submodular-optimization
4 free lessons tagged submodular-optimization across 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.
Beyond Greedy: Minimization, Non-Monotone, and Richer Constraints
The monotone, cardinality-constrained case is only the entrance. This lesson maps the rest: why submodular minimization is easy while maximization is hard, how to maximize non-monotone functions, what to do under matroid and knapsack constraints, and where submodularity keeps appearing across machine learning.
Submodularity in the Wild: Sensors, Influence, and Summaries
The theory pays off because so many real problems are submodular in disguise. This lesson works through the landmark applications: near-optimal sensor placement, influence maximization in social networks, and document summarization, each reduced to monotone submodular maximization and solved by the greedy algorithm.
The Greedy Algorithm and Its 63% Guarantee
Maximizing a submodular function is NP-hard, yet the simplest possible algorithm gets provably close to optimal. This lesson presents the greedy algorithm, the celebrated (1 - 1/e) guarantee of Nemhauser, Wolsey, and Fisher, why that bound cannot be beaten, and the lazy trick that makes greedy fast at scale.
Submodularity: The Mathematics of Diminishing Returns
Many selection problems share one property: each new item helps less than the last. Formalized, that property is submodularity, and it is what makes otherwise intractable problems solvable with guarantees. This lesson defines it precisely, shows the everyday examples, and explains why it is called the discrete analog of convexity.