning algorithm#

_update(...)
# sample all memory
$$s, a, r, s', d \leftarrow$$ states, actions, rewards, next_states, dones
# compute discounted return threshold
$$[G] \leftarrow \sum_{t=0}^{E-1}$$ discount_factor$$^{t} \, r_t$$ for each episode
$$G_{_{bound}} \leftarrow q_{th_{quantile}}([G])$$ at the given percentile
# get elite states and actions
$$s_{_{elite}} \leftarrow s[G \geq G_{_{bound}}]$$
$$a_{_{elite}} \leftarrow a[G \geq G_{_{bound}}]$$
# compute scores for the elite states
$$scores \leftarrow \theta(s_{_{elite}})$$
# compute policy loss
$$L_{\pi_\theta} \leftarrow -\sum_{i=1}^{N} a_{_{elite}} \log(scores)$$
# optimization step
reset $$\text{optimizer}_\theta$$
$$\nabla_{\theta} L_{\pi_\theta}$$
step $$\text{optimizer}_\theta$$
# update learning rate
IF there is a learning_rate_scheduler THEN
step $$\text{scheduler}_\theta (\text{optimizer}_\theta)$$

## Usage#

# import the agent and its default configuration
from skrl.agents.torch.cem import CEM, CEM_DEFAULT_CONFIG

# instantiate the agent's models
models = {}
models["policy"] = ...

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

# instantiate the agent
# (assuming a defined environment <env> and memory <memory>)
agent = CEM(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#

CEM_DEFAULT_CONFIG = {
"rollouts": 16,                 # number of rollouts before updating
"percentile": 0.70,             # percentile to compute the reward bound [0, 1]

"discount_factor": 0.99,        # discount factor (gamma)

"learning_rate": 1e-2,          # 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

"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

$$\square$$

$$\blacksquare$$

Box

$$\blacksquare$$

$$\square$$

Dict

$$\blacksquare$$

$$\square$$

### Models#

The implementation uses 1 discrete function approximator. This function approximator (model) 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

$$\pi(s)$$

Policy

"policy"

observation

action

### Features#

Support for advanced features is described in the next table

Feature

Support and remarks

RNN support

-

$$\square$$

$$\square$$

## API (PyTorch)#

skrl.agents.torch.cem.CEM_DEFAULT_CONFIG#

alias of {‘discount_factor’: 0.99, ‘experiment’: {‘checkpoint_interval’: 1000, ‘directory’: ‘’, ‘experiment_name’: ‘’, ‘store_separately’: False, ‘wandb’: False, ‘wandb_kwargs’: {}, ‘write_interval’: 250}, ‘learning_rate’: 0.01, ‘learning_rate_scheduler’: None, ‘learning_rate_scheduler_kwargs’: {}, ‘learning_starts’: 0, ‘percentile’: 0.7, ‘random_timesteps’: 0, ‘rewards_shaper’: None, ‘rollouts’: 16, ‘state_preprocessor’: None, ‘state_preprocessor_kwargs’: {}}

class skrl.agents.torch.cem.CEM(models: , memory: = None, observation_space: int | Tuple[int] | gym.Space | gymnasium.Space | None = None, action_space: int | Tuple[int] | gym.Space | gymnasium.Space | None = None, device: = None, cfg: = None)#

Bases: Agent

__init__(models: , memory: = None, observation_space: int | Tuple[int] | gym.Space | gymnasium.Space | None = None, action_space: int | Tuple[int] | gym.Space | gymnasium.Space | None = None, device: = None, cfg: = None) None#

Cross-Entropy Method (CEM)

https://ieeexplore.ieee.org/abstract/document/6796865/

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) #

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: = 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.cem.CEM_DEFAULT_CONFIG#

alias of {‘discount_factor’: 0.99, ‘experiment’: {‘checkpoint_interval’: 1000, ‘directory’: ‘’, ‘experiment_name’: ‘’, ‘store_separately’: False, ‘wandb’: False, ‘wandb_kwargs’: {}, ‘write_interval’: 250}, ‘learning_rate’: 0.01, ‘learning_rate_scheduler’: None, ‘learning_rate_scheduler_kwargs’: {}, ‘learning_starts’: 0, ‘percentile’: 0.7, ‘random_timesteps’: 0, ‘rewards_shaper’: None, ‘rollouts’: 16, ‘state_preprocessor’: None, ‘state_preprocessor_kwargs’: {}}

class skrl.agents.jax.cem.CEM(models: , memory: = None, observation_space: int | Tuple[int] | gym.Space | gymnasium.Space | None = None, action_space: int | Tuple[int] | gym.Space | gymnasium.Space | None = None, device: = None, cfg: = None)#

Bases: Agent

__init__(models: , memory: = None, observation_space: int | Tuple[int] | gym.Space | gymnasium.Space | None = None, action_space: int | Tuple[int] | gym.Space | gymnasium.Space | None = None, device: = None, cfg: = None) None#

Cross-Entropy Method (CEM)

https://ieeexplore.ieee.org/abstract/document/6796865/

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: , timestep: int, timesteps: int) #

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: = 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: , actions: , rewards: , next_states: , terminated: , truncated: , infos: Any, timestep: int, timesteps: int) None#

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