convergence
4 free lessons tagged convergence across Math, AI. Each one is a short sequence of focused steps with narration and a five-question quiz at the end — take them in any order, no signup required.
Gradient descent: choosing the step and knowing the rate
Gradient descent is three lines of code and a hundred years of theory. This lesson derives why a safe step size is one over the smoothness constant, why the condition number governs everything, and why acceleration reaching order one over k squared is provably the best any first-order method can do.
Retractions and Riemannian Algorithms
How to move along a curved space without solving differential equations: retractions as cheap approximations to geodesics, vector transport, and the Riemannian versions of gradient descent, conjugate gradients, and trust regions.
Client Drift: The Heterogeneity Problem
Why local training on non-identical data pulls clients apart, how averaging their updates produces a model that suits nobody, and the control-variate fix that corrects the drift.
Dynamic Programming: Value and Policy Iteration
When you know the full MDP model, dynamic programming finds the optimal policy exactly. Learn the Bellman optimality equation, the contraction argument that guarantees convergence, and the concrete difference between policy iteration and value iteration — with a value-iteration code walkthrough.