75 research outputs found
Distributed Extra-gradient with Optimal Complexity and Communication Guarantees
We consider monotone variational inequality (VI) problems in multi-GPU
settings where multiple processors/workers/clients have access to local
stochastic dual vectors. This setting includes a broad range of important
problems from distributed convex minimization to min-max and games.
Extra-gradient, which is a de facto algorithm for monotone VI problems, has not
been designed to be communication-efficient. To this end, we propose a
quantized generalized extra-gradient (Q-GenX), which is an unbiased and
adaptive compression method tailored to solve VIs. We provide an adaptive
step-size rule, which adapts to the respective noise profiles at hand and
achieve a fast rate of under relative noise, and an
order-optimal under absolute noise and show
distributed training accelerates convergence. Finally, we validate our
theoretical results by providing real-world experiments and training generative
adversarial networks on multiple GPUs.Comment: International Conference on Learning Representations (ICLR 2023
SARAH-based Variance-reduced Algorithm for Stochastic Finite-sum Cocoercive Variational Inequalities
Variational inequalities are a broad formalism that encompasses a vast number
of applications. Motivated by applications in machine learning and beyond,
stochastic methods are of great importance. In this paper we consider the
problem of stochastic finite-sum cocoercive variational inequalities. For this
class of problems, we investigate the convergence of the method based on the
SARAH variance reduction technique. We show that for strongly monotone problems
it is possible to achieve linear convergence to a solution using this method.
Experiments confirm the importance and practical applicability of our approach.Comment: 11 pages, 1 algorithm, 1 figure, 1 theore
An Accelerated Variance Reduced Extra-Point Approach to Finite-Sum VI and Optimization
In this paper, we develop stochastic variance reduced algorithms for solving
a class of finite-sum monotone VI, where the operator consists of the sum of
finitely many monotone VI mappings and the sum of finitely many monotone
gradient mappings. We study the gradient complexities of the proposed
algorithms under the settings when the sum of VI mappings is either strongly
monotone or merely monotone. Furthermore, we consider the case when each of the
VI mapping and gradient mapping is only accessible via noisy stochastic
estimators and establish the sample gradient complexity. We demonstrate the
application of the proposed algorithms for solving finite-sum convex
optimization with finite-sum inequality constraints and develop a zeroth-order
approach when only noisy and biased samples of objective/constraint function
values are available.Comment: 45 pages, 4 figure
A Unified View of Large-scale Zero-sum Equilibrium Computation
The task of computing approximate Nash equilibria in large zero-sum
extensive-form games has received a tremendous amount of attention due mainly
to the Annual Computer Poker Competition. Immediately after its inception, two
competing and seemingly different approaches emerged---one an application of
no-regret online learning, the other a sophisticated gradient method applied to
a convex-concave saddle-point formulation. Since then, both approaches have
grown in relative isolation with advancements on one side not effecting the
other. In this paper, we rectify this by dissecting and, in a sense, unify the
two views.Comment: AAAI Workshop on Computer Poker and Imperfect Informatio
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