We develop new accelerated first-order algorithms in the Frank-Wolfe (FW) family for minimizing smooth convex functions over compact convex sets, with a focus on two prominent constraint classes: (1) polytopes and (2) matrix domains given by the spectrahedron and the unit nuclear-norm ball. A key technical ingredient is a complementarity condition that captures solution sparsity -- face dimension for polytopes and rank for matrices. We present two algorithms: (1) a purely linear optimization oracle (LOO) method for polytopes that has optimal worst-case first-order (FO) oracle complexity and, aside of a finite \emph{burn-in} phase and up to a logarithmic factor, has LOO complexity that scales with $r/\sqrtε$, where $ε$ is the target accuracy and $r$ is the solution sparsity $r$ (independently of the ambient dimension), and (2) a hybrid scheme that combines FW with a sparse projection oracle (e.g., low-rank SVDs for matrix domains with low-rank solutions), which also has optimal FO oracle complexity, and after a finite burn-in phase, only requires $O(1/\sqrtε)$ sparse projections and LOO calls (independently of both the ambient dimension and the rank of optimal solutions). Our results close a gap on how to accelerate recent advancements in linearly-converging FW algorithms for strongly convex optimization, without paying the price of the dimension.

Classical probabilistic graphical models face fundamental challenges in modern data environments, which are characterized by high dimensionality, source heterogeneity, and stringent data-sharing constraints. In this work, we revisit the Ising model, a well-established member of the Markov Random Field (MRF) family, and develop a distributed framework that enables scalable and privacy-preserving representation learning from large-scale binary data with inherent low-rank structure. Our approach optimizes a non-convex surrogate loss function via bi-factored gradient descent, offering substantial computational and communication advantages over conventional convex approaches. We evaluate our algorithm on multi-institutional electronic health record (EHR) datasets from 58,248 patients across the University of Pittsburgh Medical Center (UPMC) and Mass General Brigham (MGB), demonstrating superior performance in global representation learning and downstream clinical tasks, including relationship detection, patient phenotyping, and patient clustering. These results highlight a broader potential for statistical inference in federated, high-dimensional settings while addressing the practical challenges of data complexity and multi-institutional integration.

Mixed-Integer Linear Programming (MILP) is a fundamental and powerful framework for modeling complex optimization problems across diverse domains. Recently, learning-based methods have shown great promise in accelerating MILP solvers by predicting high-quality solutions. However, most existing approaches are developed and evaluated in single-domain settings, limiting their ability to generalize to unseen problem distributions. This limitation poses a major obstacle to building scalable and general-purpose learning-based solvers. To address this challenge, we introduce RoME, a domain-Robust Mixture-of-Experts framework for predicting MILP solutions across domains. RoME dynamically routes problem instances to specialized experts based on learned task embeddings. The model is trained using a two-level distributionally robust optimization strategy: inter-domain to mitigate global shifts across domains, and intra-domain to enhance local robustness by introducing perturbations on task embeddings. We reveal that cross-domain training not only enhances the model's generalization capability to unseen domains but also improves performance within each individual domain by encouraging the model to capture more general intrinsic combinatorial patterns. Specifically, a single RoME model trained on three domains achieves an average improvement of 67.7% then evaluated on five diverse domains. We further test the pretrained model on MIPLIB in a zero-shot setting, demonstrating its ability to deliver measurable performance gains on challenging real-world instances where existing learning-based approaches often struggle to generalize.

This work studies the non-monotone DR-submodular Maximization over a ground set of $n$ subject to a size constraint $k$. We propose two approximation algorithms for solving this problem named FastDrSub and FastDrSub++. FastDrSub offers an approximation ratio of $0.044$ with query complexity of $O(n \log(k))$. The second one, FastDrSub++, improves upon it with a ratio of $1/4-ε$ within query complexity of $(n \log k)$ for an input parameter $ε>0$. Therefore, our proposed algorithms are the first constant-ratio approximation algorithms for the problem with the low complexity of $O(n \log(k))$. Additionally, both algorithms are experimentally evaluated and compared against existing state-of-the-art methods, demonstrating their effectiveness in solving the Revenue Maximization problem with DR-submodular objective function. The experimental results show that our proposed algorithms significantly outperform existing approaches in terms of both query complexity and solution quality.

Collaborating teams of robots show promise due in their ability to complete missions more efficiently and with improved robustness, attributes that are particularly useful for systems operating in marine environments. A key issue is how to model, analyze, and design these multi-robot systems to realize the full benefits of collaboration, a challenging task since the domain of multi-robot autonomy encompasses both collective and individual behaviors. This paper introduces a layered model of multi-robot autonomy that uses the principle of census, or a weighted count of the inputs from neighbors, for collective decision-making about teaming, coupled with multi-objective behavior optimization for individual decision-making about actions. The census component is expressed as a nonlinear opinion dynamics model and the multi-objective behavior optimization is accomplished using interval programming. This model can be reduced to recover foundational algorithms in distributed optimization and control, while the full model enables new types of collective behaviors that are useful in real-world scenarios. To illustrate these points, a new method for distributed optimization of subgroup allocation is introduced where robots use a gradient descent algorithm to minimize portions of the cost functions that are locally known, while being influenced by the opinion states from neighbors to account for the unobserved costs. With this method the group can collectively use the information contained in the Hessian matrix of the total global cost. The utility of this model is experimentally validated in three categorically different experiments with fleets of autonomous surface vehicles: an adaptive sampling scenario, a high value unit protection scenario, and a competitive game of capture the flag.

The paper is about developing a solver for maximizing a real-valued function of binary variables. The solver relies on an algorithm that estimates the optimal objective-function value of instances from the underlying distribution of objectives and their respective sub-instances. The training of the estimator is based on an inequality that facilitates the use of the expected total deviation from optimality conditions as a loss function rather than the objective-function itself. Thus, it does not calculate values of policies, nor does it rely on solved instances.

Nanopore sequencing enables real-time long-read DNA sequencing with reads exceeding 10 kilobases, but inherent error rates of 12-15 percent present significant computational challenges for read alignment. The critical seed chaining step must connect exact k-mer matches between reads and reference genomes while filtering spurious matches, yet state-of-the-art methods rely on fixed gap penalty functions unable to adapt to varying genomic contexts including tandem repeats and structural variants. This paper presents RawHash3, a hybrid framework combining graph neural networks with classical dynamic programming for adaptive seed chaining that maintains real-time performance while providing statistical guarantees. We formalize seed chaining as graph learning where seeds constitute nodes with 12-dimensional feature vectors and edges encode 8-dimensional spatial relationships including gap consistency. Our architecture employs three-layer EdgeConv GNN with confidence-based method selection that dynamically switches between learned guidance and algorithmic fallback. Comprehensive evaluation on 1,000 synthetic nanopore reads with 5,200 test seeds demonstrates RawHash3 achieves 99.94 percent precision and 40.07 percent recall, representing statistically significant 25.0 percent relative improvement over baseline with p less than 0.001. The system maintains median inference latency of 1.59ms meeting real-time constraints, while demonstrating superior robustness with 100 percent success rate under 20 percent label corruption versus baseline degradation to 30.3 percent. Cross-validation confirms stability establishing graph neural networks as viable approach for production genomics pipelines.

Parkinson's disease assessment has garnered growing interest in recent years, particularly with the advent of sensor data and machine learning techniques. Among these, multimodal approaches have demonstrated strong performance by effectively integrating complementary information from various data sources. However, two major limitations hinder their practical application: (1) the need to synchronize all modalities during training, and (2) the dependence on all modalities during inference. To address these issues, we propose the first Parkinson's assessment system that formulates multimodal learning as a multi-objective optimization (MOO) problem. This not only allows for more flexible modality requirements during both training and inference, but also handles modality collapse issue during multimodal information fusion. In addition, to mitigate the imbalance within individual modalities, we introduce a margin-based class rebalancing strategy to enhance category learning. We conduct extensive experiments on three public datasets under both synchronous and asynchronous settings. The results show that our framework-Towards Relaxed InPuts (TRIP)-achieves state-of-the-art performance, outperforming the best baselines by 16.48, 6.89, and 11.55 percentage points in the asynchronous setting, and by 4.86 and 2.30 percentage points in the synchronous setting, highlighting its effectiveness and adaptability.

Submodular functions, defined on continuous or discrete domains, arise in numerous applications. We study the minimization of the difference of two submodular (DS) functions, over both domains, extending prior work restricted to set functions. We show that all functions on discrete domains and all smooth functions on continuous domains are DS. For discrete domains, we observe that DS minimization is equivalent to minimizing the difference of two convex (DC) functions, as in the set function case. We propose a novel variant of the DC Algorithm (DCA) and apply it to the resulting DC Program, obtaining comparable theoretical guarantees as in the set function case. The algorithm can be applied to continuous domains via discretization. Experiments demonstrate that our method outperforms baselines in integer compressive sensing and integer least squares.

Zeroth-order or derivative-free optimization (MeZO) is an attractive strategy for finetuning large language models (LLMs) because it eliminates the memory overhead of backpropagation. However, it converges slowly due to the inherent curse of dimensionality when searching for descent directions in the high-dimensional parameter space of billion-scale LLMs. We propose ConMeZO, a novel zeroth-order optimizer that accelerates convergence by adaptive directional sampling. Instead of drawing the direction uniformly at random, ConMeZO restricts the sampling to a cone centered around a momentum estimate. This concentrates the search in directions where the true gradient is more likely to lie and thus reduces the effect of high dimensions. We prove that ConMeZO achieves the same worst-case convergence rate as MeZO. Empirically, when finetuning LLMs on natural language tasks, ConMeZO is up to 2X faster than MeZO while retaining the low-memory footprint of zeroth-order methods.