637de5e2a7a77f741b0b84bd61c83125-Supplemental-Conference.pdf

A.1 ProofofTheorem3.1 The proof can be found in (Hardt et al., 2016). We provide the proof in Appendix for reference. Firstly, it is easy to see that h1(w) and h2(w) are both η-approximate β-gradient Lipschitz, which satisfiesinequatilyinEq. (A.1). A.5 ProofofTheorem5.1 The proof follows the standard techniques for uniform stability. We need to replace the nonexpansive property used in standard analysis by the approximately non-expansive property.