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).

References

Moreover, we conjecture that our L-estimator has promising applications in domains beyond the strong convexity setting, and exploring this broader applicability will be another important area for future investigation.

— Adaptive Acceleration Without Strong Convexity Priors Or Restarts  (2506.13033 - Cavalcanti et al., 16 Jun 2025) in Conclusion (Section “Conclusion”, near end of paper)

Several directions remain open for future work. First, the convergence analysis relies on conservative global Lipschitz constants and sampling assumptions. Developing weaker convergence conditions and adaptive local Lipschitz estimates could reduce conservatism. Approaches that avoid requiring a known Lipschitz constant altogether provide another promising direction .

— Risk-Aware Optimal Control with Rulebooks  (2609.05199 - Wongpiromsarn, 4 Sep 2026) in Section Conclusions and Future Work