Problem with using spmd in the objective function of fmincon

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I am experiencing trouble with using spmd in the objective function of fmincon. My code is as follows:
load('outervariables.mat');
theta1 = zeros(size(outstruct.x1, 2),1);
%% load data to workers here.
spmd
data = load(['dataworker' num2str(labindex) '.mat']);
end
theta20 = sig.x;
%objective function:
fun = @(theta2)gmmobj(theta2, outstruct, data);
options = optimoptions('fmincon', ...
'SpecifyObjectiveGradient',true, 'Display', 'off', ...
'MaxFunctionEvaluations', 2, ...
'OptimalityTolerance', 1e-14, 'FunctionTolerance', 1e-14);
[x, fval] = fmincon(fun, theta20, [], [], [], [], [], [], [], options);
The objective function gmmobj() is coded as
function [f, grad] = gmmobj(theta2, outstruct, data)
spmd
[mktmval, jac] = meanutil_jacEQN(theta2, data.struct);
end
delta = cell2mat(mktmval(:));
jacobian = cell2mat(jac(:));
clear mktmval jac;
% the following deals with cases were the min algorithm drifts into region where the objective is not defined
if max(isnan(delta)) == 1
f = 1e+10
else
temp1 = outstruct.x1'*outstruct.IVs;
temp2 = delta'*outstruct.IVs;
theta1 = (temp1/outstruct.W*temp1')\(temp1/outstruct.W*temp2');
%theta1 = (temp1*temp1')\(temp1*temp2');
clear temp1 temp2
gmmresid = delta - outstruct.x1*theta1;
temp1 = gmmresid'*outstruct.IVs;
f = temp1/outstruct.W*temp1';
%f = temp1*temp1';
clear temp1
%save gmmresid gmmresid
end
if nargout > 1
grad = 2*jacobian'*outstruct.IVs/outstruct.W*outstruct.IVs'*gmmresid;
end
disp(['GMM objective: ' num2str(f)])
end
When I call the gmmobj() function on its own, it runs fine. But once I start running the optimization with "fmincon", I get the following output and error:
GMM objective: 36532.679
Error using gmmobj (line 13)
Error detected on workers 1 2 3 4 5 6.
Error in @(theta2)gmmobj(theta2,outstruct,data)
Error in barrier
Error in fmincon (line 834)
[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...
Caused by:
Error using levenbergMarquardt (line 16)
Objective function is returning undefined values at initial point. fsolve cannot continue.
Note that line 13 of the "gmmobj" function is where the "spmd" block starts. The gmmobj() function was obviously evaluated once, but on the second iteration, fmincon doesn't seem to recognize the spmd block. Can someone help me with making this work?
  5 Comments
Claire Fang
Claire Fang on 28 Aug 2020
Reason why I am doing this is: I need to back out a set of intermediate values based on my data and the parameter values of theta2. This set of intermediate values has over 77,000X17 values. Doing this sequentially takes a lot of time. So I broke down my data into 6 chunks, and distributed one chunk to each worker (I have 6 cores in total). That was outside of the gmmobj() function in the initial statement:
%% load data to workers here.
spmd
data = load(['dataworker' num2str(labindex) '.mat']);
end
These data on each work do not change once they have been distributed to the workers. However, the intermediate values at each iteration will change because of theta2, the parameters that I am searching for to minimize the objective function gmmobj(). Is that clear?

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Accepted Answer

Walter Roberson
Walter Roberson on 28 Aug 2020
spmd
data = load(['dataworker' num2str(labindex) '.mat']);
end
You are loading data into each worker, not into the client.
fun = @(theta2)gmmobj(theta2, outstruct, data);
There you make a reference to the composite on the client.
function [f, grad] = gmmobj(theta2, outstruct, data)
spmd
[mktmval, jac] = meanutil_jacEQN(theta2, data.struct);
end
There you expect data to resolve to the per-worker value. data is present as a parameter because it matches the positional parameter data wired into the fun function handle.
However, what got wired in to the function handle is the composite as a whole, not a magic reference to the appropriate member of the composite for the lab. And when you have a reference to the composite as a whole, what gets received on the client is an empty composite.
Solution: you can evalin('base') to get at the local instance of the composite.
I also notice that outstruct is being imported into each worker every time you call. I suggest instead adding it using parallel.pool.Constant
load('outervariables.mat');
theta1 = zeros(size(outstruct.x1, 2),1);
%% load data to workers here.
spmd
data = load(['dataworker' num2str(labindex) '.mat']);
end
OS = parallel.pool.Constant(outstruct);
theta20 = sig.x;
%objective function:
fun = @gmmobj;
options = optimoptions('fmincon', ...
'SpecifyObjectiveGradient',true, 'Display', 'off', ...
'MaxFunctionEvaluations', 2, ...
'OptimalityTolerance', 1e-14, 'FunctionTolerance', 1e-14);
[x, fval] = fmincon(fun, theta20, [], [], [], [], [], [], [], options);
function [f, grad] = gmmobj(theta2)
outstruct = evalin('base', 'OS.value'); %grab the parallel.pool.Constant
data = evalin('base', 'data'); %grab the local instance of the composite object
spmd
[mktmval, jac] = meanutil_jacEQN(theta2, data.struct);
end
%etc
I tested the overall idea successfully.
  3 Comments
Claire Fang
Claire Fang on 28 Aug 2020
It turns out that there is nothing wrong with the spmd block. The fmincon() travelled to parameter values that render the nested objective function for fsolve invalid. Once I added lower and upper bounds to fmincon(), the program ran very smoothly and successfully.

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More Answers (2)

Matt J
Matt J on 28 Aug 2020
Clearly, the evaluation of this line was unsuccessful due to an error within meanutil_jacEQN
[mktmval, jac] = meanutil_jacEQN(theta2, data.struct);
My recommendation would be to replace, for debugging purposes, the spmd line with an equivalent for-loop implementation
for i=1:numel(data.struct)
[mktmval{i}, jac{i}] = meanutil_jacEQN(theta2, data{i}.struct);
end
That way you can use the debugger to observe the cause of the error.
  9 Comments
Claire Fang
Claire Fang on 28 Aug 2020
yeah, you are right. I tested out the serial version by using a different sample, so I didn't see that...

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Claire Fang
Claire Fang on 28 Aug 2020
It turns out that there is nothing wrong with the spmd block. The fmincon() travelled to parameter values that render the nested objective function for fsolve invalid. Once I added lower and upper bounds to fmincon(), the program ran very smoothly and successfully.

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