Differentiating function that calls pmap

[ngiann]

I have been using ReverseDiff for some time now and my experience with it has been very positive.

I want to use ReverseDiff to differentiate a function which is expensive to evaluate. I thought that what I could do is split the computation of this expensive function between different workers using pmap. Unfortunately, this fails.

I wrote some minimal code that displays the problem. The code below implements a simple linear regression problem. In slightly more detail:

• I generate 100 5-dim inputs x and a 5-dim weight vector w.
• I then multiply them to get the 1-dimensional output targets y. I also add a bit of noise on y.
• The linear regression problem consists in recovering the weight vector w starting from some random weight vector w0
• I then set up the objective function that calculates the mean squared error. It is this objective function which contains the call to pmap.
• I then define the gradient of my objective using ReverseDiff.
• The defined objective and gradient are passed to Optim.optimize so that the objective is minimised, which leads to the estimate ŵ for the true weight vector.
• Finally, the code reports the initial weight vector w0 (where the optimisation started from) the best best estimate ŵ and the true weight vector w. If the code below works correctly, one should see that ŵ and w are very similar.

Before running the code, I add two workers with addprocs(2). If you run the code below, you will notice that it doesn't work as expected. What we actually see is that ŵ is identical to w0, i.e. it is as if the optimisation never took place.

However: if I change the pmap in the objective function to map, it all works, meaning that ŵ is indeed very close to w.

Is this a (known) issue or is there something wring with the code? Many thanks.

@everywhere using ReverseDiff
using Optim

function demo_pmap()

  # fix random seed
  srand(101)

  # generate some data for linear regression problem

  # number of data items
  N = 100
  # inputs
  x = [randn(5) for n=1:N]
  # true weights
  w = randn(5)
  # output targets
  t = [dot(w,xn)+0.01*randn() for xn in x]

  # set up objective function to minimise
  function objective(w)

      # error due to one input-output (x,t) pair
      function aux(t,x)
        return (t-dot(w,x))^2
      end

      # evaluate in parallel and return error to be minimised
      reduce(+, pmap(aux, t, x))
  end

  # define gradient using AD
  function helper!(storage, w)
    # One could pre-compute the tape for efficiency
    ReverseDiff.gradient!(storage, objective, w)
  end

  # minimise using Optim
  w0 = randn(size(w))
  ŵ  = optimize(objective, helper!, w0, LBFGS(), Optim.Options(iterations=100)).minimizer

  # report - last two should be close
  display(w0)
  display(ŵ)
  display(w)

end