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.

Public resource allocation involves the efficient distribution of resources, including urban infrastructure, energy, and transportation, to effectively meet societal demands. However, existing methods focus on optimizing the movement of individual resources independently, without considering their capacity constraints. To address this limitation, we propose a novel and more practical problem: Collaborative Public Resource Allocation (CPRA), which explicitly incorporates capacity constraints and spatio-temporal dynamics in real-world scenarios. We propose a new framework called Game-Theoretic Spatio-Temporal Reinforcement Learning (GSTRL) for solving CPRA. Our contributions are twofold: 1) We formulate the CPRA problem as a potential game and demonstrate that there is no gap between the potential function and the optimal target, laying a solid theoretical foundation for approximating the Nash equilibrium of this NP-hard problem; and 2) Our designed GSTRL framework effectively captures the spatio-temporal dynamics of the overall system. We evaluate GSTRL on two real-world datasets, where experiments show its superior performance. Our source codes are available in the supplementary materials.

Differentiating through constrained optimization problems is increasingly central to learning, control, and large-scale decision-making systems, yet practical integration remains challenging due to solver specialization and interface mismatches. This paper presents a general and streamlined framework-an updated DiffOpt.jl-that unifies modeling and differentiation within the Julia optimization stack. The framework computes forward - and reverse-mode solution and objective sensitivities for smooth, potentially nonconvex programs by differentiating the KKT system under standard regularity assumptions. A first-class, JuMP-native parameter-centric API allows users to declare named parameters and obtain derivatives directly with respect to them - even when a parameter appears in multiple constraints and objectives - eliminating brittle bookkeeping from coefficient-level interfaces. We illustrate these capabilities on convex and nonconvex models, including economic dispatch, mean-variance portfolio selection with conic risk constraints, and nonlinear robot inverse kinematics. Two companion studies further demonstrate impact at scale: gradient-based iterative methods for strategic bidding in energy markets and Sobolev-style training of end-to-end optimization proxies using solver-accurate sensitivities. Together, these results demonstrate that differentiable optimization can be deployed as a routine tool for experimentation, learning, calibration, and design-without deviating from standard JuMP modeling practices and while retaining access to a broad ecosystem of solvers.

One of the main challenges in mechanistic interpretability is circuit discovery, determining which parts of a model perform a given task. We build on the Mechanistic Interpretability Benchmark (MIB) and propose three key improvements to circuit discovery. First, we use bootstrapping to identify edges with consistent attribution scores. Second, we introduce a simple ratio-based selection strategy to prioritize strong positive-scoring edges, balancing performance and faithfulness. Third, we replace the standard greedy selection with an integer linear programming formulation. Our methods yield more faithful circuits and outperform prior approaches across multiple MIB tasks and models. Our code is available at: https://github.com/technion-cs-nlp/MIB-Shared-Task.

We consider a stochastic multi-armed bandit problem with i.i.d. rewards where the expected reward function is multimodal with at most m modes. We propose the first known computationally tractable algorithm for computing the solution to the Graves-Lai optimization problem, which in turn enables the implementation of asymptotically optimal algorithms for this bandit problem. The code for the proposed algorithms is publicly available at https://github.com/wilrev/MultimodalBandits

Online bidding is a classic optimization problem, with several applications in online decision-making, the design of interruptible systems, and the analysis of approximation algorithms. In this work, we study online bidding under learning-augmented settings that incorporate stochasticity, in either the prediction oracle or the algorithm itself. In the first part, we study bidding under distributional predictions, and find Pareto-optimal algorithms that offer the best-possible tradeoff between the consistency and the robustness of the algorithm. In the second part, we study the power and limitations of randomized bidding algorithms, by presenting upper and lower bounds on the consistency/robustness tradeoffs. Previous works focused predominantly on oracles that do not leverage stochastic information on the quality of the prediction, and deterministic algorithms.

The rapid growth of e-commerce in recent years has significantly transformed people's shopping habits [1]. Consumers increasingly favor online shopping over in-person purchases, leading to a substantial impact on product logistics, which plays a crucial role in customer satisfaction. In addition to product quality and other factors, the timely delivery of orders has become a key determinant of customer satisfaction. Picking and replenishment tasks are responsible for 65% of operating costs [2]. In a conventional manual order picking system, often referred to as a picker-to-parts system, pickers dedicate 70% of their working time to searching for items and traveling within the facility [3, 4].