The Cost of Adaptivity: Matching Lower Bounds Across Learning Problems
Adaptive procedures must work without nuisance information an oracle may use, such as a gradient scale or smoothness index, and robust procedures may have to answer queries whose coordinate and inspection time are chosen only after the data are seen. Such comparisons are meaningful only when the oracle advantage and validity contract are stated explicitly. We formalize nuisance adaptation via a slice-normalized minimax ratio retaining the worst-case instance within each nuisance slice, and separately define the robustness cost of expanding from one preannounced Gaussian query to arbitrary post-hoc inspection. Our main result is a finite-horizon composition law for Gaussian certification: ...
| Authors | Ibne Farabi Shihab, Adria Binte Habib |
|---|---|
| Primary category | cs.LG |
| Published | 9 August 2026 |
| Last updated at source | 9 August 2026 |
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