Mastering Polyak Averaging: A Hidden Gem for Smoother and Faster Convergence in Optimization

Author(s): Joseph Robinson, Ph.D.

Originally published on Towards AI.

From Gradient Descent to Polyak’s Method: A Machine Learning Tutorial

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Polyak Averaging is a powerful optimization technique often underutilized but can yield significant improvements in convergence speed and stability for iterative optimization algorithms (e.g., gradient descent).

Named after the mathematician Boris Polyak, this technique is particularly effective in scenarios where noisy gradients or unstable updates slow the learning.

We will learn about Polyak Averaging, its mathematical structure, and its comparison to traditional gradient descent. We will then implement it in Python and show its practical advantages with hands-on examples.

Polyak Averaging averages values of the previous t parameters [image source].

· 1. What is Polyak Averaging?· 2. The Mathematics Behind Polyak Averaging ∘ Standard Gradient Descent: ∘ Polyak Averaging:· 3. Why Use Polyak Averaging? Benefits and Intuition· 4. Implementing Polyak Averaging (from Scratch)· 5. Practical Example: Gradient Descent vs. Polyak Averaging ∘ A. Linear Function ∘ B. Quadratic Function ∘ C. Rosenbrock Function· 6. Conclusion· Call to Action

Polyak Averaging is designed to improve the stability and performance of iterative optimization algorithms like gradient descent. The idea is to average a model’s parameters (i.e., weights) over multiple iterations rather than just assuming their values at the final iteration.

This averaged model can yield better generalization… Read the full blog for free on Medium.

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Published via Towards AI