Author

Michael Menart

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Jul 2026

Stronger Memory-Query Tradeoffs for Convex Optimization: The Limitations of Subquadratic Memory

This work proves two lower bounds for the first order oracle complexity of minimizing a $d$-dimensional $1$-Lipschitz convex function over the unit ball with $m$ bits of memory and is the first to show a sharp oracle complexity phase transition around $m\approx d^2$.

Michael Menart, Aleksandar Nikolov, Ohad Shamir · arXiv.org · 0 citations