Broader applicability of the proposed Lipschitz estimator beyond strong convexity

Investigate the applicability of the online Lipschitz-smoothness estimator L_{t+1} = max(L_t, c_{t+1}) used within the NAG-free heuristic to optimization problems outside the strongly convex setting, and ascertain domains where this estimator provides practical benefits.

Background

The paper introduces a symmetric estimator for L alongside the m estimator, forming a parameter-free heuristic (Algorithm 2) with strong empirical performance. However, its theoretical analysis is deferred, and the authors suggest potential utility beyond strongly convex problems.

They explicitly conjecture that the L-estimator may have promising applications outside the strong convexity regime, framing an exploratory direction for future investigation about its effectiveness across broader classes (e.g., weakly convex or nonconvex problems).