Beyond Averaging in John Ellipsoid Approximation: High-Accuracy Algorithms in the Leverage-Score Model
Researchers have developed new algorithms for approximating the John ellipsoid of a symmetric polytope, improving upon existing leverage-score methods. The new approach separates the complexity into certification, identification, and accuracy costs, revealing that the traditional $\varepsilon^{-1}$ dependence is an artifact of the certification process. By focusing on the last iterate and utilizing accelerated methods and damped Newton steps, the algorithms can achieve a $(1+\varepsilon)$-John guarantee with significantly fewer queries, particularly after an initial setup phase. AI
IMPACT This research advances optimization algorithms, potentially impacting the efficiency of machine learning model training and other AI applications that rely on complex mathematical computations.