82 research outputs found
Catalyst Acceleration for Gradient-Based Non-Convex Optimization
We introduce a generic scheme to solve nonconvex optimization problems using
gradient-based algorithms originally designed for minimizing convex functions.
Even though these methods may originally require convexity to operate, the
proposed approach allows one to use them on weakly convex objectives, which
covers a large class of non-convex functions typically appearing in machine
learning and signal processing. In general, the scheme is guaranteed to produce
a stationary point with a worst-case efficiency typical of first-order methods,
and when the objective turns out to be convex, it automatically accelerates in
the sense of Nesterov and achieves near-optimal convergence rate in function
values. These properties are achieved without assuming any knowledge about the
convexity of the objective, by automatically adapting to the unknown weak
convexity constant. We conclude the paper by showing promising experimental
results obtained by applying our approach to incremental algorithms such as
SVRG and SAGA for sparse matrix factorization and for learning neural networks
Catalyst Acceleration for First-order Convex Optimization: from Theory to Practice
We introduce a generic scheme for accelerating gradient-based optimization
methods in the sense of Nesterov. The approach, called Catalyst, builds upon
the inexact accelerated proximal point algorithm for minimizing a convex
objective function, and consists of approximately solving a sequence of
well-chosen auxiliary problems, leading to faster convergence. One of the keys
to achieve acceleration in theory and in practice is to solve these
sub-problems with appropriate accuracy by using the right stopping criterion
and the right warm-start strategy. We give practical guidelines to use Catalyst
and present a comprehensive analysis of its global complexity. We show that
Catalyst applies to a large class of algorithms, including gradient descent,
block coordinate descent, incremental algorithms such as SAG, SAGA, SDCA, SVRG,
MISO/Finito, and their proximal variants. For all of these methods, we
establish faster rates using the Catalyst acceleration, for strongly convex and
non-strongly convex objectives. We conclude with extensive experiments showing
that acceleration is useful in practice, especially for ill-conditioned
problems.Comment: link to publisher website:
http://jmlr.org/papers/volume18/17-748/17-748.pd
Federated Learning on Adaptively Weighted Nodes by Bilevel Optimization
We propose a federated learning method with weighted nodes in which the
weights can be modified to optimize the model's performance on a separate
validation set. The problem is formulated as a bilevel optimization where the
inner problem is a federated learning problem with weighted nodes and the outer
problem focuses on optimizing the weights based on the validation performance
of the model returned from the inner problem. A communication-efficient
federated optimization algorithm is designed to solve this bilevel optimization
problem. Under an error-bound assumption, we analyze the generalization
performance of the output model and identify scenarios when our method is in
theory superior to training a model only locally and to federated learning with
static and evenly distributed weights
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