Based on our theoretical analysis, we propose an active learning algorithm that employs regret minimization to minimize the FIR.

Real-valued linear prediction is a fundamental problem in machine learning.

When Does Confidence-Based Cascade Deferral Suffice? A.3 Proof of Lemma 4.1 We start with Lemma A.1 which will help prove Lemma 4.1. We are ready to prove Lemma 4.1. By Lemma A.1, this is equivalent to showing that E ( 1[ η We provide an excess risk bound in Lemma A.2 and generalization bound in Lemma A.3. The excess risk for the learned deferral rule can be bounded as follows: Lemma A.2. Per Corollary 3.2, the excess risk for ˆ r can then be written as: R (ˆr; h We next bound the second term on the right-hand side.

In the differentially private non-convex setting, we provide several new algorithms for approximating stationary points of the population risk.