Optimization-Derived Learning with Essential Convergence Analysis of Training and Hyper-training

TL;DR

This paper introduces a unified optimization framework for training and hyper-training that guarantees convergence, improving efficiency and performance in applications like image deconvolution and rain streak removal.

Contribution

It proposes a Generalized Krasnoselskii-Mann scheme and a Bilevel Meta Optimization framework to jointly optimize training and hyper-training variables with convergence guarantees.

Findings

Demonstrates convergence of training and hyper-training variables.

Achieves competitive results in sparse coding tasks.

Shows effectiveness in real-world image processing applications.

Abstract

Recently, Optimization-Derived Learning (ODL) has attracted attention from learning and vision areas, which designs learning models from the perspective of optimization. However, previous ODL approaches regard the training and hyper-training procedures as two separated stages, meaning that the hyper-training variables have to be fixed during the training process, and thus it is also impossible to simultaneously obtain the convergence of training and hyper-training variables. In this work, we design a Generalized Krasnoselskii-Mann (GKM) scheme based on fixed-point iterations as our fundamental ODL module, which unifies existing ODL methods as special cases. Under the GKM scheme, a Bilevel Meta Optimization (BMO) algorithmic framework is constructed to solve the optimal training and hyper-training variables together. We rigorously prove the essential joint convergence of the fixed-point iteration for training and the process of optimizing hyper-parameters for hyper-training, both on the approximation quality, and on the stationary analysis. Experiments demonstrate the efficiency of BMO with competitive performance on sparse coding and real-world applications such as image deconvolution and rain streak removal.