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Migration presents sweeping societal challenges that have recently attracted significant attention from the scientific community. One of the prominent approaches that have been suggested employs optimization and machine learning to match…
In the classical selection problem, the input consists of a collection of elements and the goal is to pick a subset of elements from the collection such that some objective function $f$ is maximized. This problem has been studied…
Scalable spatial GPs for massive datasets can be built via sparse Directed Acyclic Graphs (DAGs) where a small number of directed edges is sufficient to flexibly characterize spatial dependence. The DAG can be used to devise fast algorithms…
Large reasoning language models are typically run with fixed inference budgets, which can waste computation or terminate reasoning prematurely. We introduce Certainty-Guided Reasoning (CGR), a model-agnostic adaptive inference procedure…
We consider the problem of approximating a maximum weighted matching, when the edges of an underlying weighted graph $G(V,E)$ are revealed in a streaming fashion. We analyze a variant of the previously best-known…
This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
We present a performant gradient method for smooth convex optimization, drawing inspiration from several recent advances in the field. Our algorithm, the Adaptive Subgame Perfect Gradient Method (ASPGM) is based on the notion of subgame…
We study the classical problem of maximizing a monotone submodular function subject to a cardinality constraint k, with two additional twists: (i) elements arrive in a streaming fashion, and (ii) m items from the algorithm's memory are…
Continual Graph Learning (CGL) enables models to incrementally learn from streaming graph-structured data without forgetting previously acquired knowledge. Experience replay is a common solution that reuses a subset of past samples during…
As the scales of data sets expand rapidly in some application scenarios, increasing efforts have been made to develop fast submodular maximization algorithms. This paper presents a currently the most efficient algorithm for maximizing…
Safety of Large Language Models (LLMs) has become a critical issue given their rapid progresses. Greedy Coordinate Gradient (GCG) is shown to be effective in constructing adversarial prompts to break the aligned LLMs, but optimization of…
Simultaneous operation of all sensors in a large-scale sensor network is power-consuming and computationally expensive. Hence, it is desirable to select fewer sensors. A greedy algorithm is widely used for sensor selection in homogeneous…
Neural network optimization remains one of the most consequential yet poorly understood challenges in modern AI research, where improvements in training algorithms can lead to enhanced feature learning in foundation models,…
For the classical maximum coverage problem, the greedy algorithm achieves a worst-case $1-1/e$ approximation, which is optimal unless $\text{P} = \text{NP}$. The notion of coverage appears in a wide range of optimization tasks, where…
Multimodal learning considers learning from multi-modality data, aiming to fuse heterogeneous sources of information. However, it is not always feasible to leverage all available modalities due to memory constraints. Further, training on…
Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such…
This paper considers a discrete-time decision problem wherein a decision maker has to track, on average, a sequence of inputs selected from a convex set $\mathcal X \subset \mathbb{R}^d$ by choosing actions from a possibly non-convex…
Greedy-GQ is a value-based reinforcement learning (RL) algorithm for optimal control. Recently, the finite-time analysis of Greedy-GQ has been developed under linear function approximation and Markovian sampling, and the algorithm is shown…
Retrieval-augmented generation (RAG) is highly sensitive to the quality of selected context, yet standard top-k retrieval often returns redundant or near-duplicate chunks that waste token budget and degrade downstream generation. We present…
We propose a continuous-time scheme for large-scale optimization that introduces individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This approach automatically adjusts to local landscape…