Research map / Learning theory and algorithms / Submodular and game algorithms
Optimal approximation for unconstrained non-submodular minimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Projected subgradient method (PGM) applied to the Lovász-extension-based approximate subgradients for non-submodular H, instead of exact submodular minimization | unconstrained non-submodular minimization H = F - G · theoretical guarantee (Corollary 1) | bicriteria bound H(S_hat) <= F(S*)/alpha - beta G(S*) + eps | Helped |
| Noisy oracle (multiplicative Gaussian noise, averaging m samples) used in place of exact H in PGM and submodular minimization algorithms | submodular minimization algorithms (MNP, CG, PGM, ACCPM) on min-cut and clustering · Genrmf-long and Two-moons | gap in discrete objective value vs number of samples m | No clear effect |
| Using range cost F^r (alpha = 1/(d-1)) instead of modified range function F^mr (submodular) as regularizer in PGM | structured sparse learning with PGM · simple linear regression, d=250, k=20 | support and estimation error | Hurt |
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