J. Zhang

A Lower Bound for the Heavy-Ball Method on Smooth Convex Functions

Can the classical Heavy-Ball method, with arbitrary horizon-dependent parameters chosen in advance, achieve Nesterov's $O(T^{-2})$ last-iterate rate on every smooth convex objective? We provide a negative answer. For every horizon $T\ge2$ and every predetermined schedule with nonnegative step sizes and momenta in $[0,1...