Research map / Learning theory and algorithms / Submodular and game algorithms
Greed is Still Good: Maximizing Monotone Submodular+Supermodular (BP) Functions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SemiGrad instead of GreedMax | BP maximization on the first contrived cardinality-constrained experiment · Contrived functions, |V| = 20, k = 10 | objective value | Helped |
| Use SemiGrad instead of GreedMax | BP maximization on the second contrived cardinality-constrained experiment · Contrived functions, |V| = 20, k = 10 | objective value | Mixed |
| Compare GreedMax's objective value with its theoretical guarantee | GreedMax · First contrived cardinality-constrained experiment | objective-value gap: 0.1852 | No clear effect |
| Use the curvature-based guarantee for the BP objective | GreedMax and SemiGrad · Cardinality constraint | approximation guarantee: \frac{1}{\kappa_f}\left[1-e^{-(1-\kappa^g)\kappa_f}\right] | Helped |
| Use the curvature-based guarantee for the BP objective | GreedMax and SemiGrad · p matroid constraints | approximation guarantee: \frac{1-\kappa^g}{(1-\kappa^g)\kappa_f + p} | Helped |
| Replace the full supermodular term with its modular singleton-value surrogate | GreedMax maximizing h'(X)=f(X)+\sum_{v\in X}g(v) · Cardinality constraint | approximation guarantee: \frac{1}{\kappa_f}\left[1-e^{-(1-\kappa^g)\kappa_f}\right] versus \frac{1-\kappa^g}{\kappa_f}\left[1-e^{-\kappa_f}\right | Hurt |
| Initialize SemiGrad with the empty set | SemiGrad · Cardinality constraint | approximation guarantee: same bound as GreedMax | No clear effect |
| Initialize SemiGrad with the empty set | SemiGrad · p matroid constraints | approximation guarantee: same bound as GreedMax | No clear effect |
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