To address this gap, we study deterministic/stochastic versions of SAM with practical configurations (i.e., constant

All models discussed in the paper use ReLU non-linearity.

Decision trees are a fundamental workhorse in machine learning. Their logical and hierarchical structure makes them easy to understand and their predictions easy to explain.

The proof of infeasibility condition (Theorem 3.2) is provided in Section B. Explanations on conditions derived in Theorem 3.2 are included in Section C. The proof of properties of the proposed model (r)LogSpecT (Proposition 3.4 The truncated Hausdorff distance based proof details of Theorem 4.1 and Corollary 4.4 are Details of L-ADMM and its convergence analysis are in Section F. Additional experiments and discussions on synthetic data are included in Section G. ( m 1) Again, from Farkas' lemma, this implies that the following linear system does not have a solution: Example 3.1 we know δ = 2|h Since the constraint set S is a cone, it follows that for all γ > 0, γ S = S . Opt(C, α) = α Opt(C, 1), which completes the proof. The proof will be conducted by constructing a feasible solution for rLogSpecT. Since the LogSpecT is a convex problem and Slater's condition holds, the KKT conditions We show that it is feasible for rLogSpecT. R, its epigraph is defined as epi f: = {( x, y) | y f ( x) }. Before presenting the proof, we first introduce the following lemma.

In this work, we investigate an alternative setting for tuning regularization parameters, namely data-driven algorithm design, following the previous line of work by Balcan et al. [