How to pretrain a stochastic actor network for PPO training?

I want to create a stochastic actor network that outputs an action array of 10 values between 0 and 1 given an observation array of 28 normalized values. I specified upper and lower limits as follows to ensure the actor's output to be between 0 and 1:

ActionInfo = rlNumericSpec([numActions 1],'LowerLimit',[0;0;0;0;0;0;0;0;0;0],'UpperLimit',[1;1;1;1;1;1;1;1;1;1]);

My stochastic network looks as follows:

I have created a normalized training data set (input dimension 28, target dimension 10). How do I use this data set to pretrain above network?

Clarification: I want to train the network before starting the PPO agent training.

Answer 1

[Anh Tran]

Hi Jan,

You can pretrain a stochastic actor with Deep Learning Toolbox's trainNetwork with some additional work. Emmanouil gave some good pointers initially but I want to add those steps:

You need a custom loss layer since the stochastic actor network outputs mean and standard deviations, while your target is action. You can try maximum log likelihood loss. You can follow the instruction here to create a custom loss layer (you don't have to implement backward pass as autodifferentiation will take care of it)

% We want to maximize objective of log f(x) where f(x) is the probability density function follows Normal(mean, sigma)

% Loss = -Objective = - log(f(x)) = 1/2*log(2*pi) + log(sigma) + 1/2*((x-mu)/sigma)^2;

Keep in mind that you must protect against log(0), adding eps is sufficient. x is your action target.

[Jan Dewez]

Hi Anh,

So by replacing the regression layer in my initial example with the custom regression layer myRegressionLayer I should be able to train the network with my initial data set? Variable Y in the code below contains means and standard devations because that is what the actor network outputs. In other words, the input dimension of the custom regression layer is 20? Because If I try to train the network I get an error (see below).

%% pretrain stochastic actor NN
classdef myRegressionLayer < nnet.layer.RegressionLayer
        
    properties
        % (Optional) Layer properties.

        % Layer properties go here.
    end
 
    methods
        function layer = myRegressionLayer(name)           
            % (Optional) Create a myRegressionLayer.
            layer.Name = name;
            layer.Description = 'maximum log likelihood loss';
            % Layer constructor function goes here.
        end

        function loss = forwardLoss(layer, Y, T)
            % Return the loss between the predictions Y and the training
            % targets T.
            %
            % Inputs:
            %         layer - Output layer
            %         Y     – Predictions made by network
            %         T     – Training targets
            %
            % Output:
            %         loss  - Loss between Y and T

            % Layer forward loss function goes here.
            numActions = length(Y)/2;
            mu = zeros(numActions);
            sigma = zeros(numActions);            
            for i = 1:numActions
                mu(i) = Y(i);
                sigma(i) = Y(i+numActions);                
            end      
            
            loss = 0.5*log(2*pi)+log(sigma+eps)+0.5*((T-mu)./(sigma+eps)).^2;
        end
    end
end

Error using trainNetwork (line 183)
Invalid training data. The output size (20) of the last layer does not
match the number of responses (10).

Error in pretraining (line 35)
net = trainNetwork(PtrainArray2,TtrainArray2,net_actor,options);

Below the stochastic network:

inPath = [featureInputLayer(numObs, 'Normalization','none','Name','myobs')  %numObs = 28
          fullyConnectedLayer(380,'Name','hidden1')
          reluLayer('Name','relu1')
          fullyConnectedLayer(195,'Name','hidden2')
          reluLayer('Name','relu2')
          fullyConnectedLayer(100,'Name','hidden3')
          reluLayer('Name','relu3')]; 

% path layers for mean value (10 by 1 input and output
meanPath = [fullyConnectedLayer(numActions,'Name','means')                  %numActions = 10
            sigmoidLayer('Name','sigmoid')
            scalingLayer('Name','scale','Scale',ActionInfo.UpperLimit,'Bias',(ActionInfo.UpperLimit-ActionInfo.LowerLimit)/2)]; 
            
% path layers for standard deviations (10 by 1 input and output)
% using softplus layer to make it non negative
sdevPath =  [fullyConnectedLayer(numActions,'Name','sdevs')
            softplusLayer('Name', 'splus')];

% concatenate two inputs (along dimension #1) to form a single (20 by 1) output layer
outLayer = [concatenationLayer(1,2,'Name','mean&sdev')
            myRegressionLayer('actions')];
% add layers to network object
net_actor = layerGraph(inPath);
net_actor = addLayers(net_actor,meanPath);
net_actor = addLayers(net_actor,sdevPath);
net_actor = addLayers(net_actor,outLayer);

% connect layers: the mean value path output MUST be connected to the FIRST input of the concatenationLayer
net_actor = connectLayers(net_actor,'relu3','means/in');             % connect output of inPath to meanPath input
net_actor = connectLayers(net_actor,'relu3','sdevs/in');             % connect output of inPath to sdevPath input
net_actor = connectLayers(net_actor,'scale','mean&sdev/in1');        % connect output of meanPath to conc layer input #1
net_actor = connectLayers(net_actor,'splus','mean&sdev/in2');  

[Anh Tran]

1. This seems to be a limitation with trainNetwork. A workaround I can think of is to dummify your target with zeros (pad your target from 10 to 20 with zeros). When computing forward loss, ignore these dummy values.
2. Your loss function only works with single data point. You may want to change it to work with batch size greater than 1. Also, instead of initializing mu and sigma with zeros then assign value from Y, you can use vector operations. e.g. mu = Y(1:numActions,:); sigma =Y(numAction+1:end,:) assuming Y has size numActions*2-by-batchSize

[Jan Dewez]

I rewrote my custom regression class like this:

classdef myRegressionLayer < nnet.layer.RegressionLayer
        
    methods
        function layer = myRegressionLayer()           
            % (Optional) Create a myRegressionLayer.
            layer.Name = name;
            layer.Description = 'maximum log likelihood loss';
            % Layer constructor function goes here.
        end

        function loss = forwardLoss(layer, Y, T)
            % Return the loss between the predictions Y and the training
            % targets T.
            %
            % Inputs:
            %         layer - Output layer
            %         Y     – Predictions made by network (20 x minibatchsize)
            %         T     – Training targets (20 x mminibatchsize)
            %
            % Output:
            %         loss  - Loss between Y and T
            numActions = height(Y)/2;
            mu = Y(1:numActions,:);         %(10 x minibatchsize)
            sigma = Y(numActions+1:end,:);  %(10 x minibatchsize)
            for i = 1:numActions
                loss(i,:) = 0.5*log(2*pi) + log(sigma(i,:)+eps) + 0.5*((T(i,:)-mu(i,:))./(sigma(i,:)+eps)).^2;
            end
            disp('loss: ');
            disp(loss);
        end        
    end
end

When I for example set MiniBatchSize to 5, loss looks like this:

loss: 
  10×5 single dlarray

    0.7065    0.7062    0.7346    0.7249    0.6832
    1.0642    1.0203    1.0669    1.0500    1.0539
    0.7998    1.0349    1.3149    1.2599    0.8729
    1.5574    1.5650    1.5613    1.6017    1.5787
    1.2772    1.1369    1.5798    1.4769    1.2660
    0.7744    0.7541    0.7840    0.7776    0.7427
    0.8501    0.8206    0.8311    0.8372    0.8288
    0.7570    0.7704    0.7467    0.8035    0.7890
    0.7789    0.7916    0.7898    0.7881    0.8122
    0.7692    0.7411    0.7553    0.7528    0.7689

Followed by this error:

Error using trainNetwork (line 183)
Error using 'backwardLoss' in Layer myRegressionLayer. The function threw an error and
could not be executed.

Error in pretraining (line 42)
net = trainNetwork(PtrainArray2,TtrainArray2_ext,net_actor,options);

Caused by:
    Error using dlarray/dlgradient (line 51)
    Value to differentiate must be a traced dlarray scalar.

I am not sure how to fix this. What should 'loss' look like?

[Anh Tran]

As mentioned from the error message, value to differentiate must be a scalar. Thus, you need to compute mean of the loss over each batch. Also, I am not sure why you need a for-loop to compute loss. We can vectorize the computation as followed (since sigma, T, mu have same size)

% vectorize loss computation
loss = 0.5*log(2*pi) + log(sigma + eps) + 0.5*((T-mu)./(sigma+eps)).^2;

% mean of the loss over each batch
loss = sum(loss,'all');
loss = loss/batchSize;

Answer 2

[Emmanouil Tzorakoleftherakis]

Hello,

Since you already have a dataset, you will have to use Deep Learning Toolbox to get your initial policy. Take a look at the examples below to get an idea:

https://www.mathworks.com/help/reinforcement-learning/ug/imitate-mpc-controller-for-lane-keeping-assist.html

https://www.mathworks.com/help/reinforcement-learning/ug/imitate-nonlinear-mpc-controller-for-flying-robot.html

[Jan Dewez]

Hello Emmanouil,

Thanks for the response, but how do I train a stochastic actor with output dimension 20 when my train data has dimension 10? Do I need to convert my train set in such a way that I obtain means & st. devs?