Corpus ID: 71146496

A Rank-1 Sketch for Matrix Multiplicative Weights

@article{Carmon2019ARS,
  title={A Rank-1 Sketch for Matrix Multiplicative Weights},
  author={Yair Carmon and John C. Duchi and Aaron Sidford and Kevin Tian},
  journal={ArXiv},
  year={2019},
  volume={abs/1903.02675}
}
  • Yair Carmon, John C. Duchi, +1 author Kevin Tian
  • Published 2019
  • Mathematics, Computer Science
  • ArXiv
  • We show that a simple randomized sketch of the matrix multiplicative weight (MMW) update enjoys (in expectation) the same regret bounds as MMW, up to a small constant factor. Unlike MMW, where every step requires full matrix exponentiation, our steps require only a single product of the form $e^A b$, which the Lanczos method approximates efficiently. Our key technique is to view the sketch as a $\textit{randomized mirror projection}$, and perform mirror descent analysis on the $\textit{expected… CONTINUE READING
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