{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T17:24:06Z","timestamp":1758821046944},"publisher-location":"California","reference-count":0,"publisher":"International Joint Conferences on Artificial Intelligence Organization","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,7]]},"abstract":"<jats:p>Riemannian gradient descent (RGD) is a simple, popular and efficient algorithm for leading eigenvector computation [AMS08]. However, the existing analysis of RGD for eigenproblem is still not tight, which is O(log(n\/epsilon)\/Delta^2) due to [Xu et al., 2018]. In this paper, we show that RGD in fact converges at rate O(log(n\/epsilon)\/Delta), and give instances to shows the tightness of our result. This improves the best prior analysis by a quadratic factor. Besides, we also give tight convergence analysis of a deterministic variant of Oja's rule due to [Oja, 1982]. We show that it also enjoys fast convergence rate of O(log(n\/epsilon)\/Delta). Previous papers only gave asymptotic characterizations [Oja, 1982; Oja, 1989; Yi et al., 2005]. Our tools for proving convergence results include an innovative reduction and chaining technique, and a noisy fixed point iteration argument. Besides, we also give empirical justifications of our convergence rates over synthetic and real data.<\/jats:p>","DOI":"10.24963\/ijcai.2020\/453","type":"proceedings-article","created":{"date-parts":[[2020,7,8]],"date-time":"2020-07-08T12:12:10Z","timestamp":1594210330000},"page":"3276-3282","source":"Crossref","is-referenced-by-count":0,"title":["Tight Convergence Rate of Gradient Descent for Eigenvalue Computation"],"prefix":"10.24963","author":[{"given":"Qinghua","family":"Ding","sequence":"first","affiliation":[{"name":"The Chinese University of Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kaiwen","family":"Zhou","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James","family":"Cheng","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"10584","event":{"number":"28","sponsor":["International Joint Conferences on Artificial Intelligence Organization (IJCAI)"],"acronym":"IJCAI-PRICAI-2020","name":"Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}","start":{"date-parts":[[2020,7,11]]},"theme":"Artificial Intelligence","location":"Yokohama, Japan","end":{"date-parts":[[2020,7,17]]}},"container-title":["Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence"],"original-title":[],"deposited":{"date-parts":[[2020,7,9]],"date-time":"2020-07-09T02:15:15Z","timestamp":1594260915000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ijcai.org\/proceedings\/2020\/453"}},"subtitle":[],"proceedings-subject":"Artificial Intelligence Research Articles","short-title":[],"issued":{"date-parts":[[2020,7]]},"references-count":0,"URL":"https:\/\/doi.org\/10.24963\/ijcai.2020\/453","relation":{},"subject":[],"published":{"date-parts":[[2020,7]]}}}