Related papers: Towards Gradient-based Bilevel Optimization with N…

Learning parameters of latent graphical models (GM) is inherently much harder than that of no-latent ones since the latent variables make the corresponding log-likelihood non-concave. Nevertheless, expectation-maximization schemes are…

Bilevel optimization (BO) is useful for solving a variety of important machine learning problems including but not limited to hyperparameter optimization, meta-learning, continual learning, and reinforcement learning. Conventional BO…

The field of simulation optimization (SO) encompasses various methods developed to optimize complex, expensive-to-sample stochastic systems. Established methods include, but are not limited to, ranking-and-selection for finite alternatives…

Continual learning (CL) presents a fundamental challenge in training neural networks on sequential tasks without experiencing catastrophic forgetting. Traditionally, the dominant approach in CL has been gradient-based optimization, where…

The theory of greedy low-rank learning (GLRL) aims to explain the impressive generalization capabilities of deep learning. It proves that stochastic gradient-based training implicitly regularizes neural networks towards low-rank solutions…

Gradient Boosting Decision Trees (GBDTs) dominate tabular machine learning, with modern implementations like XGBoost, LightGBM, and CatBoost being based on Newton boosting: a second-order descent step in the space of decision trees. Despite…

In this paper, we study a class of bilevel optimization problems where the lower-level problem is a convex composite optimization model, which arises in various applications, including bilevel hyperparameter selection for regularized…

Meta-learning owns unique effectiveness and swiftness in tackling emerging tasks with limited data. Its broad applicability is revealed by viewing it as a bi-level optimization problem. The resultant algorithmic viewpoint however, faces…

Meta learning with multiple objectives can be formulated as a Multi-Objective Bi-Level optimization Problem (MOBLP) where the upper-level subproblem is to solve several possible conflicting targets for the meta learner. However, existing…

In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle…

LLMs have shown remarkable proficiency in general language understanding and reasoning. However, they consistently underperform in spatial reasoning that severely limits their application, particularly in embodied intelligence. Inspired by…

We identify and analyze a fundamental limitation of the classical projected subgradient method in nonsmooth convex optimization: the inevitable failure caused by the absence of valid subgradients at boundary points. We show that, under…

This paper focuses on the problem of minimizing a locally Lipschitz continuous function. Motivated by the effectiveness of Bregman gradient methods in training nonsmooth deep neural networks and the recent progress in stochastic subgradient…

In this paper, we study an algorithm for solving a class of nonconvex and nonsmooth nonseparable optimization problems. Based on proximal alternating linearized minimization (PALM), we propose a new iterative algorithm which combines…

This paper presents AGGLIO (Accelerated Graduated Generalized LInear-model Optimization), a stage-wise, graduated optimization technique that offers global convergence guarantees for non-convex optimization problems whose objectives offer…

Recent advances in computationally efficient non-myopic Bayesian optimization (BO) improve query efficiency over traditional myopic methods like expected improvement while only modestly increasing computational cost. These advances have…

Projected Gradient Descent (PGD) methods offer a simple and scalable approach to topology optimization (TO), yet they often struggle with nonlinear and multi-constraint problems due to the complexity of active-set detection. This paper…

Gradient-free prompt optimization methods have made significant strides in enhancing the performance of closed-source Large Language Models (LLMs) across a wide range of tasks. However, existing approaches make light of the importance of…

While first-order optimization methods such as stochastic gradient descent (SGD) are popular in machine learning (ML), they come with well-known deficiencies, including relatively-slow convergence, sensitivity to the settings of…

We present a framework for bi-level trajectory optimization in which a system's dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem are passed to an upper-level…