Figure 3: Ex represents (c)-(d) ConB.

Let x = argminx2RdFn(x) betheglobalminimizerofFn.

Ifthext, krf(xt)k , perturbxt by , with sampled zero.

See Theorem 2 in Section 3.1 formoredetail.

Generative models have many applications in machine learning. To list a few, they have been usedtogenerate high-fidelity images [26,6],synthesize realistic speech andmusic fragments [58], improve the performance of semi-supervised learning [28, 10], detect adversarial examples and other anomalous data [54], imitation learning [22], and explore promising states in reinforcement learning [41].

In this work, we establish rapid convergence for these algorithms under distance measures more suitable for differential privacy.

Four Newton Lange /exp( ), taking (x)= log x21) l asthebarrier = 4 so Stepsizeish= 10 5. Projected constraints, directly byprojection andtheproximal solvedwith suggesting