This paper investigates the convergence properties and applications of the three-operator splitting method, also known as Davis-Yin splitting (DYS) method, integrated with extrapolation and Plug-and-Play (PnP) denoiser within a nonconvex framework. We first propose an extrapolated DYS method to effectively solve a class of structural nonconvex optimization problems that involve minimizing the sum of three possible nonconvex functions. Our approach provides an algorithmic framework that encompasses both extrapolated forward-backward splitting and extrapolated Douglas-Rachford splitting methods.To establish the convergence of the proposed method, we rigorously analyze its behavior based on the Kurdyka-{\L}ojasiewicz property, subject to some tight parameter conditions. Moreover, we introduce two extrapolated PnP-DYS methods with convergence guarantee, where the traditional regularization prior is replaced by a gradient step-based denoiser. This denoiser is designed using a differentiable neural network and can be reformulated as the proximal operator of a specific nonconvex functional. We conduct extensive experiments on image deblurring and image super-resolution problems, where our results showcase the advantage of the extrapolation strategy and the superior performance of the learning-based model that incorporates the PnP denoiser in terms of achieving high-quality recovery images.
相關內容
This paper introduces a novel zero-shot motion planning method that allows users to quickly design smooth robot motions in Cartesian space. A B\'ezier curve-based Cartesian plan is transformed into a joint space trajectory by our neuro-inspired inverse kinematics (IK) method CycleIK, for which we enable platform independence by scaling it to arbitrary robot designs. The motion planner is evaluated on the physical hardware of the two humanoid robots NICO and NICOL in a human-in-the-loop grasping scenario. Our method is deployed with an embodied agent that is a large language model (LLM) at its core. We generalize the embodied agent, that was introduced for NICOL, to also be embodied by NICO. The agent can execute a discrete set of physical actions and allows the user to verbally instruct various different robots. We contribute a grasping primitive to its action space that allows for precise manipulation of household objects. The new CycleIK method is compared to popular numerical IK solvers and state-of-the-art neural IK methods in simulation and is shown to be competitive with or outperform all evaluated methods when the algorithm runtime is very short. The grasping primitive is evaluated on both NICOL and NICO robots with a reported grasp success of 72% to 82% for each robot, respectively.
Vehicle routing problems (VRPs), which can be found in numerous real-world applications, have been an important research topic for several decades. Recently, the neural combinatorial optimization (NCO) approach that leverages a learning-based model to solve VRPs without manual algorithm design has gained substantial attention. However, current NCO methods typically require building one model for each routing problem, which significantly hinders their practical application for real-world industry problems with diverse attributes. In this work, we make the first attempt to tackle the crucial challenge of cross-problem generalization. In particular, we formulate VRPs as different combinations of a set of shared underlying attributes and solve them simultaneously via a single model through attribute composition. In this way, our proposed model can successfully solve VRPs with unseen attribute combinations in a zero-shot generalization manner. Extensive experiments are conducted on eleven VRP variants, benchmark datasets, and industry logistic scenarios. The results show that the unified model demonstrates superior performance in the eleven VRPs, reducing the average gap to around 5% from over 20% in the existing approach and achieving a significant performance boost on benchmark datasets as well as a real-world logistics application. The source code is included in //github.com/FeiLiu36/MTNCO.
In this paper, we develop a new adaptive hyperbolic-cross-space mapped Jacobi (AHMJ) method for solving multidimensional spatiotemporal integrodifferential equations in unbounded domains. By devising adaptive techniques for sparse mapped Jacobi spectral expansions defined in a hyperbolic cross space, our proposed AHMJ method can efficiently solve various spatiotemporal integrodifferential equations such as the anomalous diffusion model with reduced numbers of basis functions. Our analysis of the AHMJ method gives a uniform upper error bound for solving a class of spatiotemporal integrodifferential equations, leading to effective error control.
This paper introduces a new resource allocation framework for integrated sensing and communication (ISAC) systems, which are expected to be fundamental aspects of sixth-generation networks. In particular, we develop an augmented Lagrangian manifold optimization (ALMO) framework designed to maximize communication sum rate while satisfying sensing beampattern gain targets and base station (BS) transmit power limits. ALMO applies the principles of Riemannian manifold optimization (MO) to navigate the complex, non-convex landscape of the resource allocation problem. It efficiently leverages the augmented Lagrangian method to ensure adherence to constraints. We present comprehensive numerical results to validate our framework, which illustrates the ALMO method's superior capability to enhance the dual functionalities of communication and sensing in ISAC systems. For instance, with 12 antennas and 30 dBm BS transmit power, our proposed ALMO algorithm delivers a 10.1% sum rate gain over a benchmark optimization-based algorithm. This work demonstrates significant improvements in system performance and contributes a new algorithmic perspective to ISAC resource management.
This paper delves into a rendezvous scenario involving a chaser and a target spacecraft, focusing on the application of Model Predictive Control (MPC) to design a controller capable of guiding the chaser toward the target. The operational principle of spacecraft thrusters, requiring a minimum activation time that leads to the existence of a control deadband, introduces mixed-integer constraints into the optimization, posing a considerable computational challenge due to the exponential complexity on the number of integer constraints. We address this complexity by presenting two solver algorithms that efficiently approximate the optimal solution in significantly less time than standard solvers, making them well-suited for real-time applications.
We study in this paper the improvement of one-class support vector machines (OC-SVM) through sparse representation techniques for unsupervised anomaly detection. As Dictionary Learning (DL) became recently a common analysis technique that reveals hidden sparse patterns of data, our approach uses this insight to endow unsupervised detection with more control on pattern finding and dimensions. We introduce a new anomaly detection model that unifies the OC-SVM and DL residual functions into a single composite objective, subsequently solved through K-SVD-type iterative algorithms. A closed-form of the alternating K-SVD iteration is explicitly derived for the new composite model and practical implementable schemes are discussed. The standard DL model is adapted for the Dictionary Pair Learning (DPL) context, where the usual sparsity constraints are naturally eliminated. Finally, we extend both objectives to the more general setting that allows the use of kernel functions. The empirical convergence properties of the resulting algorithms are provided and an in-depth analysis of their parametrization is performed while also demonstrating their numerical performance in comparison with existing methods.
This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations, respectively. In particular, coupled field problems with different physics may require simultaneously the accurate evaluation of several quantities of interest, which is achieved with multi-goal oriented error control. Sensitivity measures are obtained by solving an adjoint problem. Error localization is achieved with the help of a partition-of-unity. We also review and extend theoretical results for efficiency and reliability by employing a saturation assumption. The resulting adaptive algorithms allow to balance discretization and non-linear iteration errors, and are demonstrated for four applications: Poisson's problem, non-linear elliptic boundary value problems, stationary incompressible Navier-Stokes equations, and regularized parabolic $p$-Laplace initial-boundary value problems. Therein, different finite element discretizations in two different software libraries are utilized, which are partially accompanied with open-source implementations on GitHub.
For decades, robotics researchers have pursued various tasks for multi-robot systems, from cooperative manipulation to search and rescue. These tasks are multi-robot extensions of classical robotic tasks and often optimized on dimensions such as speed or efficiency. As robots transition from commercial and research settings into everyday environments, social task aims such as engagement or entertainment become increasingly relevant. This work presents a compelling multi-robot task, in which the main aim is to enthrall and interest. In this task, the goal is for a human to be drawn to move alongside and participate in a dynamic, expressive robot flock. Towards this aim, the research team created algorithms for robot movements and engaging interaction modes such as gestures and sound. The contributions are as follows: (1) a novel group navigation algorithm involving human and robot agents, (2) a gesture responsive algorithm for real-time, human-robot flocking interaction, (3) a weight mode characterization system for modifying flocking behavior, and (4) a method of encoding a choreographer's preferences inside a dynamic, adaptive, learned system. An experiment was performed to understand individual human behavior while interacting with the flock under three conditions: weight modes selected by a human choreographer, a learned model, or subset list. Results from the experiment showed that the perception of the experience was not influenced by the weight mode selection. This work elucidates how differing task aims such as engagement manifest in multi-robot system design and execution, and broadens the domain of multi-robot tasks.
This paper surveys research works in the quickly advancing field of instruction tuning (IT), a crucial technique to enhance the capabilities and controllability of large language models (LLMs). Instruction tuning refers to the process of further training LLMs on a dataset consisting of \textsc{(instruction, output)} pairs in a supervised fashion, which bridges the gap between the next-word prediction objective of LLMs and the users' objective of having LLMs adhere to human instructions. In this work, we make a systematic review of the literature, including the general methodology of IT, the construction of IT datasets, the training of IT models, and applications to different modalities, domains and applications, along with an analysis on aspects that influence the outcome of IT (e.g., generation of instruction outputs, size of the instruction dataset, etc). We also review the potential pitfalls of IT along with criticism against it, along with efforts pointing out current deficiencies of existing strategies and suggest some avenues for fruitful research.
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191