Pytorch based implementations of proximal operators for useful functions in machine learning. The code is based on a series of blog posts in my blog - https://alexshtf.github.io. See the examples folder for usage examples.

The project consists of several modules for implementing proximal operators for various function types:

• cvxlin for compositions of a convex function onto a linear function. Useful for least squares and logistic regression.
• cvxlinreg for regularized variants of the above. Useful for Lasso, or L1 / L2 regularized logistic regression.
• minibatch_cvxlin for mini-batch variants of a convex onto linear composition. Useful for training least squares of logistic regression models using proximal operators applied to mini-batches of loss functions.
• cvxlips_quad for a composition of a convex and Lipschitz function onto a quadratic function. Useful for problems such as phase retrieval, or factorization machines for CTR prediction (experimental)

Thhe experiments directory contains numerical experimentation code which demonstrates that we indeed achieve stability w.r.t step size choice, as theory papers predict, and the execution speed of our methods compared to naive gradient descent.

Example - solving a phase retrieval problem using an incremental proximal point algorithm:

import math
import torch
from cvxlinreg import IncRegularizedConvexOnLinear, Logistic, L2Reg

w = torch.zero(dim)
opt = IncRegularizedConvexOnLinear(w, Logistic(), L2Reg(0.01)) # L2 regularized logistic regression
for t, (x, y) in enumerate(dataset):
    step_size = 1 / math.sqrt(t)
    opt.step(step_size, -y * x, 0)  # ln(1 + exp(-y * <w, x> + 0))