Integer Linear Programs (ILPs) are central to real-world optimizations but notoriously difficult to solve. Learning to Optimize (L2O) has emerged as a promising paradigm, with Graph Neural Networks (GNNs) serving as the standard backbone. However, standard anonymous GNNs are limited in expressiveness for ILPs, and the common enhancement of augmenting nodes with globally unique identifiers (UIDs) typically introduces spurious correlations that severely harm generalization. To address this tradeoff, we propose a parsimonious Local-UID scheme based on d-hop uniqueness coloring, which ensures identifiers are unique only within each node's d-hop neighborhood. Building on this scheme, we introduce ColorGNN, which incorporates color information via color-conditioned embeddings, and ColorUID, a lightweight feature-level variant. We prove that for d-layer networks, Local-UIDs achieve the expressive power of Global-UIDs while offering stronger generalization. Extensive experiments show that our approach (i) yields substantial gains on three ILP benchmarks, (ii) exhibits strong OOD generalization on linear programming datasets, and (iii) further improves a general graph-level task when paired with a state-of-the-art method.

To address this issue, we propose using probabilistic reparameterization ( PR).

With the emergence of fluid antenna (FA) in wireless communications, the capability to dynamically adjust port positions offers substantial benefits in spatial diversity and spectrum efficiency, which are particularly valuable for mobile edge computing (MEC) systems. Therefore, we propose an FA-assisted MEC offloading framework to minimize system delay. This framework faces two severe challenges, which are the complexity of channel estimation due to dynamic port configuration and the inherent non-convexity of the joint optimization problem. Firstly, we propose Information Bottleneck Metric-enhanced Channel Compressed Sensing (IBM-CCS), which advances FA channel estimation by integrating information relevance into the sensing process and capturing key features of FA channels effectively. Secondly, to address the non-convex and high-dimensional optimization problem in FA-assisted MEC systems, which includes FA port selection, beamforming, power control, and resource allocation, we propose a game theory-assisted Hierarchical Twin-Dueling Multi-agent Algorithm (HiTDMA) based offloading scheme, where the hierarchical structure effectively decouples and coordinates the optimization tasks between the user side and the base station side. Crucially, the game theory effectively reduces the dimensionality of power control variables, allowing deep reinforcement learning (DRL) agents to achieve improved optimization efficiency. Numerical results confirm that the proposed scheme significantly reduces system delay and enhances offloading performance, outperforming benchmarks. Additionally, the IBM-CCS channel estimation demonstrates superior accuracy and robustness under varying port densities, contributing to efficient communication under imperfect CSI.

We study pure exploration in structured stochastic multi-armed bandits, aiming to efficiently identify the correct hypothesis from a finite set of alternatives. For a broad class of tasks, asymptotic analyses reduce to a maximin optimization that admits a two-player zero-sum game interpretation between an experimenter and a skeptic: the experimenter allocates measurements to rule out alternatives while the skeptic proposes alternatives. We reformulate the game by allowing the skeptic to adopt a mixed strategy, yielding a concave-convex saddle-point problem. This viewpoint leads to Frank-Wolfe Self-Play (FWSP): a projection-free, regularization-free, tuning-free method whose one-hot updates on both sides match the bandit sampling paradigm. However, structural constraints introduce sharp pathologies that complicate algorithm design and analysis: our linear-bandit case study exhibits nonunique optima, optimal designs with zero mass on the best arm, bilinear objectives, and nonsmoothness at the boundary. We address these challenges via a differential-inclusion argument, proving convergence of the game value for best-arm identification in linear bandits. Our analysis proceeds through a continuous-time limit: a differential inclusion with a Lyapunov function that decays exponentially, implying a vanishing duality gap and convergence to the optimal value. Although Lyapunov analysis requires differentiability of the objective, which is not guaranteed on the boundary, we show that along continuous trajectories the algorithm steers away from pathological nonsmooth points and achieves uniform global convergence to the optimal game value. We then embed the discrete-time updates into a perturbed flow and show that the discrete game value also converges. Building on FWSP, we further propose a learning algorithm based on posterior sampling. Numerical experiments demonstrate a vanishing duality gap.

Abstract-- This paper introduces a novel framework for continuous 3D trajectory optimization in cluttered environments, leveraging online neural Euclidean Signed Distance Fields (ESDFs). Unlike prior approaches that rely on discretized ESDF grids with interpolation, our method directly optimizes smooth trajectories represented by fifth-order polynomials over a continuous neural ESDF, ensuring precise gradient information throughout the entire trajectory. Experimental results demonstrate that C-3TO produces collision-aware and dynamically feasible trajectories. Moreover, its flexibility in defining local window sizes and optimization parameters enables straightforward adaptation to diverse user's needs without compromising performance. By combining continuous trajectory parameterization with a continuously updated neural ESDF, C-3TO establishes a robust and generalizable foundation for safe and efficient local replanning in aerial robotics. The source code is open source and can be found at: https://anonymous.4open.science/r/icra2026_ I. Introduction Aerial robots have become increasingly popular for a wide range of real-world applications due to their ability to perform hazardous tasks more efficiently and, most importantly, more safely than humans [1][2]. Fast trajectory replanning remains a critical area of research, particularly in dynamic and unstructured environments. Equally important is maintaining a continuously updated representation of the drone's surroundings, which is essential for generating continuous, safe, and smooth 3D local trajectories in real time. This paper presents a framework for planning a continuous local trajectory on an online, neurally-generated, distance field.

Combinatorial optimization problems are ubiquitous in science and engineering. Still, learning-based approaches to accelerate combinatorial optimization often require solving a large number of difficult instances to collect training data, incurring significant computational cost. Existing learning-based methods require training dedicated models for each problem distribution, for each downstream task, severely limiting their scalability and generalization. We introduce Forge: Foundational Optimization Representations from Graph Embeddings, a framework that pre-trains a vector-quantized graph autoencoder on a large, diverse collection of mixed-integer programming (MIP) instances in an unsupervised manner, without relying on optimization solvers or optimal solutions. Vector quantization produces discrete code assignments that serve as a vocabulary for representing optimization instances. We evaluate Forge in both unsupervised and supervised settings. In the unsupervised setting, Forge embeddings effectively cluster unseen instances across problem domains and sizes. In the supervised setting, we fine-tune Forge embeddings and show that a single pre-trained model helps predicting both the integrality gap for cut-generation and variable hints for search guidance across multiple problem and size distributions. In both tasks, we improve the performance of a commercial optimization solver and outperform state-of-the-art learning-based methods. Finally, we open-source our training code, pre-trained Forge weights, and embeddings for multiple MIP distributions to foster further research in representation learning for optimization problems.