 We consider three settings for the objective function: (i) deterministic and smooth , (ii) stochastic and smooth , and (iii) composition of smooth and non-smooth parts.
<meaning-changed>  We consider three settings for the objective function: (i) deterministic and smooth , (ii) stochastic and smooth , and (iii) composition of smooth and non-smooth parts.
 We consider three settings for the objective function: (i) stochastic and gradient-Lipschitz (in both nonconvex and geodesic convex settings) , (ii) stochastic and smooth , and (iii) composition of smooth and non-smooth parts.