Matlab, CUDA, and GPU Computing

Main Project here: Estimating Unobserved Complementarities between Entrepreneurs and Venture Capitalists Matlab Code

Synposis

On July 2nd of 2018, Chenyu Yang, the original code author of the above main project, requested me to have "an implementation of LP (linear programming) on GPU", and Ed seconded this idea. I henceforth started exploring the possibility of such an endeavor. What is more important, such "an implementation of LP on GPU" should beat our current solver (Gurobi or Matlab's linprog). After some research, my conclusion is that we cannot beat performance of Gurobi on solving a single LP, and we should continued to use Gurobi instead of linprog. However, we might be still able to speed up our code by task-parallelising on CPU cores.

Getting Started with our GPU

We are running remotely on the Database Server via VNC. The VNC service on DB Server was configured by Wei during Summer 2018. Matlab, CUDA, and the Titan GPU were installed/configured by Office of Information Technology(OIT).

• To start/configure the VNC service on DB Server and to get connected remotely, see the documentation here.

• Once you are connected to DB Server through VNC, open a terminal on DB Server and type

matlab

This will bring up the Matlab GUI.

• To check if Matlab is working with our Nvidia graphics card, in the Matlab command window, type

gpuDevice. 

What Works, and What Doesn't

• GPU computing does not work well for linear programming. The biggest reason is that GPUs don't work well for sparse linear algebra used for most LP solver. Another case study published 3 years ago shows that "the overhead of communication between CPU and GPU grows faster than the benefit of parallelizing matrix operations via CUDA." In another technical report, it is confirmed that "all algorithms (for solving LP and MIP problems)... do not fit to the SIMT paradigm".

• For the above reason, Gurobi does not support GPU computing.

• Matlab does not have GPU-based linprog.

• Maltba does have an option to run ga in parallel.

• Gurobi does support CPU parallelism. In fact, it will use the concurrent solver for LP by default.

• In general, individual threads of GPU only perform well with simple arithmetic tasks. Task-parallelizing toolboxes/libraries/packages onto threads of GPU is NO GO.

Serial vs Parallel: solving many LPs on CPU

Using a function wrapper for Gurobi

I manage to call Gurobi solvers on many LP problems in a parallel manner. To accomplish this, one needs to wrap the LP solving part into a function, and call this function inside the parfor. See File:Parallel gurobi.pdf for a (lazy) example.

Testing performance

Testing instance 1

We used the following parameters for testing:

R = 10, K = 1, S = 2, industry = 4, monte_N = 1, monte_M = 2. quota_per_up = 1, mktsize = 3, n_trail = 2, ini_w_M = 10, n_cores = 12. 

Run serial and parallel(using the above method) versions of msmf_corr_coeff.m. With profiling, the parallel version takes much longer time than the serial one. On a closer inspection, a single call to gurobi takes a very small amount of time. Using parfor will probably not give us any benefit. However, I suspect that for large R (~1000) we will see improvements from parallelism.

Serial: 356s
Parallel: 874s

Testing instance 2

We used the following parameters:

R = 1000, K = 1, S = 2, industry = 4, monte_N = 1, monte_M = 2. quota_per_up = 1, mktsize = 3, n_trail = 2, ini_w_M = 10, n_cores = 12. 

The parallel version now is ~3.5 time faster than the serial version. I believe it might be even faster with more cores. However I do not completely understand how the computation time scales with R (and other parameters). Will run another test with R = 200.
Serial: 9000+s
Parallel: 2873s

Testing instance 3

We used the following parameters:

R = 200, K = 1, S = 2, industry = 4, monte_N = 1, monte_M = 2. quota_per_up = 1, mktsize = 3, n_trail = 2, ini_w_M = 10, n_cores = 12. 

Result: Serial: 3231 s
Parallel: 1605 s

Deliverable

Week July 2 - 6

In Matlab, use parfor for both CPU and GPU to solve a set of LPs. Profile and compare.
Just try to do CPU instead. Figure out how to do CPU-based parallel computing with Gurobi. I cannot find a way to run Gurobi solvers inside a parfor. I believe Matlab's linprog can, but linprog is much slower than Gurobi. There will be some trade off. I need to test this.
It is too hard to test this using the code written by Chenyu. Instead I will write my small piece of code to test this.

Week July 9 - 13

• Continue experimenting with calling gurobi inside parfor.
• Look at ways to speed up moments.m. I was wrong about the computational complexity of moments.m. However it might still benefit us to speed up moments.m, but it is on a lower priority now.

Reference

1. MATLAB GPU Computing Support for NVIDIA CUDA-Enabled GPUs
2. Getting Started with Parallel Computing Toolbox
3. Speeding Up Algorithms: When Parallel Computing and GPUs Do and Don't Accelerate