Related papers: An Introduction to Bi-level Optimization: Foundati…

Many mechanical engineering applications call for multiscale computational modeling and simulation. However, solving for complex multiscale systems remains computationally onerous due to the high dimensionality of the solution space.…

Bayesian optimization (BO) is an efficient framework for optimization of black-box objectives when function evaluations are costly and gradient information is not easily accessible. BO has been successfully applied to automate the task of…

Machine learning (ML) methods offer a wide range of configurable hyperparameters that have a significant influence on their performance. While accuracy is a commonly used performance objective, in many settings, it is not sufficient.…

Large Language Models (LLMs) have shown remarkable capabilities, with optimizing their input prompts playing a pivotal role in maximizing their performance. However, while LLM prompts consist of both the task-agnostic system prompts and…

Stochastic Bilevel optimization usually involves minimizing an upper-level (UL) function that is dependent on the arg-min of a strongly-convex lower-level (LL) function. Several algorithms utilize Neumann series to approximate certain…

Stochastic bilevel optimization (SBO) is becoming increasingly essential in machine learning due to its versatility in handling nested structures. To address large-scale SBO, decentralized approaches have emerged as effective paradigms in…

In this paper we propose a bilevel optimization approach for the placement of space and time observations in variational data assimilation problems. Within the framework of supervised learning, we consider a bilevel problem where the…

Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL problem is, however, to be an impediment to developing bilevel…

Bilevel optimization has found successful applications in various machine learning problems, including hyper-parameter optimization, data cleaning, and meta-learning. However, its huge computational cost presents a significant challenge for…

It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…

In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the…

Evolutionary optimization algorithms, including particle swarm optimization (PSO), have been successfully applied in oil industry for production planning and control. Such optimization studies are quite challenging due to large number of…

With the development of large-scale models, traditional distributed bilevel optimization algorithms cannot be applied directly in low-resource clients. The key reason lies in the excessive computation involved in optimizing both the lower-…

Zeroth-order (ZO) optimization is a subset of gradient-free optimization that emerges in many signal processing and machine learning applications. It is used for solving optimization problems similarly to gradient-based methods. However, it…

In recent years, Bi-Level Optimization (BLO) techniques have received extensive attentions from both learning and vision communities. A variety of BLO models in complex and practical tasks are of non-convex follower structure in nature…

Some recent works in machine learning and computer vision involve the solution of a bi-level optimization problem. Here the solution of a parameterized lower-level problem binds variables that appear in the objective of an upper-level…

Most modern supervised statistical/machine learning (ML) methods are explicitly designed to solve prediction problems very well. Achieving this goal does not imply that these methods automatically deliver good estimators of causal…

Reinforcement Learning with Human Feedback (RLHF) is the key to the success of large language models (LLMs) in recent years. In this work, we first introduce the concepts of knowledge breadth and knowledge depth, which measure the…

Machine learning (ML) has been increasingly used to aid aerodynamic shape optimization (ASO), thanks to the availability of aerodynamic data and continued developments in deep learning. We review the applications of ML in ASO to date and…

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we…