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
Paper: Proximal Policy Optimization Algorithms
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 (_update(...))
compute_gae(...)def \(\;f_{GAE} (r, d, V, V_{_{last}}') \;\rightarrow\; R, A:\)
\(adv \leftarrow 0\)
\(A \leftarrow \text{zeros}(r)\)
# advantages computation
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
\(R \leftarrow A + V\)
# normalize advantages
\(A \leftarrow \dfrac{A - \bar{A}}{A_\sigma + 10^{-8}}\)
# compute returns and advantages
\(V_{_{last}}' \leftarrow V_\phi(s')\)
\(R, A \leftarrow f_{GAE}(r, d, V, V_{_{last}}')\)
# 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 aproximate 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 \(\text{scheduler}_{\theta, \phi} (\text{optimizer}_{\theta, \phi})\)
Configuration and hyperparameters
- skrl.agents.torch.ppo.ppo.PPO_DEFAULT_CONFIG
1PPO_DEFAULT_CONFIG = {
2 "rollouts": 16, # number of rollouts before updating
3 "learning_epochs": 8, # number of learning epochs during each update
4 "mini_batches": 2, # number of mini batches during each learning epoch
5
6 "discount_factor": 0.99, # discount factor (gamma)
7 "lambda": 0.95, # TD(lambda) coefficient (lam) for computing returns and advantages
8
9 "learning_rate": 1e-3, # learning rate
10 "learning_rate_scheduler": None, # learning rate scheduler class (see torch.optim.lr_scheduler)
11 "learning_rate_scheduler_kwargs": {}, # learning rate scheduler's kwargs (e.g. {"step_size": 1e-3})
12
13 "state_preprocessor": None, # state preprocessor class (see skrl.resources.preprocessors)
14 "state_preprocessor_kwargs": {}, # state preprocessor's kwargs (e.g. {"size": env.observation_space})
15 "value_preprocessor": None, # value preprocessor class (see skrl.resources.preprocessors)
16 "value_preprocessor_kwargs": {}, # value preprocessor's kwargs (e.g. {"size": 1})
17
18 "random_timesteps": 0, # random exploration steps
19 "learning_starts": 0, # learning starts after this many steps
20
21 "grad_norm_clip": 0.5, # clipping coefficient for the norm of the gradients
22 "ratio_clip": 0.2, # clipping coefficient for computing the clipped surrogate objective
23 "value_clip": 0.2, # clipping coefficient for computing the value loss (if clip_predicted_values is True)
24 "clip_predicted_values": False, # clip predicted values during value loss computation
25
26 "entropy_loss_scale": 0.0, # entropy loss scaling factor
27 "value_loss_scale": 1.0, # value loss scaling factor
28
29 "kl_threshold": 0, # KL divergence threshold for early stopping
30
31 "rewards_shaper": None, # rewards shaping function: Callable(reward, timestep, timesteps) -> reward
32
33 "experiment": {
34 "directory": "", # experiment's parent directory
35 "experiment_name": "", # experiment name
36 "write_interval": 250, # TensorBoard writing interval (timesteps)
37
38 "checkpoint_interval": 1000, # interval for checkpoints (timesteps)
39 "store_separately": False, # whether to store checkpoints separately
40
41 "wandb": False, # whether to use Weights & Biases
42 "wandb_kwargs": {} # wandb kwargs (see https://docs.wandb.ai/ref/python/init)
43 }
44}
Spaces and models
The implementation supports the following Gym spaces / Gymnasium spaces
Gym/Gymnasium spaces |
Observation |
Action |
|---|---|---|
Discrete |
\(\square\) |
\(\blacksquare\) |
Box |
\(\blacksquare\) |
\(\blacksquare\) |
Dict |
\(\blacksquare\) |
\(\square\) |
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 |
|
observation |
action |
|
\(V_\phi(s)\) |
Value |
|
observation |
1 |
Support for advanced features is described in the next table
Feature |
Support and remarks |
|---|---|
Shared model |
for Policy and Value |
RNN support |
RNN, LSTM, GRU and any other variant |