This blog post discusses the convergence rate of the Stochastic Gradient Descent with Stochastic Polyak Step-size (SGD-SPS) algorithm for minimizing a finite sum objective. Building upon the proof of the previous post, we show that the convergence rate can be improved to O(1/t) under the additional assumption that …

The stochastic Polyak step-size (SPS) is a practical variant of the Polyak step-size for stochastic optimization. In this blog post, we'll discuss the algorithm and provide a simple analysis for convex objectives with bounded gradients.

When an optimization problem has multiple global minima, different algorithms can find different solutions, a phenomenon often referred to as the implicit bias of optimization algorithms. In this post we'll characterize the implicit bias of gradient-based methods on a class of regression problems that includes linear least squares and Huber …

This is the first of a series of blog posts on short and beautiful proofs in optimization (let me know what you think in the comments!). For this first post in the series I'll show that stochastic gradient descent (SGD) converges exponentially fast to a neighborhood of the solution.