Abstract-- Trajectory optimization in multi-vehicle scenarios faces challenges due to its non-linear, non-convex properties and sensitivity to initial values, making interactions between vehicles difficult to control. In this paper, inspired by topological planning, we propose a differentiable local homotopy invariant metric to model the interactions. By incorporating this topological metric as a constraint into multi-vehicle trajectory optimization, our framework is capable of generating multiple interactive trajectories from the same initial values, achieving controllable interactions as well as supporting user-designed interaction patterns. Extensive experiments demonstrate its superior optimality and efficiency over existing methods. The colored curves are trajectories of each vehicle.

E-commerce search optimization has evolved to include a wider range of metrics that reflect user engagement and business objectives. Modern search frameworks now incorporate advanced quality features, such as sales counts and document-query relevance, to better align search results with these goals. Traditional methods typically focus on click-through rate (CTR) as a measure of engagement or relevance, but this can miss true purchase intent, creating a gap between user interest and actual conversions. Joint training with the click-through conversion rate (CTCVR) has become essential for understanding buying behavior, although its sparsity poses challenges for reliable optimization. This study presents MOHPER, a Multi-Objective Hyperparameter Optimization framework for E-commerce Retrieval systems. Utilizing Bayesian optimization and sampling, it jointly optimizes both CTR, CTCVR, and relevant objectives, focusing on engagement and conversion of the users. In addition, to improve the selection of the best configuration from multi-objective optimization, we suggest advanced methods for hyperparameter selection, including a meta-configuration voting strategy and a cumulative training approach that leverages prior optimal configurations, to improve speeds of training and efficiency. Currently deployed in a live setting, our proposed framework substantiates its practical efficacy in achieving a balanced optimization that aligns with both user satisfaction and revenue goals.

Language models are strong few-shot learners and achieve good overall accuracy in text classification tasks, masking the fact that their results suffer from great class accuracy imbalance. We believe that the pursuit of overall accuracy should not come from enriching the strong classes, but from raising up the weak ones. To address the imbalance, we propose a post-hoc nonlinear integer programming based debiasing method that ensembles weight correction and membership correction to enable flexible rectifications of class probabilities at both class and sample levels, enhancing the performance of LLMs directly from their outputs. Evaluations with Llama-2-13B on seven text classification benchmarks show that our approach achieves state-of-the-art overall accuracy gains with balanced class accuracies. The resulted probability correction scheme demonstrates that sample-level corrections are necessary to elevate weak classes. In addition, due to effectively correcting weak classes, our method also brings significant performance gains to Llama-2-70B, especially on a biomedical domain task, demonstrating its effectiveness across both small and large model variants.

Additive models (AMs) have sparked a lot of interest in machine learning recently, allowing the incorporation of interpretable structures into a wide range of model classes. Many commonly used approaches to fit a wide variety of potentially complex additive models build on the idea of boosting additive models. While boosted additive models (BAMs) work well in practice, certain theoretical aspects are still poorly understood, including general convergence behavior and what optimization problem is being solved when accounting for the implicit regularizing nature of boosting. In this work, we study the solution paths of BAMs and establish connections with other approaches for certain classes of problems. Along these lines, we derive novel convergence results for BAMs, which yield crucial insights into the inner workings of the method. While our results generally provide reassuring theoretical evidence for the practical use of BAMs, they also uncover some ``pathologies'' of boosting for certain additive model classes concerning their convergence behavior that require caution in practice. We empirically validate our theoretical findings through several numerical experiments.

The rise of generative artificial intelligence (AI) as a novel frontier that uniquely merges advanced levels of intelligence with revolutionary user experiences is redefining the AI landscape for future cellular networks. In particular, the transition towards 6G systems has introduced a myriad of challenges inherent to their AI-native network design, requiring innovative solutions to enable real-time network orchestration, intelligent decision-making, and adaptive dynamic configurations. Meanwhile, the envisioned user experiences for 6G are growing increasingly complex, exceeding the capabilities offered by vintage wireless technologies and conventional AI solutions to satisfy their advanced demands. With its disruptive impact evident across diverse fields, generative AI possesses immense potential to tackle these challenges, leveraging its exceptional capabilities to manage complex tasks, operate autonomously, and adapt seamlessly to scenarios beyond its training domain. Remarkably, generative AI provides a transformative opportunity for telecom and cellular networks to bridge this defined gap in 6G systems, thereby shifting towards a new era with cutting-edge AI innovations across the different system and user levels.

Ensuring safety and motion consistency for robot navigation in occluded, obstacle-dense environments is a critical challenge. In this context, this study presents an occlusion-aware Consistent Model Predictive Control (CMPC) strategy. To account for the occluded obstacles, it incorporates adjustable risk regions that represent their potential future locations. Subsequently, dynamic risk boundary constraints are developed online to ensure safety. The CMPC then constructs multiple locally optimal trajectory branches (each tailored to different risk regions) to balance between exploitation and exploration. A shared consensus trunk is generated to ensure smooth transitions between branches without significant velocity fluctuations, further preserving motion consistency. To facilitate high computational efficiency and ensure coordination across local trajectories, we use the alternating direction method of multipliers (ADMM) to decompose the CMPC into manageable sub-problems for parallel solving. The proposed strategy is validated through simulation and real-world experiments on an Ackermann-steering robot platform. The results demonstrate the effectiveness of the proposed CMPC strategy through comparisons with baseline approaches in occluded, obstacle-dense environments.

Rising labor costs and increasing logistical demands pose significant challenges to modern delivery systems. Automated Electric Vehicles (AEVs) could reduce reliance on delivery personnel and increase route flexibility, but their adoption is limited due to varying customer acceptance and integration complexities. Shared Distribution Locations (SDLs) offer an alternative to door-to-door (D2D) delivery by providing a wider delivery window and serving multiple community customers, thereby improving last-mile logistics through reduced delivery time, lower costs, and higher customer satisfaction.This paper introduces the Multi-Trip Time-Dependent Hybrid Vehicle Routing Problem (MTTD-MVRP), a challenging variant of the Vehicle Routing Problem (VRP) that combines Autonomous Electric Vehicles (AEVs) with conventional vehicles. The problem's complexity arises from factors such as time-dependent travel speeds, strict time windows, battery limitations, and driver labor constraints, while integrating both SDLs and D2D deliveries. To solve the MTTD-MVRP efficiently, we develop a tailored meta-heuristic based on Adaptive Large Neighborhood Search (ALNS) augmented with column generation (CG). This approach intensively explores the solution space using problem-specific operators and adaptively refines solutions, balancing high-quality outcomes with computational effort. Extensive experiments show that the proposed method delivers near-optimal solutions for large-scale instances within practical time limits.From a managerial perspective, our findings highlight the importance of integrating autonomous and human-driven vehicles in last-mile logistics. Decision-makers can leverage SDLs to reduce operational costs and carbon footprints while still accommodating customers who require or prefer D2D services.

When operating at their full capacity, quadrupedal robots can produce loud footstep noise, which can be disruptive in human-centered environments like homes, offices, and hospitals. As a result, balancing locomotion performance with noise constraints is crucial for the successful real-world deployment of quadrupedal robots. However, achieving adaptive noise control is challenging due to (a) the trade-off between agility and noise minimization, (b) the need for generalization across diverse deployment conditions, and (c) the difficulty of effectively adjusting policies based on noise requirements. We propose QuietPaw, a framework incorporating our Conditional Noise-Constrained Policy (CNCP), a constrained learning-based algorithm that enables flexible, noise-aware locomotion by conditioning policy behavior on noise-reduction levels. We leverage value representation decomposition in the critics, disentangling state representations from condition-dependent representations and this allows a single versatile policy to generalize across noise levels without retraining while improving the Pareto trade-off between agility and noise reduction. We validate our approach in simulation and the real world, demonstrating that CNCP can effectively balance locomotion performance and noise constraints, achieving continuously adjustable noise reduction.

Robotic search and rescue, exploration, and inspection require trajectory planning across a variety of domains. A popular approach to trajectory planning for these types of missions is ergodic search, which biases a trajectory to spend time in parts of the exploration domain that are believed to contain more information. Most prior work on ergodic search has been limited to searching simple surfaces, like a 2D Euclidean plane or a sphere, as they rely on projecting functions defined on the exploration domain onto analytically obtained Fourier basis functions. In this paper, we extend ergodic search to any surface that can be approximated by a triangle mesh. The basis functions are approximated through finite element methods on a triangle mesh of the domain. We formally prove that this approximation converges to the continuous case as the mesh approximation converges to the true domain. We demonstrate that on domains where analytical basis functions are available (plane, sphere), the proposed method obtains equivalent results, and while on other domains (torus, bunny, wind turbine), the approach is versatile enough to still search effectively. Lastly, we also compare with an existing ergodic search technique that can handle complex domains and show that our method results in a higher quality exploration.

Scene flow estimation is a foundational task for many robotic applications, including robust dynamic object detection, automatic labeling, and sensor synchronization. Two types of approaches to the problem have evolved: 1) Supervised and 2) optimization-based methods. Supervised methods are fast during inference and achieve high-quality results, however, they are limited by the need for large amounts of labeled training data and are susceptible to domain gaps. In contrast, unsupervised test-time optimization methods do not face the problem of domain gaps but usually suffer from substantial runtime, exhibit artifacts, or fail to converge to the right solution. In this work, we mitigate several limitations of existing optimization-based methods. To this end, we 1) introduce a simple voxel grid-based model that improves over the standard MLP-based formulation in multiple dimensions and 2) introduce a new multiframe loss formulation. 3) We combine both contributions in our new method, termed Floxels. On the Argoverse 2 benchmark, Floxels is surpassed only by EulerFlow among unsupervised methods while achieving comparable performance at a fraction of the computational cost. Floxels achieves a massive speedup of more than ~60 - 140x over EulerFlow, reducing the runtime from a day to 10 minutes per sequence. Over the faster but low-quality baseline, NSFP, Floxels achieves a speedup of ~14x.