Task-Oriented Convex Bilevel Optimization with Latent Feasibility

Liu，Risheng1; Ma，Long2; Yuan，Xiaoming3; Zeng，Shangzhi4; Zhang，Jin5

2022

10.1109/TIP.2022.3140607

IEEE TRANSACTIONS ON IMAGE PROCESSING   影响因子和分区

1057-7149

1941-0042

This paper firstly proposes a convex bilevel optimization paradigm to formulate and optimize popular learning and vision problems in real-world scenarios. Different from conventional approaches, which directly design their iteration schemes based on given problem formulation, we introduce a task-oriented energy as our latent constraint which integrates richer task information. By explicitly re- characterizing the feasibility, we establish an efficient and flexible algorithmic framework to tackle convex models with both shrunken solution space and powerful auxiliary (based on domain knowledge and data distribution of the task). In theory, we present the convergence analysis of our latent feasibility re- characterization based numerical strategy. We also analyze the stability of the theoretical convergence under computational error perturbation. Extensive numerical experiments are conducted to verify our theoretical findings and evaluate the practical performance of our method on different applications.

Convex optimization global convergence image processing latent constraint

SCI ; EI

英语

通讯

WOS:000744536300007

20220411525153

Computation theory ; Constrained optimization ; Convex optimization ; Domain Knowledge ; Functions ; Image processing ; Job analysis ; Numerical methods

Computer Theory, Includes Formal Logic, Automata Theory, Switching Theory, Programming Theory:721.1 ; Data Processing and Image Processing:723.2 ; Artificial Intelligence:723.4 ; Mathematics:921 ; Numerical Methods:921.6 ; Systems Science:961

ENGINEERING

2-s2.0-85123301107

Scopus

1.DUT-RU International School of Information Science and Engineering,Dalian University of Technology,Dalian,China
2.Peng Cheng Laboratory,Shenzhen,China
3.Department of Mathematics,The University of Hong Kong,Hong Kong
4.Department of Mathematics and Statistics,University of Victoria,Victoria,Canada
5.Department of Mathematics,National Center for Applied Mathematics Shenzhen,SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,China

Liu，Risheng,Ma，Long,Yuan，Xiaoming,et al. Task-Oriented Convex Bilevel Optimization with Latent Feasibility[J]. IEEE TRANSACTIONS ON IMAGE PROCESSING,2022,31:1190-1203.

Liu，Risheng,Ma，Long,Yuan，Xiaoming,Zeng，Shangzhi,&Zhang，Jin.(2022).Task-Oriented Convex Bilevel Optimization with Latent Feasibility.IEEE TRANSACTIONS ON IMAGE PROCESSING,31,1190-1203.

Liu，Risheng,et al."Task-Oriented Convex Bilevel Optimization with Latent Feasibility".IEEE TRANSACTIONS ON IMAGE PROCESSING 31(2022):1190-1203.