In many applications, both data samples and features have underlying hierarchical structures. However, existing methods for learning these latent structures typically focus on either samples or features, ignoring possible coupling between them. In this paper, we introduce a coupled hierarchical structure learning method using tree-Wasserstein distance (TWD). Our method jointly computes TWDs for samples and features, representing their latent hierarchies as trees. We propose an iterative, unsupervised procedure to build these sample and feature trees based on diffusion geometry, hyperbolic geometry, and wavelet filters. We show that this iterative procedure converges and empirically improves the quality of the constructed trees. The method is also computationally efficient and scales well in high-dimensional settings. Our method can be seamlessly integrated with hyperbolic graph convolutional networks (HGCN). We demonstrate that our method outperforms competing approaches in sparse approximation and unsupervised Wasserstein distance learning on several word-document and single-cell RNA-sequencing datasets. In addition, integrating our method into HGCN enhances performance in link prediction and node classification tasks.

Bayesian Optimization (BO) is a sample-efficient black-box optimizer commonly used in search spaces where hyperparameters are independent. However, in many practical AutoML scenarios, there will be dependencies among hyperparameters, forming a conditional search space, which can be partitioned into structurally distinct subspaces. The structure and dimensionality of hyperparameter configurations vary across these subspaces, challenging the application of BO. Some previous BO works have proposed solutions to develop multiple Gaussian Process models in these subspaces. However, these approaches tend to be inefficient as they require a substantial number of observations to guarantee each GP's performance and cannot capture relationships between hyperparameters across different subspaces. To address these issues, this paper proposes a novel approach to model the response surfaces of all subspaces in one, which can model the relationships between hyperparameters elegantly via a self-attention mechanism. Concretely, we design a structure-aware hyperparameter embedding to preserve the structural information. Then, we introduce an attention-based deep feature extractor, capable of projecting configurations with different structures from various subspaces into a unified feature space, where the response surfaces can be formulated using a single standard Gaussian Process. The empirical results on a simulation function, various real-world tasks, and HPO-B benchmark demonstrate that our proposed approach improves the efficacy and efficiency of BO within conditional search spaces.

In this paper, we develop a unified machine learning (ML) approach to predict high-quality solutions for single-machine scheduling problems with a non-decreasing min-sum objective function with or without release times. Our ML approach is novel in three major aspects. First, our approach is developed for the entire class of the aforementioned problems. To achieve this, we exploit the fact that the entire class of the problems considered can be formulated as a time-indexed formulation in a unified manner. We develop a deep neural network (DNN) which uses the cost parameters in the time-indexed formulation as the inputs to effectively predict a continuous solution to this formulation, based on which a feasible discrete solution is easily constructed. The second novel aspect of our approach lies in how the DNN model is trained. In view of the NP-hard nature of the problems, labels (i.e., optimal solutions) are hard to generate for training. To overcome this difficulty, we generate and utilize a set of special instances, for which optimal solutions can be found with little computational effort, to train the ML model offline. The third novel idea we employ in our approach is that we develop an online single-instance learning approach to fine tune the parameters in the DNN for a given online instance, with the goal of generating an improved solution for the given instance. To this end, we develop a feasibility surrogate that approximates the objective value of a given instance as a continuous function of the outputs of the DNN, which then enables us to derive gradients and update the learnable parameters in the DNN. Numerical results show that our approach can efficiently generate high-quality solutions for a variety of single-machine scheduling min-sum problems with up to 1000 jobs.

The Lin-Kernighan-Helsguan (LKH) heuristic is a classic local search algorithm for the Traveling Salesman Problem (TSP). LKH introduces an $\alpha$-value to replace the traditional distance metric for evaluating the edge quality, which leads to a significant improvement. However, we observe that the $\alpha$-value does not make full use of the historical information during the search, and single guiding information often makes LKH hard to escape from some local optima. To address the above issues, we propose a novel way to extract backbone information during the TSP local search process, which is dynamic and can be updated once a local optimal solution is found. We further propose to combine backbone information, $\alpha$-value, and distance to evaluate the edge quality so as to guide the search. Moreover, we abstract their different combinations to arms in a multi-armed bandit (MAB) and use an MAB model to help the algorithm select an appropriate evaluation metric dynamically. Both the backbone information and MAB can provide diverse guiding information and learn from the search history to suggest the best metric. We apply our methods to LKH and LKH-3, which is an extension version of LKH that can be used to solve about 40 variant problems of TSP and Vehicle Routing Problem (VRP). Extensive experiments show the excellent performance and generalization capability of our proposed method, significantly improving LKH for TSP and LKH-3 for two representative TSP and VRP variants, the Colored TSP (CTSP) and Capacitated VRP with Time Windows (CVRPTW).

In the fields of robotics and biomechanics, the integration of elastic elements such as springs and tendons in legged systems has long been recognized for enabling energy-efficient locomotion. Yet, a significant challenge persists: designing a robotic leg that perform consistently across diverse operating conditions, especially varying average forward speeds. It remains unclear whether, for such a range of operating conditions, the stiffness of the elastic elements needs to be varied or if a similar performance can be obtained by changing the motion and actuation while keeping the stiffness fixed. This work explores the influence of the leg stiffness on the energy efficiency of a monopedal robot through an extensive parametric study of its periodic hopping motion. To this end, we formulate an optimal control problem parameterized by average forward speed and leg stiffness, solving it numerically using direct collocation. Our findings indicate that, compared to the use of a fixed stiffness, employing variable stiffness in legged systems improves energy efficiency by 20 % maximally and by 6.8 % on average across a range of speeds.

Autoregressive construction approaches generate solutions to vehicle routing problems in a step-by-step fashion, leading to high-quality solutions that are nearing the performance achieved by handcrafted, operations research techniques. In this work, we challenge the conventional paradigm of sequential solution construction and introduce an iterative search framework where solutions are instead deconstructed by a neural policy. Throughout the search, the neural policy collaborates with a simple greedy insertion algorithm to rebuild the deconstructed solutions. Methods that can learn to solve complex optimization problems have the potential to transform decision-making processes across virtually all domains. It is therefore unsurprising that learningbased optimization approaches have garnered significant attention and yielded substantial advancements (Bello et al., 2016; Kool et al., 2019; Kwon et al., 2020). Notably, reinforcement learning (RL) approaches are particularly promising because they do not rely on a pre-defined training set of representative solutions and can develop new strategies from scratch for novel optimization problems. These methods generally construct solutions incrementally through a sequential decision-making process and have been successfully applied to various vehicle routing problems. Despite recent progress, learning-based methods for combinatorial optimization (CO) problems usually fall short of outperforming the state-of-the-art techniques from the operations research (OR) community. For instance, while some new construction approaches for the capacitated vehicle routing problem (CVRP) have surpassed the LKH3 solver (Helsgaun, 2000), they still struggle to match the performance of the state-of-the-art HGS solver (Vidal et al., 2012), particularly for larger instances with over 100 nodes. One reason for this is their inability to explore as many solutions as traditional approaches within the same amount of time.

One of the pivotal challenges in a multi-robot system is how to give attention to accuracy and efficiency while ensuring safety. Prior arts cannot strictly guarantee collision-free for an arbitrarily large number of robots or the results are considerably conservative. Smoothness of the avoidance trajectory also needs to be further optimized. This paper proposes an accelerationactuated simultaneous obstacle avoidance and trajectory tracking method for arbitrarily large teams of robots, that provides a nonconservative collision avoidance strategy and gives approaches for deadlock avoidance. We propose two ways of deadlock resolution, one involves incorporating an auxiliary velocity vector into the error function of the trajectory tracking module, which is proven to have no influence on global convergence of the tracking error. Furthermore, unlike the traditional methods that they address conflicts after a deadlock occurs, our decision-making mechanism avoids the near-zero velocity, which is much more safer and efficient in crowed environments. Extensive comparison show that the proposed method is superior to the existing studies when deployed in a large-scale robot system, with minimal invasiveness.

The rapid rise of large language models (LLMs) has unlocked many applications but also underscores the challenge of aligning them with diverse values and preferences. Direct Preference Optimization (DPO) is central to alignment but constrained by fixed divergences and limited feature transformations. We propose DPO-Kernels, which integrates kernel methods to address these issues through four key contributions: (i) Kernelized Representations with polynomial, RBF, Mahalanobis, and spectral kernels for richer transformations, plus a hybrid loss combining embedding-based and probability-based objectives; (ii) Divergence Alternatives (Jensen-Shannon, Hellinger, Renyi, Bhattacharyya, Wasserstein, and f-divergences) for greater stability; (iii) Data-Driven Selection metrics that automatically choose the best kernel-divergence pair; and (iv) a Hierarchical Mixture of Kernels for both local precision and global modeling. Evaluations on 12 datasets demonstrate state-of-the-art performance in factuality, safety, reasoning, and instruction following. Grounded in Heavy-Tailed Self-Regularization, DPO-Kernels maintains robust generalization for LLMs, offering a comprehensive resource for further alignment research.

Mobile manipulators typically encounter significant challenges in navigating narrow, cluttered environments due to their high-dimensional state spaces and complex kinematics. While reactive methods excel in dynamic settings, they struggle to efficiently incorporate complex, coupled constraints across the entire state space. In this work, we present a novel local reactive controller that reformulates the time-domain single-step problem into a multi-step optimization problem in the spatial domain, leveraging the propagation of a serial kinematic chain. This transformation facilitates the formulation of customized, decoupled link-specific constraints, which is further solved efficiently with augmented Lagrangian differential dynamic programming (AL-DDP). Our approach naturally absorbs spatial kinematic propagation in the forward pass and processes all link-specific constraints simultaneously during the backward pass, enhancing both constraint management and computational efficiency. Notably, in this framework, we formulate collision avoidance constraints for each link using accurate geometric models with extracted free regions, and this improves the maneuverability of the mobile manipulator in narrow, cluttered spaces. Experimental results showcase significant improvements in safety, efficiency, and task completion rates. These findings underscore the robustness of the proposed method, particularly in narrow, cluttered environments where conventional approaches could falter. The open-source project can be found at https://github.com/Chunx1nZHENG/MM-with-Whole-Body-Safety-Release.git.

Federated Learning (FL) has gained significant attention in recent years due to its distributed nature and privacy preserving benefits. However, a key limitation of conventional FL is that it learns and distributes a common global model to all participants, which fails to provide customized solutions for diverse task requirements. Federated meta-learning (FML) offers a promising solution to this issue by enabling devices to finetune local models after receiving a shared meta-model from the server. In this paper, we propose a task-oriented FML framework over non-orthogonal multiple access (NOMA) networks. A novel metric, termed value of learning (VoL), is introduced to assess the individual training needs across devices. Moreover, a task-level weight (TLW) metric is defined based on task requirements and fairness considerations, guiding the prioritization of edge devices during FML training. The formulated problem, to maximize the sum of TLW-based VoL across devices, forms a non-convex mixed-integer non-linear programming (MINLP) challenge, addressed here using a parameterized deep Q-network (PDQN) algorithm to handle both discrete and continuous variables. Simulation results demonstrate that our approach significantly outperforms baseline schemes, underscoring the advantages of the proposed framework.