--In vertical federated learning (VFL), multiple enterprises address aligned sample scarcity by leveraging massive locally unaligned samples to facilitate collaborative learning. However, unaligned samples across different parties in VFL can be extremely class-imbalanced, leading to insufficient feature representation and limited model prediction space. Specifically, class-imbalanced problems consist of intra-party class imbalance and inter-party class imbalance, which can further cause local model bias and feature contribution inconsistency issues, respectively. T o address the above challenges, we propose Proto-EVFL, an enhanced VFL framework via dual prototypes. We first introduce class prototypes for each party to learn relationships between classes in the latent space, allowing the active party to predict unseen classes. We further design a probabilistic dual prototype learning scheme to dynamically select unaligned samples by conditional optimal transport cost with class prior probability. Moreover, a mixed prior guided module guides this selection process by combining local and global class prior probabilities. Finally, we adopt an adaptive gated feature aggregation strategy to mitigate feature contribution inconsistency by dynamically weighting and aggregating local features across different parties. We proved that Proto-EVFL, as the first bi-level optimization framework in VFL, has a convergence rate of 1 / T . Even in a zero-shot scenario with one unseen class, it outperforms baselines by at least 6.97%. NTRODUCTION indicates equal contribution, * represents the corresponding authors Wei Guo, Yiyang Duan and Fuzhen Zhuang are with the School of Artificial Intelligence, Beihang University, Beijing 100083, China (e-mail: { guowei, duanyiyang, zhuangfuzhen }@buaa.edu.cn). Xiao Zhang is with the School of Computer Science and Technology, Shan-dong University, Shandong 266237, China (e-mail: xiaozhang@sdu.edu.cn). Zhaojun Hu is with the Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, China (e-mail: huzhao-jun@ruc.edu.cn).

The Nearest-Better Network (NBN) is a powerful method to visualize sampled data for continuous optimization problems while preserving multiple landscape features. However, the calculation of NBN is very time-consuming, and the extension of the method to combinatorial optimization problems is challenging but very important for analyzing the algorithm's behavior. This paper provides a straightforward theoretical derivation showing that the NBN network essentially functions as the maximum probability transition network for algorithms. This paper also presents an efficient NBN computation method with logarithmic linear time complexity to address the time-consuming issue. By applying this efficient NBN algorithm to the OneMax problem and the Traveling Salesman Problem (TSP), we have made several remarkable discoveries for the first time: The fitness landscape of OneMax exhibits neutrality, ruggedness, and modality features. The primary challenges of TSP problems are ruggedness, modality, and deception. Two state-of-the-art TSP algorithms (i.e., EAX and LKH) have limitations when addressing challenges related to modality and deception, respectively. LKH, based on local search operators, fails when there are deceptive solutions near global optima. EAX, which is based on a single population, can efficiently maintain diversity. However, when multiple attraction basins exist, EAX retains individuals within multiple basins simultaneously, reducing inter-basin interaction efficiency and leading to algorithm's stagnation.

Finite element (FE) simulations of structures and materials are getting increasingly more accurate, but also more computationally expensive as a collateral result. This development happens in parallel with a growing demand of data-driven design. To reconcile the two, a robust and data-efficient optimization method called Bayesian optimization (BO) has been previously established as a technique to optimize expensive objective functions. In parallel, the mesh width of an FE model can be exploited to evaluate an objective at a lower or higher fidelity (cost & accuracy) level. The multi-fidelity setting applied to BO, called multi-fidelity BO (MFBO), has also seen previous success. However, BO and MFBO have not seen a direct comparison with when faced with with a real-life engineering problem, such as metamaterial design for deformation and absorption qualities. Moreover, sampling quality and assessing design parameter sensitivity is often an underrepresented part of data-driven design. This paper aims to address these shortcomings by employing Sobol' samples with variance-based sensitivity analysis in order to reduce design problem complexity. Furthermore, this work describes, implements, applies and compares the performance BO with that MFBO when maximizing the energy absorption (EA) problem of spinodoid cellular structures is concerned. The findings show that MFBO is an effective way to maximize the EA of a spinodoid structure and is able to outperform BO by up to 11% across various hyperparameter settings. The results, which are made open-source, serve to support the utility of multi-fidelity techniques across expensive data-driven design problems.

-- 3D Gaussian Splatting (3DGS) has recently gained popularity as a faster alternative to Neural Radiance Fields (NeRFs) in 3D reconstruction and view synthesis methods. Leveraging the spatial information encoded in 3DGS, this work proposes FOCI (Field Overlap Collision Integral), an algorithm that is able to optimize trajectories directly on the Gaussians themselves. FOCI leverages a novel and interpretable collision formulation for 3DGS using the notion of the overlap integral between Gaussians. Contrary to other approaches, which represent the robot with conservative bounding boxes that underestimate the traversability of the environment, we propose to represent the environment and the robot as Gaussian Splats. This not only has desirable computational properties, but also allows for orientation-aware planning, allowing the robot to pass through very tight and narrow spaces. We extensively test our algorithm in both synthetic and real Gaussian Splats, showcasing that collision-free trajectories for the ANYmal legged robot that can be computed in a few seconds, even with hundreds of thousands of Gaussians making up the environment. The project page and code are available at https://rffr .leggedrobotics.com/works/foci/

Abstract-- V ertical T otal Electron Content (vTEC) is an iono-spheric characteristic used to derive the signal delay impo sed by the ionosphere on near-vertical trans-ionospheric link s. The major aim of this paper is to design a prediction model based o n the main factors that influence the variability of this param eter on a diurnal, seasonal and long-term time-scale. The model should be accurate and general (comprehensive) enough for efficiently approximating the high variations of vTEC. Howe ver, good approximation and generalization are conflicting obje ctives. For this reason a Genetic Programming (GP) with Multi-objec tive Evolutionary Algorithm based on Decomposition characteri stics (GP-MOEA/D) is designed and proposed for modeling vTEC over Cyprus. Experimental results show that the Multi-Objectiv e GPmodel, considering real vTEC measurements obtained over a period of 11 years, has produced a good approximation of the modeled parameter and can be implemented as a local model to account for the ionospheric imposed error in positioning . Particulary, the GP-MOEA/D approach performs better than a Single Objective Optimization GP, a GP with Non-dominated Sorting Genetic Algorithm-II (NSGA-II) characteristics a nd the previously proposed Neural Network-based approach in most cases. The ionosphere is defined as a region of the earth's upper atmosphere where sufficient ionisation can exist to affect t he propagation of radio waves. It ranges in height above the surface of the earth from approximately 50 km to 1000 km.

Tree ensembles are non-parametric methods widely recognized for their accuracy and ability to capture complex interactions. While these models excel at prediction, they are difficult to interpret and may fail to uncover useful relationships in the data. We propose an estimator to extract compact sets of decision rules from tree ensembles. The extracted models are accurate and can be manually examined to reveal relationships between the predictors and the response. A key novelty of our estimator is the flexibility to jointly control the number of rules extracted and the interaction depth of each rule, which improves accuracy. We develop a tailored exact algorithm to efficiently solve optimization problems underlying our estimator and an approximate algorithm for computing regularization paths, sequences of solutions that correspond to varying model sizes. We also establish novel non-asymptotic prediction error bounds for our proposed approach, comparing it to an oracle that chooses the best data-dependent linear combination of the rules in the ensemble subject to the same complexity constraint as our estimator. The bounds illustrate that the large-sample predictive performance of our estimator is on par with that of the oracle. Through experiments, we demonstrate that our estimator outperforms existing algorithms for rule extraction.

Any agents we can possibly build are subject to capacity constraints, as memory and compute resources are inherently finite. However, comparatively little attention has been dedicated to understanding how agents with limited capacity should allocate their resources for optimal performance. The goal of this paper is to shed some light on this question by studying a simple yet relevant continual learning problem: the capacity-constrained linear-quadratic-Gaussian (LQG) sequential prediction problem. We derive a solution to this problem under appropriate technical conditions. Moreover, for problems that can be decomposed into a set of sub-problems, we also demonstrate how to optimally allocate capacity across these sub-problems in the steady state. We view the results of this paper as a first step in the systematic theoretical study of learning under capacity constraints.

The state-of-the-art DGF techniques redefine and optimize the fitness metric to reach the target sites precisely and quickly. However, optimizations for fitness metrics are mainly based on heuristic algorithms, which usually rely on historical execution information and lack foresight on paths that have not been exercised yet. Thus, those hard-to-execute paths with complex constraints would hinder DGF from reaching the targets, making DGF less efficient. In this paper, we propose DeepGo, a predictive directed grey-box fuzzer that can combine historical and predicted information to steer DGF to reach the target site via an optimal path. We first propose the path transition model, which models DGF as a process of reaching the target site through specific path transition sequences. The new seed generated by mutation would cause the path transition, and the path corresponding to the high-reward path transition sequence indicates a high likelihood of reaching the target site through it. Then, to predict the path transitions and the corresponding rewards, we use deep neural networks to construct a Virtual Ensemble Environment (VEE), which gradually imitates the path transition model and predicts the rewards of path transitions that have not been taken yet. To determine the optimal path, we develop a Reinforcement Learning for Fuzzing (RLF) model to generate the transition sequences with the highest sequence rewards. The RLF model can combine historical and predicted path transitions to generate the optimal path transition sequences, along with the policy to guide the mutation strategy of fuzzing. Finally, to exercise the high-reward path transition sequence, we propose the concept of an action group, which comprehensively optimizes the critical steps of fuzzing to realize the optimal path to reach the target efficiently.

One major recurring challenge in deploying manipulation robots is determining the optimal placement of manipulators to maximize performance. This challenge is exacerbated in complex, cluttered agricultural environments of high-value crops, such as flowers, fruits, and vegetables, that could greatly benefit from robotic systems tailored to their specific requirements. However, the design of such systems remains a challenging, intuition-driven process, limiting the affordability and adoption of robotics-based automation by domain experts like farmers. To address this challenge, we propose a four-part design optimization methodology for automating the development of task-specific robotic systems. This framework includes (a) a robot design model, (b) task and environment representations for simulation, (c) task-specific performance metrics, and (d) optimization algorithms for refining configurations. We demonstrate our framework by optimizing a dual-arm robotic system for pepper harvesting using two off-the-shelf redundant manipulators. To enhance performance, we introduce novel task metrics that leverage self-motion manifolds to characterize manipulator redundancy comprehensively. Our results show that our framework achieves simultaneous improvements in reachability success rates and improvements in dexterity. Specifically, our approach improves reachability success by at least 14\% over baseline methods and achieves over 30\% improvement in dexterity based on our task-specific metric.

Dynamic programming (DP) is a fundamental tool used across many engineering fields. The main goal of DP is to solve Bellman's optimality equations for a given Markov decision process (MDP). Standard methods like policy iteration exploit the fixed-point nature of these equations to solve them iteratively. However, these algorithms can be computationally expensive when the state-action space is large or when the problem involves long-term dependencies. Here we propose a new approach that unrolls and truncates policy iterations into a learnable parametric model dubbed BellNet, which we train to minimize the so-termed Bellman error from random value function initializations. Viewing the transition probability matrix of the MDP as the adjacency of a weighted directed graph, we draw insights from graph signal processing to interpret (and compactly re-parameterize) BellNet as a cascade of nonlinear graph filters. This fresh look facilitates a concise, transferable, and unifying representation of policy and value iteration, with an explicit handle on complexity during inference. Preliminary experiments conducted in a grid-like environment demonstrate that BellNet can effectively approximate optimal policies in a fraction of the iterations required by classical methods.