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Hai-Han Zhang

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Preprint Sep 2026

Matching Higher-Order Oracle Complexity for Smooth Monotone Variational Inequalities

A matching $\Omega_p(Q^{2/(3p-1)})$ lower bound is proved for arbitrary adaptive deterministic algorithms and randomized algorithms with per-instance success probability at least $2/3$, without span or tensor-update restrictions.

Hai-Han Zhang, Wen-Dao Wu, Chen-Heng Zhang et al. · 2 citations · ⚡1
Preprint Sep 2026

Near-Optimal Deterministic Exact-Value Complexity for Smooth Convex Optimization

A single fixed smooth convex hard instance is constructed using a Moreau-smoothed biased max chain, an exact prefix-shielding mechanism, and batched delayed rotations to preserve consistency with the full adaptive transcript and establish the optimality of the square-root complexity branch for deterministic bounded-que...

Wen-Dao Wu, Hai-Han Zhang, Chen-Heng Zhang et al. · 0 citations
Preprint Jul 2026

Near-Optimal Lower Bounds for Randomized Algorithms in Exact Value Zeroth-Order Convex Optimization

This work proves the first near-optimal lower bound for arbitrary adaptive randomized algorithms throughout both accuracy regimes of exact value Lipschitz convex optimization, and develops a posterior mean energy method for adaptive exact max observations.

Haihan Zhang, Chen-Heng Zhang, Zhiquan Qi et al. · 1 citation

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