This repo contains basic implementations of a few optimization algorithms (see this blog post). The primary purpose of this repo is for me to learn and have bare bones implementations sitting around for future use.

The important folders are:

• models: This folder contains a few simple optimization models (e.g. least squares, logistic regression). Each model is an object and has functions such as F or grad_F (the function value and the gradient) that return data used by various optimization algorithms.

• opt_algos: Various optimization algorithms (gradient descent, SGD, etc) are implemented in python. Each optimization function takes a model object (see above) as an argument plus various optimization hyperparameters (e.g. learning rate, max iterations, etc).

Notation: since I am a statistician I am using beta for the function variables, and X/y for the data for the optimization problem. Capital F is the objective function (usually a negative log likelihood). Lower case f is the likelihood of an individual data point for ERM problems (e.g. least squares). eta is the learning rate. L_F and mu_F are the Lipshitiz and strong convexity constants for the objective function.

Most of the code is based on the lecture notes from STOR 892: Convex Optimization. Some additional useful references include

• An overview of gradient descent optimization algorithms by Sebastian Ruder (this is a good high level intro)
• Optimization Methods for Large-Scale Machine Learning by Léon Bottou, Frank E. Curtis, and Jorge Nocedal (more indepth overview of first/second order and stochastic methods)