The Lagrangian Structure of Cost-Penalized Active Feature Acquisition
Active Feature Acquisition (AFA) sequentially selects features to maximize predictive accuracy under an acquisition budget. A natural heuristic greedily maximizes Expected Information Gain minus a cost penalty, EIG(j|x_S)-lam*c_j (EIG-Cost), but its theoretical guarantees are unclear. We provide an a-posteriori certificate decomposing the gap to the optimal hard-budget policy into a budget-slack term and a greedy-suboptimality term Del_lam. The certificate is computable when the penalized optimum is tractable; on small heterogeneous-cost instances, we verify it exactly, finding Del_lam near zero across 4,000 solved cases. On the large clinical task, Del_lam is not computable, so the decom...
| Authors | Joseph Bingham |
|---|---|
| Primary category | cs.LG |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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