README.md

Smoothing Based Optimization

Source code for the numerical results presented in the paper "Gaussian smoothing gradient descent for minimizing high-dimensional non-convex functions".

Benchmark different types of optimization algorithms on various test functions. Experiment results will be saved to the ./images/ folder that will be created.

File Organization

Currently includes the following files:

• target_functions.py -- set up a target function and sample an initial guess
• benchmark_algorithms.py -- compare optimization algoritms on series of tests
• hyperparameter_search.py -- test different hyperparameters for each function and algorithm
• visualization.py -- plot optimization values from the logged data

Implemented algorithms (in ./algorithms/):

• adam.py -- Adam optimizer
• rmsprop.py -- RMSProp optimizer
• nag.py -- Nesterov's Accelerated Gradient Descent
• dgs.py -- Directional Gaussian Smoothing
• adgs.py -- DGS with exponential decay on sigma
• lsgd.py -- Laplacian Smooth Gradient Descent
• mcgs.py -- Monte Carlo Gaussian Smoothing
• slgh.py -- Single Loop Gaussian Homotopy

Old files that are now in ./extra_scripts/:

• main.py -- use to launch numerical optimization
• main_tf.py -- use to launch network training (very slow)
• bfgs_dgs.py -- define BFGS+DGS algorithm
• sbfgs.py -- define Smoothed BFGS (it doesn't really work though)
• smoothing_visualization.py -- create interactive smoothing plot