Related papers: Online basis construction for goal-oriented adapti…
We introduce a hyperreduced reduced basis element method for model reduction of parameterized, component-based systems in continuum mechanics governed by nonlinear partial differential equations. In the offline phase, the method constructs,…
This paper presents and analyses a Constraint Energy Minimization Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving single-phase non-linear compressible flows in highly heterogeneous media. The construction of CEM-GMsFEM…
A critical challenge of federated learning is data heterogeneity and imbalance across clients, which leads to inconsistency between local networks and unstable convergence of global models. To alleviate the limitations, we propose a novel…
Imitation learning is a promising approach for enabling generalist capabilities in humanoid robots, but its scaling is fundamentally constrained by the scarcity of high-quality expert demonstrations. This limitation can be mitigated by…
This paper introduces a dual-based algorithm framework for solving the regularized online resource allocation problems, which have potentially non-concave cumulative rewards, hard resource constraints, and a non-separable regularizer. Under…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
Learning-augmented algorithms have received significant attention in recent years, particularly in the context of online optimization. Motivated by the high computational cost of generating predictions, a growing line of work studies the…
In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on…
We consider online optimization in the 1-lookahead setting, where the objective does not decompose additively over the rounds of the online game. The resulting formulation enables us to deal with non-stationary and/or long-term constraints…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
We formulate and analyze a goal-oriented adaptive finite element method (GOAFEM) for a semilinear elliptic PDE and a linear goal functional. The strategy involves the finite element solution of a linearized dual problem, where the…
Online allocation is a broad class of problems where items arriving online have to be allocated to agents who have a fixed utility/cost for each assigned item so to maximize/minimize some objective. This framework captures a broad range of…
Training large language models with data collected from various domains can improve their performance on downstream tasks. However, given a fixed training budget, the sampling proportions of these different domains significantly impact the…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
In this paper we propose a general framework to characterize and solve the stochastic optimization problems with multiple objectives underlying many real world learning applications. We first propose a projection based algorithm which…
We introduce a framework for incremental-decremental maximization that captures the gradual transformation or renewal of infrastructures. In our model, an initial solution is transformed one element at a time and the utility of an…
In this paper, we study a certain class of online optimization problems, where the goal is to maximize a function that is not necessarily concave and satisfies the Diminishing Returns (DR) property under budget constraints. We analyze a…
Similarity/Distance measures play a key role in many machine learning, pattern recognition, and data mining algorithms, which leads to the emergence of metric learning field. Many metric learning algorithms learn a global distance function…
We consider sequential maximization of performance metrics that are general functions of a confusion matrix of a classifier (such as precision, F-measure, or G-mean). Such metrics are, in general, non-decomposable over individual instances,…
Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…