7 papers
Exact Universality of Online Discrepancy
Sunghyeon Jo, Taekyun Lee
We study online vector balancing with random vectors in revealed sequentially, where each vector must be assigned an irrevocable sign upon arrival. The goal is t…
On Minimax Optimality and Uniqueness of Fixed-Step First-Order Methods for Smooth Convex Optimization
Benjamin Grimmer, Sunghyeon Jo, Chanwoo Park
This paper considers the design of optimal fixed-step first-order methods for high-dimensional minimization of -smooth convex functions. For optimizing worst-case performance me…
An Improved Upper Bound for Multicolour Ramsey Numbers
Sunghyeon Jo
Let denote the diagonal -colour Ramsey number. We prove that there exist absolute constants such that $R_r(k)\le r^{rk}\exp\!\left(-c\frac{k}{r\log^2(2r)}\right…
The Exact Online Threshold for the Asymmetric Binary Perceptron
Sunghyeon Jo, Taekyun Lee
Let have independent standard Gaussian entries. For a fixed margin , the asymmetric binary perceptron asks for such th…
A counterexample to Haagerup's problem on subadditive weights
Ikhan Choi, Sunghyeon Jo
We construct a subadditive weight on the type I factor that preserves directed suprema but is not -weakly lower semi-continuous. This provides a counterexample to Haage…
Fidelity Estimation to a Known Quantum State Is Nearly Quadratic in the Smaller Rank
Gye Jin Lee, Sunghyeon Jo
We study the number of copies needed to estimate the root Uhlmann fidelity between an unknown quantum state and a classically known reference, under collective measurements. If the…
Tighter Bounds for the Random-Offerer Mechanism in Bilateral Trade
Sunghyeon Jo
The random-offerer mechanism for bilateral trade selects the seller or the buyer uniformly and lets the selected agent make a profit-maximizing take-it-or-leave-it offer. Let $ρ_{\…