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• W2918466682 abstract "We target the problem of finding a local minimum in non-convex finite-sum minimization. Towards this goal, we first prove that the trust region method with inexact gradient and Hessian estimation can achieve a convergence rate of order $mathcal{O}(1/{k^{2/3}})$ as long as those differential estimations are sufficiently accurate. Combining such result with a novel Hessian estimator, we propose the sample-efficient stochastic trust region (STR) algorithm which finds an $(epsilon, sqrt{epsilon})$-approximate local minimum within $mathcal{O}({sqrt{n}}/{epsilon^{1.5}})$ stochastic Hessian oracle queries. This improves state-of-the-art result by $mathcal{O}(n^{1/6})$. Experiments verify theoretical conclusions and the efficiency of STR." @default.
• W2918466682 created "2019-03-11" @default.
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• W2918466682 date "2019-09-25" @default.
• W2918466682 modified "2023-09-27" @default.
• W2918466682 title "A Stochastic Trust Region Method for Non-convex Minimization" @default.
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