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accelerate

(Not recommended) Option to accelerate computation of gradient for approximator object based on neural network

Since R2022a

    accelerate is not recommended. Use dlaccelerate on your loss function instead. For more information, see accelerate is not recommended.

    Description

    example

    newAppx = accelerate(oldAppx,useAcceleration) returns the new neural-network-based function approximator object newAppx, which has the same configuration as the original object, oldAppx, and the option to accelerate the gradient computation set to the logical value useAcceleration.

    Examples

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    Create observation and action specification objects (or alternatively use getObservationInfo and getActionInfo to extract the specification objects from an environment). For this example, define an observation space with two channels. The first channel carries an observation from a continuous four-dimensional space. The second carries a discrete scalar observation that can be either zero or one. Finally, the action space is a three-dimensional vector in a continuous action space.

    obsInfo = [rlNumericSpec([4 1]) 
               rlFiniteSetSpec([0 1])];
    
    actInfo =  rlNumericSpec([3 1]);

    To approximate the Q-value function within the critic, create a recurrent deep neural network. The output layer must be a scalar expressing the value of executing the action given the observation.

    Define each network path as an array of layer objects. Get the dimensions of the observation and action spaces from the environment specification objects, and specify a name for the input layers, so you can later explicitly associate them with the appropriate environment channel. Since the network is recurrent, use sequenceInputLayer as the input layer and include an lstmLayer as one of the other network layers.

    % Define paths
    inPath1 = [ 
        sequenceInputLayer( ...
            prod(obsInfo(1).Dimension), ...
            Name="netObsIn1")
        fullyConnectedLayer(5,Name="infc1")
        ];
    
    inPath2 = [ 
        sequenceInputLayer( ...
            prod(obsInfo(2).Dimension), ...
            Name="netObsIn2")
        fullyConnectedLayer(5,Name="infc2")
        ];
    
    inPath3 = [
        sequenceInputLayer( ...
            prod(actInfo(1).Dimension), ...
            Name="netActIn")
         fullyConnectedLayer(5,Name="infc3") 
         ];
    
    % Concatenate 3 previous layer outputs along dim 1
    jointPath = [ 
        concatenationLayer(1,3,Name="cct")
        tanhLayer
        lstmLayer(8,"OutputMode","sequence")
        fullyConnectedLayer(1,Name="jntfc") 
        ];

    Assemble dlnetwork object.

    net = dlnetwork;
    net = addLayers(net,inPath1);
    net = addLayers(net,inPath2);
    net = addLayers(net,inPath3);
    net = addLayers(net,jointPath);

    Connect layers.

    net = connectLayers(net,"infc1","cct/in1");
    net = connectLayers(net,"infc2","cct/in2");
    net = connectLayers(net,"infc3","cct/in3");

    Plot network.

    plot(net)

    Initialize network and display the number of weights.

    net = initialize(net);
    summary(net)
       Initialized: true
    
       Number of learnables: 832
    
       Inputs:
          1   'netObsIn1'   Sequence input with 4 dimensions
          2   'netObsIn2'   Sequence input with 1 dimensions
          3   'netActIn'    Sequence input with 3 dimensions
    

    Create the critic with rlQValueFunction, using the network, and the observation and action specification objects.

    critic = rlQValueFunction(net, ...
                obsInfo, ...
                actInfo, ...
                ObservationInputNames=["netObsIn1","netObsIn2"], ...
                ActionInputNames="netActIn");

    To return the value of the actions as a function of the current observation, use getValue or evaluate.

    val = evaluate(critic, ...
                    { rand(obsInfo(1).Dimension), ...
                      rand(obsInfo(2).Dimension), ...
                      rand(actInfo(1).Dimension) })
    val = 1×1 cell array
        {[0.0089]}
    
    

    When you use evaluate, the result is a single-element cell array containing the value of the action in the input, given the observation.

    val{1}
    ans = single
        0.0089
    

    Calculate the gradients of the sum of the three outputs with respect to the inputs, given a random observation.

    gro = gradient(critic,"output-input", ...
                    { rand(obsInfo(1).Dimension) , ...
                      rand(obsInfo(2).Dimension) , ...
                      rand(actInfo(1).Dimension) } )
    gro=3×1 cell array
        {4×1 single}
        {[ -0.0945]}
        {3×1 single}
    
    

    The result is a cell array with as many elements as the number of input channels. Each element contains the derivatives of the sum of the outputs with respect to each component of the input channel. Display the gradient with respect to the element of the second channel.

    gro{2}
    ans = single
        -0.0945
    

    Obtain the gradient with respect of five independent sequences, each one made of nine sequential observations.

    gro_batch = gradient(critic,"output-input", ...
                    { rand([obsInfo(1).Dimension 5 9]) , ...
                      rand([obsInfo(2).Dimension 5 9]) , ...
                      rand([actInfo(1).Dimension 5 9]) } )
    gro_batch=3×1 cell array
        {4×1×5×9 single}
        {1×1×5×9 single}
        {3×1×5×9 single}
    
    

    Display the derivative of the sum of the outputs with respect to the third observation element of the first input channel, after the seventh sequential observation in the fourth independent batch.

    gro_batch{1}(3,1,4,7)
    ans = single
        0.0693
    

    Set the option to accelerate the gradient computations.

    critic = accelerate(critic,true);

    Calculate the gradients of the sum of the outputs with respect to the parameters, given a random observation.

    grp = gradient(critic,"output-parameters", ...
                    { rand(obsInfo(1).Dimension) , ...
                      rand(obsInfo(2).Dimension) , ...
                      rand(actInfo(1).Dimension) } )
    grp=11×1 cell array
        { 5×4  single                                                   }
        { 5×1  single                                                   }
        { 5×1  single                                                   }
        { 5×1  single                                                   }
        { 5×3  single                                                   }
        { 5×1  single                                                   }
        {32×15 single                                                   }
        {32×8  single                                                   }
        {32×1  single                                                   }
        {[-0.0140 -0.0424 -0.0676 -0.0266 -0.0166 -0.0915 0.0405 0.0315]}
        {[                                                            1]}
    
    

    Each array within a cell contains the gradient of the sum of the outputs with respect to a group of parameters.

    grp_batch = gradient(critic,"output-parameters", ...
                    { rand([obsInfo(1).Dimension 5 9]) , ...
                      rand([obsInfo(2).Dimension 5 9]) , ...
                      rand([actInfo(1).Dimension 5 9]) } )
    grp_batch=11×1 cell array
        { 5×4  single                                                     }
        { 5×1  single                                                     }
        { 5×1  single                                                     }
        { 5×1  single                                                     }
        { 5×3  single                                                     }
        { 5×1  single                                                     }
        {32×15 single                                                     }
        {32×8  single                                                     }
        {32×1  single                                                     }
        {[-2.0333 -10.3220 -10.6084 -1.2850 -4.4681 -8.0848 9.0716 3.0989]}
        {[                                                             45]}
    
    

    If you use a batch of inputs, gradient uses the whole input sequence (in this case nine steps), and all the gradients with respect to the independent batch dimensions (in this case five) are added together. Therefore, the returned gradient always has the same size as the output from getLearnableParameters.

    Create observation and action specification objects (or alternatively use getObservationInfo and getActionInfo to extract the specification objects from an environment). For this example, define an observation space with two channels. The first channel carries an observation from a continuous four-dimensional space. The second carries a discrete scalar observation that can be either zero or one. Finally, the action space consist of a scalar that can be -1, 0, or 1.

    obsInfo = [rlNumericSpec([4 1]) 
               rlFiniteSetSpec([0 1])];
    
    actInfo =  rlFiniteSetSpec([-1 0 1]);

    Create a deep neural network to be used as approximation model within the actor. The output layer must have three elements, each one expressing the value of executing the corresponding action, given the observation. To create a recurrent neural network, use sequenceInputLayer as the input layer and include an lstmLayer as one of the other network layers.

    % Define paths
    inPath1 = [ 
        sequenceInputLayer(prod(obsInfo(1).Dimension))
        fullyConnectedLayer(prod(actInfo.Dimension),Name="fc1") 
        ];
    
    inPath2 = [ 
        sequenceInputLayer(prod(obsInfo(2).Dimension))
        fullyConnectedLayer(prod(actInfo.Dimension),Name="fc2") 
        ];
    
    % Concatenate previous paths outputs along first dimension
    jointPath = [ 
        concatenationLayer(1,2,Name="cct")
        tanhLayer
        lstmLayer(8,OutputMode="sequence")
        fullyConnectedLayer( ...
            prod(numel(actInfo.Elements)), ...
            Name="jntfc")
            ];
    
    % Assemble dlnetwork object
    net = dlnetwork;
    net = addLayers(net,inPath1);
    net = addLayers(net,inPath2);
    net = addLayers(net,jointPath);
    
    % Connect layers
    net = connectLayers(net,"fc1","cct/in1");
    net = connectLayers(net,"fc2","cct/in2");
    
    % Plot network
    plot(net)

    Figure contains an axes object. The axes object contains an object of type graphplot.

    % initialize network and display the number of weights.
    net = initialize(net);
    summary(net)
       Initialized: true
    
       Number of learnables: 386
    
       Inputs:
          1   'sequenceinput'     Sequence input with 4 dimensions
          2   'sequenceinput_1'   Sequence input with 1 dimensions
    

    Since each element of the output layer must represent the probability of executing one of the possible actions the software automatically adds a softmaxLayer as a final output layer if you do not specify it explicitly.

    Create the actor with rlDiscreteCategoricalActor, using the network and the observations and action specification objects. When the network has multiple input layers, they are automatically associated with the environment observation channels according to the dimension specifications in obsInfo.

    actor = rlDiscreteCategoricalActor(net, obsInfo, actInfo);

    To return a vector of probabilities for each possible action, use evaluate.

    [prob,state] = evaluate(actor, ...
                    { rand(obsInfo(1).Dimension) , ...
                      rand(obsInfo(2).Dimension) });
    prob{1}
    ans = 3x1 single column vector
    
        0.3403
        0.3114
        0.3483
    
    

    To return an action sampled from the distribution, use getAction.

    act = getAction(actor, ...
                    { rand(obsInfo(1).Dimension) , ...
                      rand(obsInfo(2).Dimension) });
    act{1}
    ans = 1
    

    Set the option to accelerate the gradient computations.

    actor = accelerate(actor,true);

    Each array within a cell contains the gradient of the sum of the outputs with respect to a group of parameters.

    grp_batch = gradient(actor,"output-parameters", ...
                            { rand([obsInfo(1).Dimension 5 9]) , ...
                              rand([obsInfo(2).Dimension 5 9])} )
    grp_batch=9×1 cell array
        {[-3.1996e-09 -4.5687e-09 -4.4820e-09 -4.6439e-09]}
        {[                                    -1.1544e-08]}
        {[                                    -1.1321e-08]}
        {[                                    -2.8436e-08]}
        {32x2 single                                      }
        {32x8 single                                      }
        {32x1 single                                      }
        { 3x8 single                                      }
        { 3x1 single                                      }
    
    

    If you use a batch of inputs, the gradient uses the whole input sequence (in this case nine steps), and all the gradients with respect to the independent batch dimensions (in this case five) are added together. Therefore, the returned gradient always has the same size as the output from getLearnableParameters.

    Input Arguments

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    Function approximator object, specified as one of the following:

    Option to use acceleration for gradient computations, specified as a logical value. When useAcceleration is true, the gradient computations are accelerated by optimizing and caching some inputs needed by the automatic-differentiation computation graph. For more information, see Deep Learning Function Acceleration for Custom Training Loops.

    Output Arguments

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    New actor or critic, returned as an approximator object with the same type as oldAppx but with the gradient acceleration option set to useAcceleration.

    Version History

    Introduced in R2022a

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