Do you want to publish a course? Click here

Solving Constrained CASH Problems with ADMM

212   0   0.0 ( 0 )
 Added by Parikshit Ram
 Publication date 2020
and research's language is English




Ask ChatGPT about the research

The CASH problem has been widely studied in the context of automated configurations of machine learning (ML) pipelines and various solvers and toolkits are available. However, CASH solvers do not directly handle black-box constraints such as fairness, robustness or other domain-specific custom constraints. We present our recent approach [Liu, et al., 2020] that leverages the ADMM optimization framework to decompose CASH into multiple small problems and demonstrate how ADMM facilitates incorporation of black-box constraints.

rate research

Read More

487 - Yu Sun , Zihui Wu , Xiaojian Xu 2020
Plug-and-play priors (PnP) is a broadly applicable methodology for solving inverse problems by exploiting statistical priors specified as denoisers. Recent work has reported the state-of-the-art performance of PnP algorithms using pre-trained deep neural nets as denoisers in a number of imaging applications. However, current PnP algorithms are impractical in large-scale settings due to their heavy computational and memory requirements. This work addresses this issue by proposing an incremental variant of the widely used PnP-ADMM algorithm, making it scalable to large-scale datasets. We theoretically analyze the convergence of the algorithm under a set of explicit assumptions, extending recent theoretical results in the area. Additionally, we show the effectiveness of our algorithm with nonsmooth data-fidelity terms and deep neural net priors, its fast convergence compared to existing PnP algorithms, and its scalability in terms of speed and memory.
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of combinatorial problems, which involve a number of constraints that is polynomial in the problem dimension. The most important feature of our framework is that only a subset of the constraints is processed at each iteration, thus gaining a computational advantage over prior works that require full passes. Our algorithms rely on variance reduction and smoothing used in conjunction with conditional gradient steps, and are accompanied by rigorous convergence guarantees. Preliminary numerical experiments are provided for illustrating the practical performance of the methods.
Many tasks in modern machine learning can be formulated as finding equilibria in emph{sequential} games. In particular, two-player zero-sum sequential games, also known as minimax optimization, have received growing interest. It is tempting to apply gradient descent to solve minimax optimization given its popularity and success in supervised learning. However, it has been noted that naive application of gradient descent fails to find some local minimax and can converge to non-local-minimax points. In this paper, we propose emph{Follow-the-Ridge} (FR), a novel algorithm that provably converges to and only converges to local minimax. We show theoretically that the algorithm addresses the notorious rotational behaviour of gradient dynamics, and is compatible with preconditioning and emph{positive} momentum. Empirically, FR solves toy minimax problems and improves the convergence of GAN training compared to the recent minimax optimization algorithms.
88 - Zhongjie Lu 2021
The main difficulty in solving the discrete constrained problem is its poor and even ill condition. In this paper, we transform the discrete constrained problems on de Rham complex to Laplace-like problems. This transformation not only make the constrained problems solvable, but also make it easy to use the existing iterative methods and preconditioning techniques to solving large-scale discrete constrained problems.
86 - Yan Yan , Yi Xu , Qihang Lin 2019
Previous studies on stochastic primal-dual algorithms for solving min-max problems with faster convergence heavily rely on the bilinear structure of the problem, which restricts their applicability to a narrowed range of problems. The main contribution of this paper is the design and analysis of new stochastic primal-dual algorithms that use a mixture of stochastic gradient updates and a logarithmic number of deterministic dual updates for solving a family of convex-concave problems with no bilinear structure assumed. Faster convergence rates than $O(1/sqrt{T})$ with $T$ being the number of stochastic gradient updates are established under some mild conditions of involved functions on the primal and the dual variable. For example, for a family of problems that enjoy a weak strong convexity in terms of the primal variable and has a strongly concave function of the dual variable, the convergence rate of the proposed algorithm is $O(1/T)$. We also investigate the effectiveness of the proposed algorithms for learning robust models and empirical AUC maximization.

suggested questions

comments
Fetching comments Fetching comments
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا