Optimal Stochastic Convex Optimization Through The Lens Of Active Learning

The large fields of convex optimization and active learning have been developed fairly independent of each other, from the design of algorithms to the techniques of proof. Given the growing literature in both these subjects, we believe that understanding the connections between them is important to people in both areas. Here, we establish few such interesting relationships in upper and lower bound techniques that bring out these similarities. Our prime result is showing upper and lower bounds for precisely how the minimax rate for optimizing a given function depends solely on a flatness/noise condition for the function around its minimum.