In this work, we provide a new convergence theory for plug-and-play proximal gradient descent (PnP-PGD) under prior mismatch where the denoiser is trained on a different data distribution to the inference task at hand. To the best of our knowledge, this is the first convergence proof of PnP-PGD under prior mismatch. Compared with the existing theoretical results for PnP algorithms, our new results removed the need for several restrictive and unverifiable assumptions. Moreover, we derive the convergence theory for equivariant PnP (EPnP) under the prior mismatch setting, proving that EPnP reduces error variance and explicitly tightens the convergence bound.
The Plug-and-Play (PnP) framework makes it possible to integrate advanced image denoising priors into optimization algorithms, to efficiently solve a variety of image restoration tasks generally formulated as Maximum A Posteriori (MAP) estimation problems. The Plug-and-Play alternating direction method of multipliers (ADMM) and the Regularization by Denoising (RED) algorithms are two examples of such methods that made a breakthrough in image restoration. However, while the former method only applies to proximal algorithms, it has recently been shown that there exists no regularization that exp…
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Research Institute of Big Data（深圳大数据研究院）
In this work, we provide a fundamental unified convergence theorem used for deriving expected and almost sure convergence results for a series of stochastic optimization methods. Our unified theorem only requires to verify several representative conditions and is not tailored to any specific algorithm. As a direct application, we recover expected and almost sure convergence results of the stochastic gradient method (SGD) and random reshuffling (RR) under more general settings. Moreover, we establish new expected and almost sure convergence results for the stochastic proximal gradient method (p…
Instituto de Sistemas e Robótica, Instituto Superior Técnico（系统与机器人研究所，高等技术学院）；Carnegie Mellon University（卡内基梅隆大学）
First-order methods for stochastic optimization have undeniable relevance, in part due to their pivotal role in machine learning. Variance reduction for these algorithms has become an important research topic. In contrast to common approaches, which rarely leverage global models of the objective function, we exploit convexity and L-smoothness to improve the noisy estimates outputted by the stochastic gradient oracle. Our method, named COCO denoiser, is the joint maximum likelihood estimator of multiple function gradients from their noisy observations, subject to co-coercivity constraints betwe…
Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Models
Department of Electrical & Systems Engineering, Washington University in St. Louis, USA（华盛顿大学圣路易斯分校电气与系统工程系）；Computer Science Department, ENS, PSL University, 75005, France（巴黎高等师范学院计算机科学系）；MAP5, CNRS, Université Paris Cité, 75006, France（巴黎城市大学MAP5研究所）；Department of Computer Science & Engineering, Washington University in St. Louis, USA（华盛顿大学圣路易斯分校计算机科学与工程系）
New York University（纽约大学）；Washington University in St. Louis（圣路易斯华盛顿大学）；Tandon School of Engineering（坦登工程学院）；Department of Electrical and Computer Engineering（电子与计算机工程系）；Department of Computer Science and Engineering（计算机科学与工程系）；Department of Electrical and Systems Engineering（电气与系统工程系）
The past few years have seen a surge of activity around integration of deep learning networks and optimization algorithms for solving inverse problems. Recent work on plug-and-play priors (PnP), regularization by denoising (RED), and deep unfolding has shown the state-of-the-art performance of such integration in a variety of applications. However, the current paradigm for designing such algorithms is inherently Euclidean, due to the usage of the quadratic norm within the projection and proximal operators. We propose to broaden this perspective by considering a non-Euclidean setting based on t…
Path-Space Mirror Descent for On-Policy Reinforcement Learning under the Generalized Schrödinger Bridge
School of Data Science, Fudan University（复旦大学数据科学学院）；Laboratory for Big Data and Decision, National University of Defense Technology（国防科技大学大数据与决策实验室）；ShanghaiTech University（上海科技大学）；College of Computer Science and Artificial Intelligence, Fudan University（复旦大学计算机科学与人工智能学院）；Shanghai Innovation Institute（上海创新研究院）
This paper presents a novel method for restoring digital videos via a Deep Plug-and-Play (PnP) approach. Under a Bayesian formalism, the method consists in using a deep convolutional denoising network in place of the proximal operator of the prior in an alternating optimization scheme. We distinguish ourselves from prior PnP work by directly applying that method to restore a digital video from a degraded video observation. This way, a network trained once for denoising can be repurposed for other video restoration tasks. Our experiments in video deblurring, super-resolution, and interpolation …
Deep learning methods for inverse problems using connections between proximal operators and Hamilton-Jacobi equations
Industrial and Systems Engineering, Lehigh University（工业与系统工程，莱维大学）；Department of Mathematics, University of Illinois Urbana-Champaign（数学系，伊利诺伊大学厄巴纳-香槟分校）
Tsinghua University（清华大学）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
Neural network quantum states (NQS), incorporating with variational Monte Carlo (VMC) method, are shown to be a promising way to investigate quantum many-body physics. Whereas vanilla VMC methods perform one gradient update per sample, we introduce a novel objective function with proximal optimization (PO) that enables multiple updates via reusing the mismatched samples. Our VMC-PO method keeps the advantage of the previous importance sampling gradient optimization algorithm [L. Yang, {\it et al}, Phys. Rev. Research {\bf 2}, 012039(R)(2020)] that efficiently uses sampled states. PO mitigates …
There is a growing interest in deep model-based architectures (DMBAs) for solving imaging inverse problems by combining physical measurement models and learned image priors specified using convolutional neural nets (CNNs). For example, well-known frameworks for systematically designing DMBAs include plug-and-play priors (PnP), deep unfolding (DU), and deep equilibrium models (DEQ). While the empirical performance and theoretical properties of DMBAs have been widely investigated, the existing work in the area has primarily focused on their performance when the desired image prior is known exact…
A Plug-and-Play Fully On-the-Job Real-Time Reinforcement Learning Algorithm for a Direct-Drive Tandem-Wing Experiment Platforms Under Multiple Random Operating Conditions
