Proximal Policy Optimization (PPO) Agent

Proximal policy optimization (PPO) is an on-policy, policy gradient reinforcement learning method for environments with a discrete or continuous action space. It directly estimates a stochastic policy and uses a value function critic to estimate the value of the policy. This algorithm alternates between sampling data through environmental interaction and optimizing a clipped surrogate objective function using stochastic gradient descent. The clipped surrogate objective function improves training stability by limiting the size of the policy change at each step [1]. For continuous action spaces, this agent does not enforce constraints set in the action specification; therefore, if you need to enforce action constraints, you must do so within the environment.

PPO is a simplified version of TRPO. Specifically, PPO has less hyperparameters and therefore is easier to tune, and less computationally expensive than TRPO. For more information on TRPO agents, see Trust Region Policy Optimization (TRPO) Agent. For more information on the different types of reinforcement learning agents, see Reinforcement Learning Agents.

In Reinforcement Learning Toolbox™, a proximal policy optimization agent is implemented by an rlPPOAgent object.

Proximal policy optimization agents can be trained in environments with the following observation and action spaces.

Observation Space	Action Space
Discrete or continuous	Discrete or continuous

Proximal policy optimization agents use the following actor and critics.

Critic	Actor
Value function critic V(S), which you create using rlValueFunction	Stochastic policy actor π(S), which you create using rlDiscreteCategoricalActor (for discrete action spaces) or rlContinuousGaussianActor (for continuous action spaces)

During training, a Proximal policy optimization agent:

• Estimates probabilities of taking each action in the action space and randomly selects actions based on the probability distribution.

• Interacts with the environment for multiple steps using the current policy before using mini-batches to update the actor and critic properties over multiple epochs.

If the UseExplorationPolicy option of the agent is set to false the action with maximum likelihood is always used in sim and generatePolicyFunction. As a result, the simulated agent and generated policy behave deterministically.

If the UseExplorationPolicy is set to true the agent selects its actions by sampling its probability distribution. As a result the policy is stochastic and the agent explores its observation space.

This option affects only simulation and deployment; it does not affect training.

Actor and Critic Function Approximators

To estimate the policy and value function, a proximal policy optimization agent maintains two function approximators.

• Actor π(A|S;θ) — The actor, with parameters θ, outputs the conditional probability of taking each action A when in state S as one of the following:

  • Discrete action space — The probability of taking each discrete action. The sum of these probabilities across all actions is 1.

  • Continuous action space — The mean and standard deviation of the Gaussian probability distribution for each continuous action.

• Critic V(S;ϕ) — The critic, with parameters ϕ, takes observation S and returns the corresponding expectation of the discounted long-term reward.

For more information on creating actors and critics for function approximation, see Create Policies and Value Functions.

During training, the agent tunes the parameter values in θ. After training, the parameters remain at their tuned value and the trained actor function approximator is stored in π(A|S).

Agent Creation

You can create and train proximal policy optimization agents at the MATLAB^® command line or using the Reinforcement Learning Designer app. For more information on creating agents using Reinforcement Learning Designer, see Create Agents Using Reinforcement Learning Designer.

At the command line, you can create a PPO agent with default actor and critic based on the observation and action specifications from the environment. To do so, perform the following steps.

1. Create observation specifications for your environment. If you already have an environment object, you can obtain these specifications using getObservationInfo.

2. Create action specifications for your environment. If you already have an environment object, you can obtain these specifications using getActionInfo.

3. If needed, specify the number of neurons in each learnable layer of the default network or whether to use an LSTM layer. To do so, create an agent initialization option object using rlAgentInitializationOptions.

4. Specify agent options using an rlPPOAgentOptions object (alternatively, you can skip this step and then modify the agent options later using dot notation).

5. Create the agent using an rlPPOAgent object.

Alternatively, you can create actor and critic and use these objects to create your agent. In this case, ensure that the input and output dimensions of the actor and critic match the corresponding action and observation specifications of the environment.

1. Create an actor using an rlDiscreteCategoricalActor object (for discrete action spaces) or an rlContinuousGaussianActor object (for continuous action spaces).

2. Create a critic using an rlValueFunction object.

3. If needed, specify agent options using an rlPPOAgentOptions object.

4. Create the agent using the rlPPOAgent function.

PPO agents support actors and critics that use recurrent deep neural networks as function approximators.

For more information on creating actors and critics for function approximation, see Create Policies and Value Functions.

Training Algorithm

Proximal policy optimization agents use the following training algorithm. To configure the training algorithm, specify options using an rlPPOAgentOptions object.

1. Initialize the actor π(A|S;θ) with random parameter values θ.

2. Initialize the critic V(S;ϕ) with random parameter values ϕ.

3. Generate N experiences by following the current policy. The experience sequence is

   $$S_{ts},A_{ts},R_{ts+1},S_{ts+1},\dots ,S_{ts+N-1},A_{ts+N-1},R_{ts+N},S_{ts+N}$$

   Here, S_t is a state observation, A_t is an action taken from that state, S_t+1 is the next state, and R_t+1 is the reward received for moving from S_t to S_t+1.

   When in state S_t, the agent computes the probability of taking each action in the action space using π(A|S_t;θ) and randomly selects action A_t based on the probability distribution.

   ts is the starting time step of the current set of N experiences. At the beginning of the training episode, ts = 1. For each subsequent set of N experiences in the same training episode, ts ← ts + N.

   For each experience sequence that does not contain a terminal state, N is equal to the ExperienceHorizon option value. Otherwise, N is less than ExperienceHorizon and S_N is the terminal state.

4. For each episode step t = ts, ts+1, …, ts+N-1, compute the return and advantage function using the method specified by the AdvantageEstimateMethod option.

   • Finite Horizon (AdvantageEstimateMethod = "finite-horizon") — Compute the return G_t, which is the sum of the reward for that step and the discounted future reward [2].

     $$G_t={\displaystyle \sum _{k=t+1}^{ts+N}\left({\gamma }^{k-t-1}{R}_k\right)}+b{\gamma }^{ts+N-t}V\left(S_{ts+N};\varphi \right)$$

     Here, b is 0 if S_ts+N is a terminal state and 1 otherwise. That is, if S_ts+N is not a terminal state, the discounted future reward includes the discounted state value function, computed using the critic network V.

     Compute the advantage function D_t.

     $$D_t=G_t-V\left(S_t;\varphi \right)$$

   • Generalized Advantage Estimator (AdvantageEstimateMethod = "gae") — Compute the advantage function D_t, which is the discounted sum of temporal difference errors [3].

     $$\begin{array}{c}{D}_t={\displaystyle \sum _{k=t}^{ts+N-1}{\left(\gamma \lambda \right)}^{k-t}{\delta }_k}\\ {\delta }_k=R_{k+1}+b\gamma V\left(S_{k+1};\varphi \right)-V\left(S_k;\varphi \right)\end{array}$$

     Here, b is 0 if S_ts+N is a terminal state and 1 otherwise. λ is a smoothing factor specified using the GAEFactor option.

     Compute the return G_t.

     $$G_t=D_t+V\left(S_t;\varphi \right)$$

   To specify the discount factor γ for either method, use the DiscountFactor option.

5. Learn from mini-batches of experiences over K epochs. To specify K, use the NumEpoch option. For each learning epoch:

   1. Sample a random mini-batch data set of size M from the current set of experiences. To specify M, use the MiniBatchSize option. Each element of the mini-batch data set contains a current experience and the corresponding return and advantage function values.

   2. Update the critic parameters by minimizing the loss L_critic across all sampled mini-batch data.

      $$L_{critic}\left(\varphi \right)=\frac{1}{2M}{\displaystyle \sum _{i=1}^M{\left(G_i-V\left(S_i;\varphi \right)\right)}^2}$$

   3. Normalize the advantage values D_i based on recent unnormalized advantage values.

      • If the NormalizedAdvantageMethod option is 'none', do not normalize the advantage values.

        $${\widehat{D}}_i\leftarrow D_i$$

      • If the NormalizedAdvantageMethod option is 'current', normalize the advantage values based on the unnormalized advantages in the current mini-batch.

        $${\widehat{D}}_i\leftarrow \frac{D_i-mean\left(D_1,D_2,\dots ,D_M\right)}{std\left(D_1,D_2,\dots ,D_M\right)}$$

      • If the NormalizedAdvantageMethod option is 'moving', normalize the advantage values based on the unnormalized advantages for the N most recent advantages, including the current advantage value. To specify the window size N, use the AdvantageNormalizingWindow option.

        $${\widehat{D}}_i\leftarrow \frac{D_i-mean\left(D_1,D_2,\dots ,D_N\right)}{std\left(D_1,D_2,\dots ,D_N\right)}$$

   4. Update the actor parameters by minimizing the actor loss function L_actor across all sampled mini-batch data.

      $$\begin{array}{c}{L}_{actor}\left(\theta \right)=\frac{1}{M}{\displaystyle \sum _{i=1}^M\left(-\min \left(r_i\left(\theta \right)\cdot {\widehat{D}}_i,c_i\left(\theta \right)\cdot {\widehat{D}}_i\right)+w{\mathscr{H}}_i\left(\theta ,S_i\right)\right)}\\ r_i\left(\theta \right)=\frac{\pi \left(A_i|S_i;\theta \right)}{\pi \left(A_i|S_i;{\theta }_{old}\right)}\\ c_i\left(\theta \right)=\max \left(\min \left(r_i\left(\theta \right),1+\epsilon \right),1-\epsilon \right)\end{array}$$

      Here:

      • D_i and G_i are the advantage function and return value for the ith element of the mini-batch, respectively.

      • π(A_i|S_i;θ) is the probability of taking action A_i when in state S_i, given the updated policy parameters θ.

      • π(A_i|S_i;θ_old) is the probability of taking action A_i when in state S_i, given the previous policy parameters θ_old from before the current learning epoch.

      • ε is the clip factor specified using the ClipFactor option.

      • ℋ_i(θ) is the entropy loss and w is the entropy loss weight factor, specified using the EntropyLossWeight option. For more information on entropy loss, see Entropy Loss.

6. Repeat steps 3 through 5 until the training episode reaches a terminal state.

Entropy Loss

To promote agent exploration, you can add an entropy loss term wℋ_i(θ,S_i) to the actor loss function, where w is the entropy loss weight and ℋ_i(θ,S_i) is the entropy.

The entropy value is higher when the agent is more uncertain about which action to take next. Therefore, maximizing the entropy loss term (minimizing the negative entropy loss) increases the agent uncertainty, thus encouraging exploration. To promote additional exploration, which can help the agent move out of local optima, you can specify a larger entropy loss weight.

For a discrete action space, the agent uses the following entropy value. In this case, the actor outputs the probability of taking each possible discrete action.

$${\mathscr{H}}_i\left(\theta ,S_i\right)=-{\displaystyle \sum _{k=1}^P\pi \left(A_k|S_i;\theta \right)\ln \pi \left(A_k|S_i;\theta \right)}$$

Here:

• P is the number of possible discrete actions.

• π(A_k|S_i;θ) is the probability of taking action A_k when in state S_i following the current policy.

For a continuous action space, the agent uses the following entropy value. In this case, the actor outputs the mean and standard deviation of the Gaussian distribution for each continuous action.

$${\mathscr{H}}_i\left(\theta ,S_i\right)=\frac{1}{2}{\displaystyle \sum _{k=1}^C\ln \left(2\pi \cdot e\cdot {\sigma }_{k,i}^2\right)}$$

Here:

• C is the number of continuous actions output by the actor.

• σ_k,i is the standard deviation for action k when in state S_i following the current policy.

References

[1] Schulman, John, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. “Proximal Policy Optimization Algorithms.” ArXiv:1707.06347 [Cs], July 19, 2017. https://arxiv.org/abs/1707.06347.

[2] Mnih, Volodymyr, Adrià Puigdomènech Badia, Mehdi Mirza, Alex Graves, Timothy P. Lillicrap, Tim Harley, David Silver, and Koray Kavukcuoglu. “Asynchronous Methods for Deep Reinforcement Learning.” ArXiv:1602.01783 [Cs], February 4, 2016. https://arxiv.org/abs/1602.01783.

[3] Schulman, John, Philipp Moritz, Sergey Levine, Michael Jordan, and Pieter Abbeel. “High-Dimensional Continuous Control Using Generalized Advantage Estimation.” ArXiv:1506.02438 [Cs], October 20, 2018. https://arxiv.org/abs/1506.02438.