Keep the gradient flowing

Optimization Nuggets: Stochastic Polyak Step-size, Part 2

Faster rates under strong convexity

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 …

Optimization Nuggets: Stochastic Polyak Step-size

A simple step-size tuner with optimal rates

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.

Optimization Nuggets: Exponential Convergence of SGD

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.