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no code implementations • 11 Apr 2022 • Blake Woodworth, Francis Bach, Alessandro Rudi

We consider potentially non-convex optimization problems, for which optimal rates of approximation depend on the dimension of the parameter space and the smoothness of the function to be optimized.

no code implementations • NeurIPS 2021 • Brian Bullins, Kumar Kshitij Patel, Ohad Shamir, Nathan Srebro, Blake Woodworth

We propose and analyze a stochastic Newton algorithm for homogeneous distributed stochastic convex optimization, where each machine can calculate stochastic gradients of the same population objective, as well as stochastic Hessian-vector products (products of an independent unbiased estimator of the Hessian of the population objective with arbitrary vectors), with many such stochastic computations performed between rounds of communication.

no code implementations • 1 Sep 2021 • Blake Woodworth

In this setting, I analyze the theoretical properties of the popular Local Stochastic Gradient Descent (SGD) algorithm in convex setting, both for homogeneous and heterogeneous objectives.

2 code implementations • 14 Jul 2021 • Jianyu Wang, Zachary Charles, Zheng Xu, Gauri Joshi, H. Brendan McMahan, Blaise Aguera y Arcas, Maruan Al-Shedivat, Galen Andrew, Salman Avestimehr, Katharine Daly, Deepesh Data, Suhas Diggavi, Hubert Eichner, Advait Gadhikar, Zachary Garrett, Antonious M. Girgis, Filip Hanzely, Andrew Hard, Chaoyang He, Samuel Horvath, Zhouyuan Huo, Alex Ingerman, Martin Jaggi, Tara Javidi, Peter Kairouz, Satyen Kale, Sai Praneeth Karimireddy, Jakub Konecny, Sanmi Koyejo, Tian Li, Luyang Liu, Mehryar Mohri, Hang Qi, Sashank J. Reddi, Peter Richtarik, Karan Singhal, Virginia Smith, Mahdi Soltanolkotabi, Weikang Song, Ananda Theertha Suresh, Sebastian U. Stich, Ameet Talwalkar, Hongyi Wang, Blake Woodworth, Shanshan Wu, Felix X. Yu, Honglin Yuan, Manzil Zaheer, Mi Zhang, Tong Zhang, Chunxiang Zheng, Chen Zhu, Wennan Zhu

Federated learning and analytics are a distributed approach for collaboratively learning models (or statistics) from decentralized data, motivated by and designed for privacy protection.

no code implementations • NeurIPS 2021 • Blake Woodworth, Nathan Srebro

We present and analyze an algorithm for optimizing smooth and convex or strongly convex objectives using minibatch stochastic gradient estimates.

no code implementations • 19 Feb 2021 • Shahar Azulay, Edward Moroshko, Mor Shpigel Nacson, Blake Woodworth, Nathan Srebro, Amir Globerson, Daniel Soudry

Recent work has highlighted the role of initialization scale in determining the structure of the solutions that gradient methods converge to.

no code implementations • 2 Feb 2021 • Blake Woodworth, Brian Bullins, Ohad Shamir, Nathan Srebro

We resolve the min-max complexity of distributed stochastic convex optimization (up to a log factor) in the intermittent communication setting, where $M$ machines work in parallel over the course of $R$ rounds of communication to optimize the objective, and during each round of communication, each machine may sequentially compute $K$ stochastic gradient estimates.

no code implementations • NeurIPS 2020 • Edward Moroshko, Suriya Gunasekar, Blake Woodworth, Jason D. Lee, Nathan Srebro, Daniel Soudry

We provide a detailed asymptotic study of gradient flow trajectories and their implicit optimization bias when minimizing the exponential loss over "diagonal linear networks".

no code implementations • NeurIPS 2020 • Blake Woodworth, Kumar Kshitij Patel, Nathan Srebro

the average objective; and machines can only communicate intermittently.

no code implementations • 2 Apr 2020 • Suriya Gunasekar, Blake Woodworth, Nathan Srebro

We present a primal only derivation of Mirror Descent as a "partial" discretization of gradient flow on a Riemannian manifold where the metric tensor is the Hessian of the Mirror Descent potential.

1 code implementation • 20 Feb 2020 • Blake Woodworth, Suriya Gunasekar, Jason D. Lee, Edward Moroshko, Pedro Savarese, Itay Golan, Daniel Soudry, Nathan Srebro

We provide a complete and detailed analysis for a family of simple depth-$D$ models that already exhibit an interesting and meaningful transition between the kernel and rich regimes, and we also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.

no code implementations • ICML 2020 • Blake Woodworth, Kumar Kshitij Patel, Sebastian U. Stich, Zhen Dai, Brian Bullins, H. Brendan McMahan, Ohad Shamir, Nathan Srebro

We study local SGD (also known as parallel SGD and federated averaging), a natural and frequently used stochastic distributed optimization method.

no code implementations • 5 Dec 2019 • Yossi Arjevani, Yair Carmon, John C. Duchi, Dylan J. Foster, Nathan Srebro, Blake Woodworth

We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods.

no code implementations • 6 Nov 2019 • Mark Braverman, Elad Hazan, Max Simchowitz, Blake Woodworth

We investigate the computational complexity of several basic linear algebra primitives, including largest eigenvector computation and linear regression, in the computational model that allows access to the data via a matrix-vector product oracle.

no code implementations • 1 Jul 2019 • Blake Woodworth, Nathan Srebro

We note that known methods achieving the optimal oracle complexity for first order convex optimization require quadratic memory, and ask whether this is necessary, and more broadly seek to characterize the minimax number of first order queries required to optimize a convex Lipschitz function subject to a memory constraint.

1 code implementation • 21 Jun 2019 • Ryan Rogers, Aaron Roth, Adam Smith, Nathan Srebro, Om Thakkar, Blake Woodworth

We design a general framework for answering adaptive statistical queries that focuses on providing explicit confidence intervals along with point estimates.

1 code implementation • 13 Jun 2019 • Blake Woodworth, Suriya Gunasekar, Pedro Savarese, Edward Moroshko, Itay Golan, Jason Lee, Daniel Soudry, Nathan Srebro

A recent line of work studies overparametrized neural networks in the "kernel regime," i. e. when the network behaves during training as a kernelized linear predictor, and thus training with gradient descent has the effect of finding the minimum RKHS norm solution.

no code implementations • 13 Feb 2019 • Dylan J. Foster, Ayush Sekhari, Ohad Shamir, Nathan Srebro, Karthik Sridharan, Blake Woodworth

Notably, we show that in the global oracle/statistical learning model, only logarithmic dependence on smoothness is required to find a near-stationary point, whereas polynomial dependence on smoothness is necessary in the local stochastic oracle model.

1 code implementation • 29 Jun 2018 • Andrew Cotter, Maya Gupta, Heinrich Jiang, Nathan Srebro, Karthik Sridharan, Serena Wang, Blake Woodworth, Seungil You

Classifiers can be trained with data-dependent constraints to satisfy fairness goals, reduce churn, achieve a targeted false positive rate, or other policy goals.

no code implementations • NeurIPS 2018 • Blake Woodworth, Jialei Wang, Adam Smith, Brendan Mcmahan, Nathan Srebro

We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph.

no code implementations • NeurIPS 2018 • Blake Woodworth, Vitaly Feldman, Saharon Rosset, Nathan Srebro

The problem of handling adaptivity in data analysis, intentional or not, permeates a variety of fields, including test-set overfitting in ML challenges and the accumulation of invalid scientific discoveries.

no code implementations • NeurIPS 2017 • Suriya Gunasekar, Blake Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, Nathan Srebro

We study implicit regularization when optimizing an underdetermined quadratic objective over a matrix $X$ with gradient descent on a factorization of $X$.

no code implementations • 20 Feb 2017 • Blake Woodworth, Suriya Gunasekar, Mesrob I. Ohannessian, Nathan Srebro

We consider learning a predictor which is non-discriminatory with respect to a "protected attribute" according to the notion of "equalized odds" proposed by Hardt et al. [2016].

no code implementations • NeurIPS 2016 • Blake Woodworth, Nathan Srebro

We provide tight upper and lower bounds on the complexity of minimizing the average of $m$ convex functions using gradient and prox oracles of the component functions.

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