Sublinear Classical and Quantum Algorithms for General Matrix Games

We investigate sublinear classical and quantum algorithms for matrix games, a fundamental problem in optimization machine learning, with provable guarantees. Given matrix, the game were previously known only two special cases: (1) maximizing vectors live L1-norm unit ball, (2) minimizing either L1- or L2-norm ball. give algorithm that can interpolate smoothly between these any fixed q 1 2, we solve, within some additive error, games where are an Lq-norm also provide corresponding solves same task quadratic improvement dimensions of vectors. Both our optimal dimension parameters up to poly-logarithmic factors. Finally, propose approximate Carathéodory Lq-margin support vector machines as applications.