# Task-Oriented Convex Bilevel Optimization with Latent Feasibility

arXiv: https://arxiv.org/abs/1907.03083 · HTML: https://mlsanity.com/paper/1907.03083/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2019.

## Built on by (most cited first, 6 of 6)

- [Target-aware Dual Adversarial Learning and a Multi-scenario Multi-Modality Benchmark to Fuse Infrared and Visible for Object Detection](https://mlsanity.com/paper/2203.16220/) (2022)
- [A Task-guided, Implicitly-searched and Meta-initialized Deep Model for Image Fusion](https://mlsanity.com/paper/2305.15862/) (2023)
- [HQG-Net: Unpaired Medical Image Enhancement with High-Quality Guidance](https://mlsanity.com/paper/2307.07829/) (2023)
- [From Text to Pixels: A Context-Aware Semantic Synergy Solution for Infrared and Visible Image Fusion](https://mlsanity.com/paper/2401.00421/) (2023)
- [Bilevel Layer-Positioning LoRA for Real Image Dehazing](https://mlsanity.com/paper/2603.10872/) (2026)
- [Towards Multimodal Metaphor Understanding: A Chinese Dataset and Model for Metaphor Mapping Identification](https://mlsanity.com/paper/2501.02434/) (2025)

## Abstract (arXiv)

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.