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- W2803236178 abstract "Block-coordinate descent algorithms and alternating minimization methods are fundamental optimization algorithms and an important primitive in large-scale optimization and machine learning. While various block-coordinate-descent-type methods have been studied extensively, only alternating minimization -- which applies to the setting of only two blocks -- is known to have convergence time that scales independently of the least smooth block. A natural question is then: is the setting of two blocks special? We show that the answer is no as long as the least smooth block can be optimized exactly -- an assumption that is also needed in the setting of alternating minimization. We do so by introducing a novel algorithm AR-BCD, whose convergence time scales independently of the least smooth (possibly non-smooth) block. The basic algorithm generalizes both alternating minimization and randomized block coordinate (gradient) descent, and we also provide its accelerated version -- AAR-BCD. As a special case of AAR-BCD, we obtain the first nontrivial accelerated alternating minimization algorithm." @default.
- W2803236178 created "2018-06-01" @default.
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- W2803236178 date "2018-05-23" @default.
- W2803236178 modified "2023-09-27" @default.
- W2803236178 title "Alternating Randomized Block Coordinate Descent" @default.
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