In mobile and IoT systems, Federated Learning (FL) is increasingly important for effectively using data while maintaining user privacy. One key challenge in FL is managing statistical heterogeneity, such as non-i.i.d. data, arising from numerous clients and diverse data sources. This requires strategic cooperation, often with clients having similar characteristics. However, we are interested in a fundamental question: does achieving optimal cooperation necessarily entail cooperating with the most similar clients? Typically, significant model performance improvements are often realized not by partnering with the most similar models, but through leveraging complementary data. Our theoretical and empirical analyses suggest that optimal cooperation is achieved by enhancing complementarity in feature distribution while restricting the disparity in the correlation between features and targets. Accordingly, we introduce a novel framework, \texttt{FedSaC}, which balances similarity and complementarity in FL cooperation. Our framework aims to approximate an optimal cooperation network for each client by optimizing a weighted sum of model similarity and feature complementarity. The strength of \texttt{FedSaC} lies in its adaptability to various levels of data heterogeneity and multimodal scenarios. Our comprehensive unimodal and multimodal experiments demonstrate that \texttt{FedSaC} markedly surpasses other state-of-the-art FL methods.

The $K$-medoids problem is a challenging combinatorial clustering task, widely used in data analysis applications. While numerous algorithms have been proposed to solve this problem, none of these are able to obtain an exact (globally optimal) solution for the problem in polynomial time. In this paper, we present EKM: a novel algorithm for solving this problem exactly with worst-case $O\left(N^{K+1}\right)$ time complexity. EKM is developed according to recent advances in transformational programming and combinatorial generation, using formal program derivation steps. The derived algorithm is provably correct by construction. We demonstrate the effectiveness of our algorithm by comparing it against various approximate methods on numerous real-world datasets. We show that the wall-clock run time of our algorithm matches the worst-case time complexity analysis on synthetic datasets, clearly outperforming the exponential time complexity of benchmark branch-and-bound based MIP solvers. To our knowledge, this is the first, rigorously-proven polynomial time, practical algorithm for this ubiquitous problem.

The problem of an optimal mapping between Hilbert spaces $IN$ of $\left|\psi\right\rangle$ and $OUT$ of $\left|\phi\right\rangle$ based on a set of wavefunction measurements (within a phase) $\psi_l \to \phi_l$, $l=1\dots M$, is formulated as an optimization problem maximizing the total fidelity $\sum_{l=1}^{M} \omega^{(l)} \left|\langle\phi_l|\mathcal{U}|\psi_l\rangle\right|^2$ subject to probability preservation constraints on $\mathcal{U}$ (partial unitarity). Constructed operator $\mathcal{U}$ can be considered as a $IN$ to $OUT$ quantum channel; it is a partially unitary rectangular matrix of the dimension $\dim(OUT) \times \dim(IN)$ transforming operators as $A^{OUT}=\mathcal{U} A^{IN} \mathcal{U}^{\dagger}$. An iteration algorithm finding the global maximum of this optimization problem is developed and it's application to a number of problems is demonstrated. A software product implementing the algorithm is available from the authors.

Model Predictive Control (MPC)-based trajectory planning has been widely used in robotics, and incorporating Control Barrier Function (CBF) constraints into MPC can greatly improve its obstacle avoidance efficiency. Unfortunately, traditional optimizers are resource-consuming and slow to solve such non-convex constrained optimization problems (COPs) while learning-based methods struggle to satisfy the non-convex constraints. In this paper, we propose SOMTP algorithm, a self-supervised learning-based optimizer for CBF-MPC trajectory planning. Specifically, first, SOMTP employs problem transcription to satisfy most of the constraints. Then the differentiable SLPG correction is proposed to move the solution closer to the safe set and is then converted as the guide policy in the following training process. After that, inspired by the Augmented Lagrangian Method (ALM), our training algorithm integrated with guide policy constraints is proposed to enable the optimizer network to converge to a feasible solution. Finally, experiments show that the proposed algorithm has better feasibility than other learning-based methods and can provide solutions much faster than traditional optimizers with similar optimality.

Ensuring data privacy in machine learning models is critical, particularly in distributed settings where model gradients are typically shared among multiple parties to allow collaborative learning. Motivated by the increasing success of recovering input data from the gradients of classical models, this study addresses a central question: How hard is it to recover the input data from the gradients of quantum machine learning models? Focusing on variational quantum circuits (VQC) as learning models, we uncover the crucial role played by the dynamical Lie algebra (DLA) of the VQC ansatz in determining privacy vulnerabilities. While the DLA has previously been linked to the classical simulatability and trainability of VQC models, this work, for the first time, establishes its connection to the privacy of VQC models. In particular, we show that properties conducive to the trainability of VQCs, such as a polynomial-sized DLA, also facilitate the extraction of detailed snapshots of the input. We term this a weak privacy breach, as the snapshots enable training VQC models for distinct learning tasks without direct access to the original input. Further, we investigate the conditions for a strong privacy breach where the original input data can be recovered from these snapshots by classical or quantum-assisted polynomial time methods. We establish conditions on the encoding map such as classical simulatability, overlap with DLA basis, and its Fourier frequency characteristics that enable such a privacy breach of VQC models. Our findings thus play a crucial role in detailing the prospects of quantum privacy advantage by guiding the requirements for designing quantum machine learning models that balance trainability with robust privacy protection.

Training neural networks requires optimizing a loss function that may be highly irregular, and in particular neither convex nor smooth. Popular training algorithms are based on stochastic gradient descent with momentum (SGDM), for which classical analysis applies only if the loss is either convex or smooth. We show that a very small modification to SGDM closes this gap: simply scale the update at each time point by an exponentially distributed random scalar. The resulting algorithm achieves optimal convergence guarantees. Intriguingly, this result is not derived by a specific analysis of SGDM: instead, it falls naturally out of a more general framework for converting online convex optimization algorithms to non-convex optimization algorithms.

One goal of dexterous robotic grasping is to allow robots to handle objects with the same level of flexibility and adaptability as humans. However, it remains a challenging task to generate an optimal grasping strategy for dexterous hands, especially when it comes to delicate manipulation and accurate adjustment the desired grasping poses for objects of varying shapes and sizes. In this paper, we propose a novel dexterous grasp generation scheme called GrainGrasp that provides fine-grained contact guidance for each fingertip. In particular, we employ a generative model to predict separate contact maps for each fingertip on the object point cloud, effectively capturing the specifics of finger-object interactions. In addition, we develop a new dexterous grasping optimization algorithm that solely relies on the point cloud as input, eliminating the necessity for complete mesh information of the object. By leveraging the contact maps of different fingertips, the proposed optimization algorithm can generate precise and determinable strategies for human-like object grasping. Experimental results confirm the efficiency of the proposed scheme.

Multi-objective Bayesian optimization (MOBO) has shown promising performance on various expensive multi-objective optimization problems (EMOPs). However, effectively modeling complex distributions of the Pareto optimal solutions is difficult with limited function evaluations. Existing Pareto set learning algorithms may exhibit considerable instability in such expensive scenarios, leading to significant deviations between the obtained solution set and the Pareto set (PS). In this paper, we propose a novel Composite Diffusion Model based Pareto Set Learning algorithm, namely CDM-PSL, for expensive MOBO. CDM-PSL includes both unconditional and conditional diffusion model for generating high-quality samples. Besides, we introduce an information entropy based weighting method to balance different objectives of EMOPs. This method is integrated with the guiding strategy, ensuring that all the objectives are appropriately balanced and given due consideration during the optimization process; Extensive experimental results on both synthetic benchmarks and real-world problems demonstrates that our proposed algorithm attains superior performance compared with various state-of-the-art MOBO algorithms.

Rendezvous aims at gathering all robots at a specific location, which is an important collaborative behavior for multirobot systems. However, in an unknown environment, it is challenging to achieve rendezvous. Previous researches mainly focus on special scenarios where communication is not allowed and each robot executes a random searching strategy, which is highly time-consuming, especially in large-scale environments. In this work, we focus on rendezvous in unknown environments where communication is available. We divide this task into two steps: rendezvous based environment exploration with relative pose (RP) estimation and rendezvous point election. A new strategy called partitioned and incomplete exploration for rendezvous (PIER) is proposed to efficiently explore the unknown environment, where lightweight topological maps are constructed and shared among robots for RP estimation with very few communications. Then, a rendezvous point selection algorithm based on the merged topological map is proposed for efficient rendezvous for multi-robot systems. The effectiveness of the proposed methods is validated in both simulations and real-world experiments.

In SLAM (Simultaneous localization and mapping) problems, Pose Graph Optimization (PGO) is a technique to refine an initial estimate of a set of poses (positions and orientations) from a set of pairwise relative measurements. The optimization procedure can be negatively affected even by a single outlier measurement, with possible catastrophic and meaningless results. Although recent works on robust optimization aim to mitigate the presence of outlier measurements, robust solutions capable of handling large numbers of outliers are yet to come. This paper presents IPC, acronym for Incremental Probabilistic Consensus, a method that approximates the solution to the combinatorial problem of finding the maximally consistent set of measurements in an incremental fashion. It evaluates the consistency of each loop closure measurement through a consensus-based procedure, possibly applied to a subset of the global problem, where all previously integrated inlier measurements have veto power. We evaluated IPC on standard benchmarks against several state-of-the-art methods. Although it is simple and relatively easy to implement, IPC competes with or outperforms the other tested methods in handling outliers while providing online performances. We release with this paper an open-source implementation of the proposed method.