# Reproduction: Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function

## Pages

| Page |
| --- |
| [Executive summary](#/executive-summary) |
| [Claim 1: C1: Theorem 4.1 establishes a general first-order-logic framework giving p...](#/claim-1-c1-theorem-4-1-establishes-a-general-first-order-logic-framework-giving-p) |
| [Claim 2: C2: Theorem 5.1 bounds the pseudo-dimension of piecewise-polynomial traini...](#/claim-2-c2-theorem-5-1-bounds-the-pseudo-dimension-of-piecewise-polynomial-traini) |
| [Claim 3: C3: Theorem 6.1 extends the framework to the bi-level validation-loss sett...](#/claim-3-c3-theorem-6-1-extends-the-framework-to-the-bi-level-validation-loss-sett) |
| [Claim 4: C4: Theorem 7.2 shows that when the optimal parameter path theta*(x, alpha...](#/claim-4-c4-theorem-7-2-shows-that-when-the-optimal-parameter-path-theta-x-alpha) |
| [Claim 5: C5: Theorem 8.1 provides the first learnability guarantee for weighted gro...](#/claim-5-c5-theorem-8-1-provides-the-first-learnability-guarantee-for-weighted-gro) |
| [Claim 6: C6: Theorem 8.2 derives a Pdim(L) = O(d^2) bound for weighted fused LASSO ...](#/claim-6-c6-theorem-8-2-derives-a-pdim-l-o-d-2-bound-for-weighted-fused-lasso) |
| [Conclusion](#/conclusion) |