Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCommunication-Efficient Asynchronous Stochastic Frank-Wolfe over Nuclear-norm Balls
282
0
0.0
(
0
)
Added by
Jiacheng Zhuo
Publication date
2019
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Large-scale machine learning training suffers from two prior challenges, specifically for nuclear-norm constrained problems with distributed systems: the synchronization slowdown due to the straggling workers, and high communication costs. In this work, we propose an asynchronous Stochastic Frank Wolfe (SFW-asyn) method, which, for the first time, solves the two problems simultaneously, while successfully maintaining the same convergence rate as the vanilla SFW. We implement our algorithm in python (with MPI) to run on Amazon EC2, and demonstrate that SFW-asyn yields speed-ups almost linear to the number of machines compared to the vanilla SFW.
rate research
Read More
We propose a variant of the Frank-Wolfe algorithm for solving a class of sparse/low-rank optimization problems. Our formulation includes Elastic Net, regularized SVMs and phase retrieval as special cases. The proposed Primal-Dual Block Frank-Wolfe algorithm reduces the per-iteration cost while maintaining linear convergence rate. The per iteration cost of our method depends on the structural complexity of the solution (i.e. sparsity/low-rank) instead of the ambient dimension. We empirically show that our algorithm outperforms the state-of-the-art methods on (multi-class) classification tasks.
We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic subgradients with efficient incremental SVD updates, made possible by highly optimized and parallelizable dense linear algebra operations on small matrices. Our practical algorithms always maintain a low-rank factorization of iterates that can be conveniently held in memory and efficiently multiplied to generate predictions in matrix completion settings. Empirical comparisons confirm that our approach is highly competitive with several recently proposed state-of-the-art solvers for such problems.
Stochastic gradient methods (SGMs) are the predominant approaches to train deep learning models. The adapti
In this work, we propose an infinite restricted Boltzmann machine~(RBM), whose maximum likelihood estimation~(MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each iteration, so that the optimization process takes the form of a sequence of finite models of increasing complexity. As a side benefit, this can be used to easily and efficiently identify an appropriate number of hidden units during the optimization. The resulting model can also be used as an initialization for typical state-of-the-art RBM training algorithms such as contrastive divergence, leading to models with consistently higher test likelihood than random initialization.
We study asynchronous finite sum minimization in a distributed-data setting with a central parameter server. While asynchrony is well understood in parallel settings where the data is accessible by all machines -- e.g., modifications of variance-reduced gradient algorithms like SAGA work well -- little is known for the distributed-data setting. We develop an algorithm ADSAGA based on SAGA for the distributed-data setting, in which the data is partitioned between many machines. We show that with $m$ machines, under a natural stochastic delay model with an mean delay of $m$, ADSAGA converges in $tilde{O}left(left(n + sqrt{m}kapparight)log(1/epsilon)right)$ iterations, where $n$ is the number of component functions, and $kappa$ is a condition number. This complexity sits squarely between the complexity $tilde{O}left(left(n + kapparight)log(1/epsilon)right)$ of SAGA textit{without delays} and the complexity $tilde{O}left(left(n + mkapparight)log(1/epsilon)right)$ of parallel asynchronous algorithms where the delays are textit{arbitrary} (but bounded by $O(m)$), and the data is accessible by all. Existing asynchronous algorithms with distributed-data setting and arbitrary delays have only been shown to converge in $tilde{O}(n^2kappalog(1/epsilon))$ iterations. We empirically compare on least-squares problems the iteration complexity and wallclock performance of ADSAGA to existing parallel and distributed algorithms, including synchronous minibatch algorithms. Our results demonstrate the wallclock advantage of variance-reduced asynchronous approaches over SGD or synchronous approaches.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
