2021 IEEE International Conference on Acoustics, Speech and Signal Processing

6-11 June 2021 • Toronto, Ontario, Canada

Extracting Knowledge from Information

2021 IEEE International Conference on Acoustics, Speech and Signal Processing

6-11 June 2021 • Toronto, Ontario, Canada

Extracting Knowledge from Information
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Paper Detail

Paper IDSPTM-21.5
Paper Title ON THE CONVERGENCE OF RANDOMIZED BREGMAN COORDINATE DESCENT FOR NON-LIPSCHITZ COMPOSITE PROBLEMS
Authors Tianxiang Gao, Iowa State University, United States; Songtao Lu, IBM, United States; Jia Liu, Ohio Stat University, United States; Chris Chu, Iowa Stat University, United States
SessionSPTM-21: Optimization Methods for Signal Processing
LocationGather.Town
Session Time:Friday, 11 June, 13:00 - 13:45
Presentation Time:Friday, 11 June, 13:00 - 13:45
Presentation Poster
Topic Signal Processing Theory and Methods: [OPT] Optimization Methods for Signal Processing
IEEE Xplore Open Preview  Click here to view in IEEE Xplore
Abstract We propose a new randomized Bregman (block) coordinate de- scent (RBCD) method for minimizing a composite problem, where the objective function could be either convex or nonconvex, and the smooth part are freed from the global Lipschitz-continuous (partial) gradient assumption. Under the notion of relative smoothness based on the Bregman distance, we prove that every limit point of the gen- erated sequence is a stationary point. Further, we show that the it- eration complexity of the proposed method is O(nε−2) to achieve ε-stationary point, where n is the number of blocks of coordinates. If the objective is assumed to be convex, the iteration complexity is improved to O(nε−1). If, in addition, the objective is strongly convex (relative to the reference function), the global linear conver- gence rate is recovered. We also present the accelerated version of the RBCD method, which attains an O(nε−1/γ ) iteration complex- ity for the convex case, where the scalar γ ∈ [1, 2] is determined by the generalized translation variant of the Bregman distance. Con- vergence analysis without assuming the global Lipschitz-continuous (partial) gradient sets our results apart from the existing works in the composite problems.