ArticleJournal of the American Statistical Association2023
Convex and Nonconvex Optimization Are Both Minimax-Optimal for Noisy Blind Deconvolution under Random Designs.
Article in Journal of the American Statistical Association, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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Who cites it
2 citing papers in PubMed.
- Sample-Efficient Reinforcement Learning for Linearly-Parameterized MDPs with a Generative Model.Advances in neural information processing systems · 2021Article
- BRIDGING CONVEX AND NONCONVEX OPTIMIZATION IN ROBUST PCA: NOISE, OUTLIERS, AND MISSING DATA.Annals of statistics · 2021Article
Corrections and comments
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Authors and funding
4 authors.
Funding
Abstract
We investigate the effectiveness of convex relaxation and nonconvex optimization in solving bilinear systems of equations under two different designs (i.e. a sort of random Fourier design and Gaussian design). Despite the wide applicability, the theoretical understanding about these two paradigms remains largely inadequate in the presence of random noise. The current paper makes two contributions by demonstrating that: (1) a two-stage nonconvex algorithm attains minimax-optimal accuracy within a logarithmic number of iterations, and (2) convex relaxation also achieves minimax-optimal statistical accuracy vis-à-vis random noise. Both results significantly improve upon the state-of-the-art theoretical guarantees.
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Registered trials
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