Parallel computing Monte Carlo

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cedric W 2018-9-25

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评论： Joss Knight 2018-10-11

I'm running 1M simulations on a Monte Carlo basis. I'd like to improve the computation speed and I was thinking about parallel computing but wanted to have a guess about what to expect in term of improvment.

I'd like to understand a little more about modifications that have to be made in my code.

I actually have an almost fully vectorized version of MC simulations and therefore I don't run any loop for i=1:10^6 loop.

How should I modify my code for the parallel computing to be efficient ? I guess – since MATLAB’s strength is to work vectorised – I must not introduce a “ parfor i=1:10^6 “ loop. I was thinking about splitting my computation, i.e. vectorising batches of 10^4 simulations (instead of a single 10^6) and then running a parfor loop 10^2 times. Would this method be ok or would it lead to poorer results (I know it's hard to guess without trying, which is something I haven't done yet, but I need a guess to know if I'm going wrong way) ? What could be an efficient solution ?

FYI, I'm running simulations on a test computer, 4 cores, utilization at around 75% of each core when running.

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cedric W 2018-9-25

No. At least, not on my test machine. I don't know yet if I'll have one. Does it change a lot?

KSSV 2018-9-25

Yes..it will if you have one deserving..read about gpuDevice, gpuArrays etc.

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Answer 1

Joss Knight 2018-9-30

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You seem to have the right idea. For highly vectorized code, parallelization should be done in batches. However, it does depend on what you are doing as to whether you will gain anything using a parallel pool. Many matrix operations in MATLAB are already heavily multi-threaded. Use the system tools to determine whether any of your CPU cores are idle and so available.

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cedric W 2018-10-9

编辑：cedric W 2018-10-9

在 MATLAB Online 中打开

I'm not sure I understand correctly.

My code looks like this:

...
  parfor ix = 1:nGPUs 
      S(ix,:,:,:) = runSimulationOnOneGPU(...);
  end
...
function S = runSimulationOnOneGPU(...)
   rng(0);
   x=log(S0).*gpuArray.ones(NbAssets,1);
   MCPaths= arrayfun( @Heston_One_Simulation,x,...);
   S = gather(MCPaths);
end
function [S] = Heston_One_Simulation(x,...)
    U_V = rand(NbAssets,1);
    DrawNormalLaw=randn(NbAssets,1);
...  
end

The "1" in rand and randn is here to specify that it's in 1D, not in the vectorized way. My goal is to have something like this:

Say NbAssets=1. On a vectorized way the code would have been DrawNormalLaw=randn(1,M)

As an example, if M=5 and seed=0 then I have DrawNormalLaw=rand(1,5)=[0.8147 0.9058 0.1270 0.9134 0.6324]. Therefore, for each simulation a different value would be used.

What I meant, is that if I set the seed to 0 in function runSimulationOnOneGPU, then DrawNormalLaw in Heston_One_Simulation will always be equal to 0.8147 for each simulation, leading to 1M identical simulations.

And therefore I don't understand your point. Could you please advise ? My goal is to be able to reproduce MC runs when restarting the algorithm. The idea to me would be to generate 1M upfront couples (rand,randn) values and then tell each GPU run to take at each simulation a different couple.

cedric W 2018-10-11

编辑：cedric W 2018-10-11

This setup, from what I understood, is going to generate the same simulations on each worker, and this is not the goal.

The aim is to have a run on a worker with twister' algo in example, and a parallel run with a different algo.

Do you agree this is not solving the issue ? Am I also limited to 3 possible algorithms on the GPU as stated here ? https://fr.mathworks.com/help/distcomp/control-random-number-streams.html

Joss Knight 2018-10-11

No, it'll generate the same set of numbers in a particular iterate each time you run your code, which may be a different worker because of the way parfor scheduling works, but appears to be what you want.

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