Uniqueness of ITEM in smooth strongly convex minimization

Determine whether Taylor–Drori’s ITEM is the uniquely minimax optimal deterministic first-order algorithm for smooth strongly convex minimization using the gradient oracle, i.e., ascertain if any other deterministic first-order method achieves the exact optimal worst-case rate on this problem class.

Background

For smooth strongly convex minimization, ITEM has been identified as achieving exact optimality. The authors explicitly note that, despite exact optimality, the uniqueness of ITEM among deterministic first-order methods is not known.

This question parallels the unknown uniqueness of OGM (smooth convex) and OptISTA (composite minimization), emphasizing the need to investigate whether multiple distinct algorithms can be exactly minimax optimal in these classes.