Dec-AltProjGDmin: Fully-Decentralized Alternating Projected Gradient Descent for Low Rank Column-wise Compressive Sensing
Dec-AltProjGDmin: Fully-Decentralized Alternating Projected Gradient Descent for Low Rank Column-wise Compressive Sensing
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DOI：
10.1109/cdc51059.2022.9992928
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发表时间：
2022-12
期刊：
影响因子：
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通讯作者：
Shana Moothedath;Namrata Vaswani
中科院分区：
文献类型：
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作者：
Shana Moothedath;Namrata Vaswani
这项工作开发了一个完全占中心的预测梯度下降算法，称为DEC-Altprojgdmin，用于求解以下低级别（LR）矩阵恢复问题：从独立柱状线性线性预测（LR柱 - 柱及压缩感传感）中恢复LR矩阵。我们证明了它在简单的假设下的正确性，并认为DEC-Altprojgdmin既比其他潜在的解决方案方法更快又更高，此外还拥有最佳的样本复杂性保证之一。据我们所知，这项工作是第一次尝试为任何涉及使用交替投影的GD算法的问题开发出可证明正确的完全截然不同的算法的尝试，当时约束集（将投影到）是非convex时。
This work develops a fully-decentralized alternating projected gradient descent algorithm, called Dec-AltProjGDmin, for solving the following low-rank (LR) matrix recovery problem: recover an LR matrix from independent columnwise linear projections (LR column-wise Compressive Sensing). We prove its correctness under simple assumptions and argue that Dec-AltProjGDmin is both faster and more communication-efficient than various other potential solution approaches, in addition to also having one of the best sample complexity guarantees. To our best knowledge, this work is the first attempt to develop a provably correct fully-decentralized algorithm for any problem involving the use of an alternating projected GD algorithm when the constraint set (the set to be projected onto) is non-convex.