We provide convergence rates for Krylov subspace solutions to the trust-region and cubic-regularized (nonconvex) quadratic problems. Such solutions may be efficiently computed by the Lanczos method and have long been used in practice. We prove error bounds of the form 1/t2 and e4t/p, where is a condition number for the problem, and t is the Krylov subspace order (number of Lanczos iterations). We also provide lower bounds showing that our analysis is sharp.
|Number of pages
|Advances in Neural Information Processing Systems
|Published - 2018
|32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
Duration: 2 Dec 2018 → 8 Dec 2018