# Proximal Policy Optimization (PPO)#

PPO is a model-free, stochastic on-policy policy gradient algorithm that alternates between sampling data through interaction with the environment, and optimizing a surrogate objective function while avoiding that the new policy does not move too far away from the old one

## Algorithm#

For each iteration do:
$$\bullet \;$$ Collect, in a rollout memory, a set of states $$s$$, actions $$a$$, rewards $$r$$, dones $$d$$, log probabilities $$logp$$ and values $$V$$ on policy using $$\pi_\theta$$ and $$V_\phi$$
$$\bullet \;$$ Estimate returns $$R$$ and advantages $$A$$ using Generalized Advantage Estimation (GAE($$\lambda$$)) from the collected data [$$r, d, V$$]
$$\bullet \;$$ Compute the entropy loss $${L}_{entropy}$$
$$\bullet \;$$ Compute the clipped surrogate objective (policy loss) with $$ratio$$ as the probability ratio between the action under the current policy and the action under the previous policy: $$L^{clip}_{\pi_\theta} = \mathbb{E}[\min(A \; ratio, A \; \text{clip}(ratio, 1-c, 1+c))]$$
$$\bullet \;$$ Compute the value loss $$L_{V_\phi}$$ as the mean squared error (MSE) between the predicted values $$V_{_{predicted}}$$ and the estimated returns $$R$$
$$\bullet \;$$ Optimize the total loss $$L = L^{clip}_{\pi_\theta} - c_1 \, L_{V_\phi} + c_2 \, {L}_{entropy}$$

### Algorithm implementation#

Main notation/symbols:
- policy function approximator ($$\pi_\theta$$), value function approximator ($$V_\phi$$)
- states ($$s$$), actions ($$a$$), rewards ($$r$$), next states ($$s'$$), dones ($$d$$)
- values ($$V$$), advantages ($$A$$), returns ($$R$$)
- log probabilities ($$logp$$)
- loss ($$L$$)

#### Learning algorithm#

compute_gae(...)
def $$\;f_{GAE} (r, d, V, V_{_{last}}') \;\rightarrow\; R, A:$$
$$adv \leftarrow 0$$
$$A \leftarrow \text{zeros}(r)$$
FOR each reverse iteration $$i$$ up to the number of rows in $$r$$ DO
IF $$i$$ is not the last row of $$r$$ THEN
$$V_i' = V_{i+1}$$
ELSE
$$V_i' \leftarrow V_{_{last}}'$$
$$adv \leftarrow r_i - V_i \, +$$ discount_factor $$\neg d_i \; (V_i' \, -$$ lambda $$adv)$$
$$A_i \leftarrow adv$$
# returns computation
$$R \leftarrow A + V$$
$$A \leftarrow \dfrac{A - \bar{A}}{A_\sigma + 10^{-8}}$$

_update(...)
$$V_{_{last}}' \leftarrow V_\phi(s')$$
$$R, A \leftarrow f_{GAE}(r, d, V, V_{_{last}}')$$
# sample mini-batches from memory
[[$$s, a, logp, V, R, A$$]] $$\leftarrow$$ states, actions, log_prob, values, returns, advantages
# learning epochs
FOR each learning epoch up to learning_epochs DO
# mini-batches loop
FOR each mini-batch [$$s, a, logp, V, R, A$$] up to mini_batches DO
$$logp' \leftarrow \pi_\theta(s, a)$$
# compute approximate KL divergence
$$ratio \leftarrow logp' - logp$$
$$KL_{_{divergence}} \leftarrow \frac{1}{N} \sum_{i=1}^N ((e^{ratio} - 1) - ratio)$$
# early stopping with KL divergence
IF $$KL_{_{divergence}} >$$ kl_threshold THEN
BREAK LOOP
# compute entropy loss
IF entropy computation is enabled THEN
$${L}_{entropy} \leftarrow \, -$$ entropy_loss_scale $$\frac{1}{N} \sum_{i=1}^N \pi_{\theta_{entropy}}$$
ELSE
$${L}_{entropy} \leftarrow 0$$
# compute policy loss
$$ratio \leftarrow e^{logp' - logp}$$
$$L_{_{surrogate}} \leftarrow A \; ratio$$
$$L_{_{clipped\,surrogate}} \leftarrow A \; \text{clip}(ratio, 1 - c, 1 + c) \qquad$$ with $$c$$ as ratio_clip
$$L^{clip}_{\pi_\theta} \leftarrow - \frac{1}{N} \sum_{i=1}^N \min(L_{_{surrogate}}, L_{_{clipped\,surrogate}})$$
# compute value loss
$$V_{_{predicted}} \leftarrow V_\phi(s)$$
IF clip_predicted_values is enabled THEN
$$V_{_{predicted}} \leftarrow V + \text{clip}(V_{_{predicted}} - V, -c, c) \qquad$$ with $$c$$ as value_clip
$$L_{V_\phi} \leftarrow$$ value_loss_scale $$\frac{1}{N} \sum_{i=1}^N (R - V_{_{predicted}})^2$$
# optimization step
reset $$\text{optimizer}_{\theta, \phi}$$
$$\nabla_{\theta, \, \phi} (L^{clip}_{\pi_\theta} + {L}_{entropy} + L_{V_\phi})$$
$$\text{clip}(\lVert \nabla_{\theta, \, \phi} \rVert)$$ with grad_norm_clip
step $$\text{optimizer}_{\theta, \phi}$$
# update learning rate
IF there is a learning_rate_scheduler THEN
step $$\text{scheduler}_{\theta, \phi} (\text{optimizer}_{\theta, \phi})$$

## Usage#

Note

Support for recurrent neural networks (RNN, LSTM, GRU and any other variant) is implemented in a separate file (ppo_rnn.py) to maintain the readability of the standard implementation (ppo.py)

# import the agent and its default configuration
from skrl.agents.torch.ppo import PPO, PPO_DEFAULT_CONFIG

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

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

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

PPO_DEFAULT_CONFIG = {
"rollouts": 16,                 # number of rollouts before updating
"learning_epochs": 8,           # number of learning epochs during each update
"mini_batches": 2,              # number of mini batches during each learning epoch

"discount_factor": 0.99,        # discount factor (gamma)
"lambda": 0.95,                 # TD(lambda) coefficient (lam) for computing returns and advantages

"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})
"value_preprocessor": None,             # value preprocessor class (see skrl.resources.preprocessors)
"value_preprocessor_kwargs": {},        # value preprocessor's kwargs (e.g. {"size": 1})

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

"ratio_clip": 0.2,                  # clipping coefficient for computing the clipped surrogate objective
"value_clip": 0.2,                  # clipping coefficient for computing the value loss (if clip_predicted_values is True)
"clip_predicted_values": False,     # clip predicted values during value loss computation

"entropy_loss_scale": 0.0,      # entropy loss scaling factor
"value_loss_scale": 1.0,        # value loss scaling factor

"kl_threshold": 0,              # KL divergence threshold for early stopping

"rewards_shaper": None,         # rewards shaping function: Callable(reward, timestep, timesteps) -> reward
"time_limit_bootstrap": False,  # bootstrap at timeout termination (episode truncation)

"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

$$\square$$

$$\blacksquare$$

Box

$$\blacksquare$$

$$\blacksquare$$

Dict

$$\blacksquare$$

$$\square$$

### Models#

The implementation uses 1 stochastic (discrete or continuous) and 1 deterministic function approximator. 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

$$\pi_\theta(s)$$

Policy

"policy"

observation

action

$$V_\phi(s)$$

Value

"value"

observation

1

Deterministic

### Features#

Support for advanced features is described in the next table

Feature

Support and remarks  Shared model

for Policy and Value

$$\blacksquare$$

$$\square$$

RNN support

RNN, LSTM, GRU and any other variant

$$\blacksquare$$

$$\square$$

## API (PyTorch)#

skrl.agents.torch.ppo.PPO_DEFAULT_CONFIG#

alias of {‘clip_predicted_values’: False, ‘discount_factor’: 0.99, ‘entropy_loss_scale’: 0.0, ‘experiment’: {‘checkpoint_interval’: 1000, ‘directory’: ‘’, ‘experiment_name’: ‘’, ‘store_separately’: False, ‘wandb’: False, ‘wandb_kwargs’: {}, ‘write_interval’: 250}, ‘grad_norm_clip’: 0.5, ‘kl_threshold’: 0, ‘lambda’: 0.95, ‘learning_epochs’: 8, ‘learning_rate’: 0.001, ‘learning_rate_scheduler’: None, ‘learning_rate_scheduler_kwargs’: {}, ‘learning_starts’: 0, ‘mini_batches’: 2, ‘random_timesteps’: 0, ‘ratio_clip’: 0.2, ‘rewards_shaper’: None, ‘rollouts’: 16, ‘state_preprocessor’: None, ‘state_preprocessor_kwargs’: {}, ‘time_limit_bootstrap’: False, ‘value_clip’: 0.2, ‘value_loss_scale’: 1.0, ‘value_preprocessor’: None, ‘value_preprocessor_kwargs’: {}}

class skrl.agents.torch.ppo.PPO(models: Dict[str, Model], 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: Dict[str, Model], 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#

Proximal Policy Optimization (PPO)

https://arxiv.org/abs/1707.06347

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: Dict[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

class skrl.agents.torch.ppo.PPO_RNN(models: Dict[str, Model], 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: Dict[str, Model], 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#

Proximal Policy Optimization (PPO) with support for Recurrent Neural Networks (RNN, GRU, LSTM, etc.)

https://arxiv.org/abs/1707.06347

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: Dict[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.ppo.PPO_DEFAULT_CONFIG#

alias of {‘clip_predicted_values’: False, ‘discount_factor’: 0.99, ‘entropy_loss_scale’: 0.0, ‘experiment’: {‘checkpoint_interval’: 1000, ‘directory’: ‘’, ‘experiment_name’: ‘’, ‘store_separately’: False, ‘wandb’: False, ‘wandb_kwargs’: {}, ‘write_interval’: 250}, ‘grad_norm_clip’: 0.5, ‘kl_threshold’: 0, ‘lambda’: 0.95, ‘learning_epochs’: 8, ‘learning_rate’: 0.001, ‘learning_rate_scheduler’: None, ‘learning_rate_scheduler_kwargs’: {}, ‘learning_starts’: 0, ‘mini_batches’: 2, ‘random_timesteps’: 0, ‘ratio_clip’: 0.2, ‘rewards_shaper’: None, ‘rollouts’: 16, ‘state_preprocessor’: None, ‘state_preprocessor_kwargs’: {}, ‘time_limit_bootstrap’: False, ‘value_clip’: 0.2, ‘value_loss_scale’: 1.0, ‘value_preprocessor’: None, ‘value_preprocessor_kwargs’: {}}

class skrl.agents.jax.ppo.PPO(models: Dict[str, Model], 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: Dict[str, Model], 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#

Proximal Policy Optimization (PPO)

https://arxiv.org/abs/1707.06347

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: Dict[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: , 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