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

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Executive summary
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 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 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 ...
Conclusion