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Deep learning based approaches like Physics-informed neural networks (PINNs) and DeepONets have shown promise on solving PDE constrained optimization (PDECO) problems. However, existing methods are insufficient to handle those PDE…

Machine Learning · Computer Science 2023-04-12 Zhongkai Hao , Chengyang Ying , Hang Su , Jun Zhu , Jian Song , Ze Cheng

This paper studies a class of simple bilevel optimization problems where we minimize a composite convex function at the upper-level subject to a composite convex lower-level problem. Existing methods either provide asymptotic guarantees for…

Optimization and Control · Mathematics 2024-03-06 Jiulin Wang , Xu Shi , Rujun Jiang

Multi-objective learning under user-specified preference is common in real-world problems such as multi-lingual speech recognition under fairness. In this work, we frame such a problem as a semivectorial bilevel optimization problem, whose…

Optimization and Control · Mathematics 2025-04-07 Lisha Chen , Quan Xiao , Ellen Hidemi Fukuda , Xinyi Chen , Kun Yuan , Tianyi Chen

Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems consist of two nested sub-problems, called the outer and inner problems,…

Machine Learning · Computer Science 2022-12-29 Paul Vicol , Jonathan Lorraine , Fabian Pedregosa , David Duvenaud , Roger Grosse

This paper presents a new approach and algorithm for solving a class of constrained Bi-Level Optimization (BLO) problems in which the lower-level problem involves constraints coupling both upper-level and lower-level variables. Such…

Machine Learning · Computer Science 2024-01-30 Wei Yao , Chengming Yu , Shangzhi Zeng , Jin Zhang

We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by…

Machine Learning · Computer Science 2018-08-23 Atilim Gunes Baydin , Robert Cornish , David Martinez Rubio , Mark Schmidt , Frank Wood

Many strategic decision-making problems, such as environment design for warehouse robots, can be naturally formulated as bi-level reinforcement learning (RL), where a leader agent optimizes its objective while a follower solves a Markov…

Machine Learning · Computer Science 2026-04-01 Mikoto Kudo , Takumi Tanabe , Akifumi Wachi , Youhei Akimoto

Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…

Optimization and Control · Mathematics 2024-12-25 Quan Xiao , Tianyi Chen

This paper considers the simple bilevel optimization (SBO) problem, which minimizes a composite convex function over the optimal solution set of another composite convex minimization problem. We first show that this bilevel problem is…

Optimization and Control · Mathematics 2025-07-11 Rujun Jiang , Xu Shi , Weizheng Song , Jiulin Wang

In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve $m\gg 1$ lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its…

Optimization and Control · Mathematics 2023-06-05 Quanqi Hu , Zi-Hao Qiu , Zhishuai Guo , Lijun Zhang , Tianbao Yang

Bayesian meta-learning enables robust and fast adaptation to new tasks with uncertainty assessment. The key idea behind Bayesian meta-learning is empirical Bayes inference of hierarchical model. In this work, we extend this framework to…

Machine Learning · Computer Science 2020-11-19 Yayi Zou , Xiaoqi Lu

Due to the hierarchical structure of many machine learning problems, bilevel programming is becoming more and more important recently, however, the complicated correlation between the inner and outer problem makes it extremely challenging…

Machine Learning · Computer Science 2020-09-03 Junyi Li , Bin Gu , Heng Huang

Meta-learning is a promising method to achieve efficient training method towards deep neural net and has been attracting increases interests in recent years. But most of the current methods are still not capable to train complex neuron net…

Machine Learning · Computer Science 2018-09-10 Boyu Chen , Wenlian Lu , Ernest Fokoue

In traditional machine learning techniques, the degree of closeness between true and predicted values generally measures the quality of predictions. However, these learning algorithms do not consider prescription problems where the…

Machine Learning · Computer Science 2021-01-05 Mehmet Kolcu , Alper E. Murat

Bilevel optimization has been widely used in many machine learning applications such as hyperparameter optimization and meta learning. Recently, many simple stochastic gradient descent(SGD) type algorithms(without using momentum and…

Optimization and Control · Mathematics 2023-06-21 Haimei Huo , Risheng Liu , Zhixun Su

Motivated by high-dimensional nonlinear optimization problems as well as ill-posed optimization problems arising in image processing, we consider a bilevel optimization model where we seek among the optimal solutions of the inner level…

Optimization and Control · Mathematics 2018-09-27 Harshal Kaushik , Farzad Yousefian

We propose a decentralized penalty method for general convex constrained multi-agent optimization problems. Each auxiliary penalized problem is solved approximately with a special parallel descent splitting method. The method can be…

Optimization and Control · Mathematics 2020-08-11 Igor Konnov

We propose a federated learning method with weighted nodes in which the weights can be modified to optimize the model's performance on a separate validation set. The problem is formulated as a bilevel optimization where the inner problem is…

Machine Learning · Computer Science 2022-10-11 Yankun Huang , Qihang Lin , Nick Street , Stephen Baek

We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…

Computational Finance · Quantitative Finance 2022-05-23 William Lefebvre , Grégoire Loeper , Huyên Pham

We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE…

Mathematical Finance · Quantitative Finance 2026-04-07 Yunfei Peng , Pengyu Wei , Wei Wei