About this course
A derive-it-and-build-it theory course: no memorizing theorems, no proof drills. In every
session an AI mentor walks you through a few lines of numpy, fixes a random seed, and runs
out a curve — then you look back and see that curve landing exactly inside the bound the
theorem promised. We start from "what does learnable even mean" and verify PAC sample
complexity with your own Monte-Carlo runs; use shattering and VC dimension to measure how
expressive a hypothesis class really is; hand-build AdaBoost from scratch and watch training
error decay exponentially while margins march rightward; and finally enter online learning —
weighted majority, multiplicative weights, regret minimization — watching average regret
vanish at the √(logN / T) rate. Theory here isn't chalkboard symbols; it's real,
checkable experiments in your sandbox: formulas are typeset for you, shattering is drawn as
cells, and you drag the knobs on the regret curve yourself. You'll end up actually believing
these bounds — because every one of them, you made hold with your own hands.
What you'll learn
- Verify PAC sample complexity with your own Monte-Carlo runs, and explain what (ε, δ) actually guarantees
- Count a hypothesis class's shattering power, pin down its VC dimension, and read the VC generalization bound
- Hand-build AdaBoost from scratch and watch training error decay exponentially while margins shift right
- Implement Weighted Majority and Multiplicative Weights (Hedge), pushing mistakes and regret inside the theorem's bound
- Plot regret curves and explain why average regret vanishes at the √(logN / T) rate
- Explain how online learning, Boosting and game theory all rest on the same no-regret idea
Syllabus
1PAC Foundations: What Does Learnable Mean3 sessions
2VC Dimension: Measuring a Class's Expressive Power3 sessions
3Boosting: From Weak to Strong, Build AdaBoost by Hand3 sessions
4Online Learning: Weighted Majority & Regret Minimization3 sessions
5Online Convex Optimization: Regret Bounds of Gradient Descent0 sessions
Sessions are on the way.
6Bandits: The Explore-Exploit Tradeoff0 sessions
Sessions are on the way.
7Learning & Games: No-Regret Dynamics & Minimax0 sessions
Sessions are on the way.
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