Adding entropic regularization to Optimal Transport (OT) problems has become a standard approach for designing efficient and scalable solvers. However, regularization introduces a bias from the true solution. To mitigate this bias while still benefiting from the acceleration provided by regularization, a natural solver would adaptively decrease the regularization as it approaches the solution. Although some algorithms heuristically implement this idea, their theoretical guarantees and the extent of their acceleration compared to using a fixed regularization remain largely open. In the setting of semi-discrete OT, where the source measure is continuous and the target is discrete, we prove that decreasing the regularization can indeed accelerate convergence. To this end, we introduce DRAG: Decreasing (entropic) Regularization Averaged Gradient, a stochastic gradient descent algorithm where the regularization decreases with the number of optimization steps. We provide a theoretical analysis showing that DRAG benefits from decreasing regularization compared to a fixed scheme, achieving an unbiased $\mathcal{O}(1/t)$ sample and iteration complexity for both the OT cost and the potential estimation, and a $\mathcal{O}(1/\sqrt{t})$ rate for the OT map. Our theoretical findings are supported by numerical experiments that validate the effectiveness of DRAG and highlight its practical advantages.

Federated Learning (FL) enables collaborative model training without data sharing, yet participants face a fundamental challenge, e.g., simultaneously ensuring fairness across demographic groups while protecting sensitive client data. We introduce a differentially private fair FL algorithm (\textit{FedPF}) that transforms this multi-objective optimization into a zero-sum game where fairness and privacy constraints compete against model utility. Our theoretical analysis reveals a surprising inverse relationship, i.e., stricter privacy protection fundamentally limits the system's ability to detect and correct demographic biases, creating an inherent tension between privacy and fairness. Counterintuitively, we prove that moderate fairness constraints initially improve model generalization before causing performance degradation, where a non-monotonic relationship that challenges conventional wisdom about fairness-utility tradeoffs. Experimental validation demonstrates up to 42.9 % discrimination reduction across three datasets while maintaining competitive accuracy, but more importantly, reveals that the privacy-fairness tension is unavoidable, i.e., achieving both objectives simultaneously requires carefully balanced compromises rather than optimization of either in isolation. The source code for our proposed algorithm is publicly accessible at https://github.com/szpsunkk/FedPF.

Dynamic offloading of Machine Learning (ML) model partitions across different resource orchestration services, such as Function-as-a-Service (FaaS) and Infrastructure-as-a-Service (IaaS), can balance processing and transmission delays while minimizing costs of adaptive inference applications. However, prior work often overlooks real-world factors, such as Virtual Machine (VM) cold starts, requests under long-tail service time distributions, etc. To tackle these limitations, we model each ML query (request) as traversing an acyclic sequence of stages, wherein each stage constitutes a contiguous block of sparse model parameters ending in an internal or final classifier where requests may exit. Since input-dependent exit rates vary, no single resource configuration suits all query distributions. IaaS-based VMs become underutilized when many requests exit early, yet rapidly scaling to handle request bursts reaching deep layers is impractical. SERFLOW addresses this challenge by leveraging FaaS-based serverless functions (containers) and using stage-specific resource provisioning that accounts for the fraction of requests exiting at each stage. By integrating this provisioning with adaptive load balancing across VMs and serverless functions based on request ingestion, SERFLOW reduces cloud costs by over $23\%$ while efficiently adapting to dynamic workloads.

Database Management Systems (DBMSs) are fundamental for managing large-scale and heterogeneous data, and their performance is critically influenced by configuration parameters. Effective tuning of these parameters is essential for adapting to diverse workloads and maximizing throughput while minimizing latency. Recent research has focused on automated configuration optimization using machine learning; however, existing approaches still exhibit several key limitations. Most tuning frameworks disregard the dependencies among parameters, assuming that each operates independently. This simplification prevents optimizers from leveraging relational effects across parameters, limiting their capacity to capture performancesensitive interactions. Moreover, to reduce the complexity of the high-dimensional search space, prior work often selects only the top few parameters for optimization, overlooking others that contribute meaningfully to performance. Bayesian Optimization (BO), the most common method for automatic tuning, is also constrained by its reliance on surrogate models, which can lead to unstable predictions and inefficient exploration. To overcome these limitations, we propose RelTune, a novel framework that represents parameter dependencies as a Relational Graph and learns GNN-based latent embeddings that encode performancerelevant semantics. RelTune further introduces Hybrid-Score-Guided Bayesian Optimization (HBO), which combines surrogate predictions with an Affinity Score measuring proximity to previously high-performing configurations. Experimental results on multiple DBMSs and workloads demonstrate that RelTune achieves faster convergence and higher optimization efficiency than conventional BO-based methods, achieving state-of-the-art performance across all evaluated scenarios.

Heterogeneous robot teams operating in realistic settings often must accomplish complex missions requiring collaboration and adaptation to information acquired online. Because robot teams frequently operate in unstructured environments -- uncertain, open-world settings without prior maps -- subtasks must be grounded in robot capabilities and the physical world. While heterogeneous teams have typically been designed for fixed specifications, generative intelligence opens the possibility of teams that can accomplish a wide range of missions described in natural language. However, current large language model (LLM)-enabled teaming methods typically assume well-structured and known environments, limiting deployment in unstructured environments. We present SPINE-HT, a framework that addresses these limitations by grounding the reasoning abilities of LLMs in the context of a heterogeneous robot team through a three-stage process. Given language specifications describing mission goals and team capabilities, an LLM generates grounded subtasks which are validated for feasibility. Subtasks are then assigned to robots based on capabilities such as traversability or perception and refined given feedback collected during online operation. In simulation experiments with closed-loop perception and control, our framework achieves nearly twice the success rate compared to prior LLM-enabled heterogeneous teaming approaches. In real-world experiments with a Clearpath Jackal, a Clearpath Husky, a Boston Dynamics Spot, and a high-altitude UAV, our method achieves an 87\% success rate in missions requiring reasoning about robot capabilities and refining subtasks with online feedback. More information is provided at https://zacravichandran.github.io/SPINE-HT.

This paper presents a physics-aware cyberphysical resilience framework for radial microgrids under coordinated cyberattacks. The proposed approach models the attacker through a hypergraph neural network (HGNN) enhanced with model agnostic metalearning (MAML) to rapidly adapt to evolving defense strategies and predict high-impact contingencies. The defender is modeled via a bi-level Stackelberg game, where the upper level selects optimal tie-line switching and distributed energy resource (DER) dispatch using an Alternating Direction Method of Multipliers (ADMM) coordinator embedded within the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The framework simultaneously optimizes load served, operational cost, and voltage stability, ensuring all post-defense states satisfy network physics constraints. The methodology is first validated on the IEEE 69-bus distribution test system with 12 DERs, 8 critical loads, and 5 tie-lines, and then extended to higher bus systems including the IEEE 123-bus feeder and a synthetic 300-bus distribution system. Results show that the proposed defense strategy restores nearly full service for 90% of top-ranked attacks, mitigates voltage violations, and identifies Feeder 2 as the principal vulnerability corridor. Actionable operating rules are derived, recommending pre-arming of specific tie-lines to enhance resilience, while higher bus system studies confirm scalability of the framework on the IEEE 123-bus and 300-bus systems.

This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that sequentially update a Gaussian process surrogate model of the objective to guide the acquisition of query points. To ensure that the surrogates are tailored to the network's geometry, we adopt Whittle-Matérn Gaussian process prior models defined via stochastic partial differential equations on metric graphs. In addition to establishing regret bounds for optimizing sufficiently smooth objective functions, we analyze the practical case in which the smoothness of the objective is unknown and the Whittle-Matérn prior is represented using finite elements. Numerical results demonstrate the effectiveness of our algorithms for optimizing benchmark objective functions on a synthetic metric graph and for Bayesian inversion via maximum a posteriori estimation on a telecommunication network.

Kernel methods represent a fundamental class of machine learning techniques and have gained widespread adoption across diverse domains [32], including computer vision [22, 13], natural language processing (NLP) [36, 4], and bioinformatics [29], among others. The core idea underlying kernel methods is to employ a kernel function that implicitly maps the input data into a high-dimensional feature space, thereby enabling the use of linear models to solve nonlinear learning tasks in the original space. Consequently, the selection of an appropriate kernel function is critical to the performance of the method. Traditional kernel methods predominantly rely on positive definite (PD) kernels, such as the polynomial kernel and the Gaussian kernel. According to Mercer's Theorem, a PD kernel ensures that the resulting kernel matrix is positive semidefinite (PSD), thereby facilitating the analysis of the learning problem within the framework of reproducing kernel Hilbert spaces (RKHS) [9]. The PSD property guarantees that the corresponding optimization problem is convex and thus tractable. These authors contributed equally to this work.

We propose a data-driven framework for efficiently solving quadratic programming (QP) problems by reducing the number of variables in high-dimensional QPs using instance-specific projection. A graph neural network-based model is designed to generate projections tailored to each QP instance, enabling us to produce high-quality solutions even for previously unseen problems. The model is trained on heterogeneous QPs to minimize the expected objective value evaluated on the projected solutions. This is formulated as a bilevel optimization problem; the inner optimization solves the QP under a given projection using a QP solver, while the outer optimization updates the model parameters. We develop an efficient algorithm to solve this bilevel optimization problem, which computes parameter gradients without backpropagating through the solver. We provide a theoretical analysis of the generalization ability of solving QPs with projection matrices generated by neural networks. Experimental results demonstrate that our method produces high-quality feasible solutions with reduced computation time, outperforming existing methods.

Stochastic state estimation methods for continuum robots (CRs) often struggle to balance accuracy and computational efficiency. While several recent works have explored sliding-window formulations for CRs, these methods are limited to simplified, discrete-time approximations and do not provide stochastic representations. In contrast, current stochastic filter methods must run at the speed of measurements, limiting their full potential. Recent works in continuous-time estimation techniques for CRs show a principled approach to addressing this runtime constraint, but are currently restricted to offline operation. In this work, we present a sliding-window filter (SWF) for continuous-time state estimation of CRs that improves upon the accuracy of a filter approach while enabling continuous-time methods to operate online, all while running at faster-than-real-time speeds. This represents the first stochastic SWF specifically designed for CRs, providing a promising direction for future research in this area.