A Learned Proximal Alternating Minimization Algorithm and Its Induced Network for a Class of Two-block Nonconvex and Nonsmooth Optimization
- URL: http://arxiv.org/abs/2411.06333v1
- Date: Sun, 10 Nov 2024 02:02:32 GMT
- Title: A Learned Proximal Alternating Minimization Algorithm and Its Induced Network for a Class of Two-block Nonconvex and Nonsmooth Optimization
- Authors: Yunmei Chen, Lezhi Liu, Lei Zhang,
- Abstract summary: This work proposes a general learned alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth problems.
The proposed LPAM-net is parameter-efficient and has favourable performance in comparison with some state-of-the-art methods.
- Score: 4.975853671529418
- License:
- Abstract: This work proposes a general learned proximal alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth and nonconvex optimization problems. We tackle the nonsmoothness by an appropriate smoothing technique with automatic diminishing smoothing effect. For smoothed nonconvex problems we modify the proximal alternating linearized minimization (PALM) scheme by incorporating the residual learning architecture, which has proven to be highly effective in deep network training, and employing the block coordinate decent (BCD) iterates as a safeguard for the convergence of the algorithm. We prove that there is a subsequence of the iterates generated by LPAM, which has at least one accumulation point and each accumulation point is a Clarke stationary point. Our method is widely applicable as one can employ various learning problems formulated as two-block optimizations, and is also easy to be extended for solving multi-block nonsmooth and nonconvex optimization problems. The network, whose architecture follows the LPAM exactly, namely LPAM-net, inherits the convergence properties of the algorithm to make the network interpretable. As an example application of LPAM-net, we present the numerical and theoretical results on the application of LPAM-net for joint multi-modal MRI reconstruction with significantly under-sampled k-space data. The experimental results indicate the proposed LPAM-net is parameter-efficient and has favourable performance in comparison with some state-of-the-art methods.
Related papers
- Alternating Minimization Schemes for Computing Rate-Distortion-Perception Functions with $f$-Divergence Perception Constraints [10.564071872770146]
We study the computation of the rate-distortion-perception function (RDPF) for discrete memoryless sources.
We characterize the optimal parametric solutions.
We provide sufficient conditions on the distortion and the perception constraints.
arXiv Detail & Related papers (2024-08-27T12:50:12Z) - Federated Conditional Stochastic Optimization [110.513884892319]
Conditional optimization has found in a wide range of machine learning tasks, such as in-variant learning tasks, AUPRC, andAML.
This paper proposes algorithms for distributed federated learning.
arXiv Detail & Related papers (2023-10-04T01:47:37Z) - An inexact LPA for DC composite optimization and application to matrix completions with outliers [5.746154410100363]
This paper concerns a class of composite optimization problems.
By leveraging the composite structure, we provide a condition for the potential function to have the KL property of $1/2$ at the iterate sequence.
arXiv Detail & Related papers (2023-03-29T16:15:34Z) - Composite Optimization Algorithms for Sigmoid Networks [3.160070867400839]
We propose the composite optimization algorithms based on the linearized proximal algorithms and the alternating direction of multipliers.
Numerical experiments on Frank's function fitting show that the proposed algorithms perform satisfactorily robustly.
arXiv Detail & Related papers (2023-03-01T15:30:29Z) - Adaptive Federated Minimax Optimization with Lower Complexities [82.51223883622552]
We propose an efficient adaptive minimax optimization algorithm (i.e., AdaFGDA) to solve these minimax problems.
It builds our momentum-based reduced and localSGD techniques, and it flexibly incorporate various adaptive learning rates.
arXiv Detail & Related papers (2022-11-14T12:32:18Z) - Optimizing Objective Functions from Trained ReLU Neural Networks via
Sampling [0.0]
This paper introduces scalable, sampling-based algorithms that optimize trained neural networks with ReLU activations.
We first propose an iterative algorithm that takes advantage of the piecewise linear structure of ReLU neural networks.
We then extend this approach by searching around the neighborhood of the LP solution computed at each iteration.
arXiv Detail & Related papers (2022-05-27T18:35:48Z) - Large-scale Optimization of Partial AUC in a Range of False Positive
Rates [51.12047280149546]
The area under the ROC curve (AUC) is one of the most widely used performance measures for classification models in machine learning.
We develop an efficient approximated gradient descent method based on recent practical envelope smoothing technique.
Our proposed algorithm can also be used to minimize the sum of some ranked range loss, which also lacks efficient solvers.
arXiv Detail & Related papers (2022-03-03T03:46:18Z) - Robust Multi-view Registration of Point Sets with Laplacian Mixture
Model [25.865100974015412]
We propose a novel probabilistic generative method to align multiple point sets based on the heavy-tailed Laplacian distribution.
We demonstrate the advantages of our method by comparing it with representative state-of-the-art approaches on benchmark challenging data sets.
arXiv Detail & Related papers (2021-10-26T14:49:09Z) - Lower Bounds and Optimal Algorithms for Smooth and Strongly Convex
Decentralized Optimization Over Time-Varying Networks [79.16773494166644]
We consider the task of minimizing the sum of smooth and strongly convex functions stored in a decentralized manner across the nodes of a communication network.
We design two optimal algorithms that attain these lower bounds.
We corroborate the theoretical efficiency of these algorithms by performing an experimental comparison with existing state-of-the-art methods.
arXiv Detail & Related papers (2021-06-08T15:54:44Z) - Adaptive Sampling for Best Policy Identification in Markov Decision
Processes [79.4957965474334]
We investigate the problem of best-policy identification in discounted Markov Decision (MDPs) when the learner has access to a generative model.
The advantages of state-of-the-art algorithms are discussed and illustrated.
arXiv Detail & Related papers (2020-09-28T15:22:24Z) - Iterative Algorithm Induced Deep-Unfolding Neural Networks: Precoding
Design for Multiuser MIMO Systems [59.804810122136345]
We propose a framework for deep-unfolding, where a general form of iterative algorithm induced deep-unfolding neural network (IAIDNN) is developed.
An efficient IAIDNN based on the structure of the classic weighted minimum mean-square error (WMMSE) iterative algorithm is developed.
We show that the proposed IAIDNN efficiently achieves the performance of the iterative WMMSE algorithm with reduced computational complexity.
arXiv Detail & Related papers (2020-06-15T02:57:57Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.