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Uniform stability is a notion of algorithmic stability that bounds the worst case change in the model output by the algorithm when a single data point in the dataset is replaced. An influential work of Hardt et al. [2016] provides strong upper bounds on the uniform stability of the stochastic gradient descent (SGD) algorithm on sufficiently smooth convex losses. These results led to important progress in understanding of the generalization properties of SGD and several applications to differentially private convex optimization for smooth losses.
Our work is the first to address uniform stability of SGD on nonsmooth convex losses. Specifically, we provide sharp upper and lower bounds for several forms of SGD and full-batch GD on arbitrary Lipschitz nonsmooth convex losses. Our lower bounds show that, in the nonsmooth case, (S)GD can be inherently less stable than in the smooth case. On the other hand, our upper bounds show that (S)GD is sufficiently stable for deriving new and useful bounds on generalization error. Most notably, we obtain the first dimension-independent generalization bounds for multi-pass SGD in the nonsmooth case. In addition, our bound allow us to derive a new algorithm for differentially private nonsmooth stochastic convex optimization with optimal excess population risk. Our algorithm is simpler and more efficient than the best known algorithm for the nonsmooth case, due to Feldman et al. [2020].
Author Information
Raef Bassily (The Ohio State University)
Vitaly Feldman (Apple)
Cristóbal Guzmán (PUC-Chile)
Kunal Talwar (Apple)
Related Events (a corresponding poster, oral, or spotlight)
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2020 Spotlight: Stability of Stochastic Gradient Descent on Nonsmooth Convex Losses »
Thu. Dec 10th 03:00 -- 03:10 PM Room Orals & Spotlights: Optimization/Theory
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Clement Canonne · Kwang-Sung Jun · Seth Neel · Di Wang · Giuseppe Vietri · Liwei Song · Jonathan Lebensold · Huanyu Zhang · Lovedeep Gondara · Ang Li · FatemehSadat Mireshghallah · Jinshuo Dong · Anand D Sarwate · Antti Koskela · Joonas Jälkö · Matt Kusner · Dingfan Chen · Mi Jung Park · Ashwin Machanavajjhala · Jayashree Kalpathy-Cramer · · Vitaly Feldman · Andrew Tomkins · Hai Phan · Hossein Esfandiari · Mimansa Jaiswal · Mrinank Sharma · Jeff Druce · Casey Meehan · Zhengli Zhao · Hsiang Hsu · Davis Railsback · Abraham Flaxman · · Julius Adebayo · Aleksandra Korolova · Jiaming Xu · Naoise Holohan · Samyadeep Basu · Matthew Joseph · My Thai · Xiaoqian Yang · Ellen Vitercik · Michael Hutchinson · Chenghong Wang · Gregory Yauney · Yuchao Tao · Chao Jin · Si Kai Lee · Audra McMillan · Rauf Izmailov · Jiayi Guo · Siddharth Swaroop · Tribhuvanesh Orekondy · Hadi Esmaeilzadeh · Kevin Procopio · Alkis Polyzotis · Jafar Mohammadi · Nitin Agrawal -
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