Federated learning (FL) is a privacy-preserving learning technique that enables distributed computing devices to train shared learning models across data silos collaboratively. Existing FL works mostly focus on designing advanced FL algorithms to improve the model performance. However, the economic considerations of the clients, such as fairness and incentive, are yet to be fully explored. Without such considerations, self-motivated clients may lose interest and leave the federation. To address this problem, we designed a novel incentive mechanism that involves a client selection process to remove low-quality clients and a money transfer process to ensure a fair reward distribution. Our experimental results strongly demonstrate that the proposed incentive mechanism can effectively improve the duration and fairness of the federation.

In this paper, a non-iterative spatio-temporal multi-task assignment approach is used for playing piano music by a team of robots. This paper considers the piano playing problem, in which an algorithm needs to compute the trajectories for a dynamically sized team of robots who will play the musical notes by traveling through the specific locations associated with musical notes at their respective specific times. A two-step dynamic resource allocation based on a spatio-temporal multi-task assignment problem (DREAM), has been implemented to assign robots for playing the musical tune. The algorithm computes the required number of robots to play the music in the first step. In the second step, optimal assignments are computed for the updated team of robots, which minimizes the total distance traveled by the team. Even for the individual feasible trajectories, the multi-robot execution may fail if robots encounter a collision. As some time will be utilized for this conflict resolution, robots may not be able to reach the desired location on time. This paper analyses and proves that, if robots are operating in a convex region, the solution of the DREAM approach provides collision-free trajectories. The working of the DREAM approach has been illustrated with the help of the high fidelity simulations in Gazebo operated using ROS2. The result clearly shows that the DREAM approach computes the required number of robots and assigns multiple tasks to robots in at most two steps. The simulation of the robots playing music, using computed assignments, is demonstrated in the attached video. video link: \url{https://youtu.be/XToicNm-CO8}

While low-rank matrix prior has been exploited in dynamic MR image reconstruction and has obtained satisfying performance, tensor low-rank models have recently emerged as powerful alternative representations for three-dimensional dynamic MR datasets. In this paper, we introduce a novel deep unrolling network for dynamic MRI, namely the learned transform-based tensor low-rank network (LT$^2$LR-Net). First, we generalize the tensor singular value decomposition (t-SVD) into an arbitrary unitary transform-based version and subsequently propose the novel transformed tensor nuclear norm (TTNN). Then, we design a novel TTNN-based iterative optimization algorithm based on the alternating direction method of multipliers (ADMM) to exploit the tensor low-rank prior in the transformed domain. The corresponding iterative steps are unrolled into the proposed LT$^2$LR-Net, where the convolutional neural network (CNN) is incorporated to adaptively learn the transformation from the dynamic MR dataset for more robust and accurate tensor low-rank representations. Experimental results on the cardiac cine MR dataset demonstrate that the proposed framework can provide improved recovery results compared with the state-of-the-art methods.

Domain adaptation manages to transfer the knowledge of well-labeled source data to unlabeled target data. Many recent efforts focus on improving the prediction accuracy of target pseudo-labels to reduce conditional distribution shift. In this paper, we propose a novel domain adaptation method, which infers target pseudo-labels through cross-domain label propagation, such that the underlying manifold structure of two domain data can be explored. Unlike existing cross-domain label propagation methods that separate domain-invariant feature learning, affinity matrix constructing and target labels inferring into three independent stages, we propose to integrate them into a unified optimization framework. In such way, these three parts can boost each other from an iterative optimization perspective and thus more effective knowledge transfer can be achieved. Furthermore, to construct a high-quality affinity matrix, we propose a discriminative graph self-learning strategy, which can not only adaptively capture the inherent similarity of the data from two domains but also effectively exploit the discriminative information contained in well-labeled source data and pseudo-labeled target data. An efficient iterative optimization algorithm is designed to solve the objective function of our proposal. Notably, the proposed method can be extended to semi-supervised domain adaptation in a simple but effective way and the corresponding optimization problem can be solved with the identical algorithm. Extensive experiments on six standard datasets verify the significant superiority of our proposal in both unsupervised and semi-supervised domain adaptation settings.

We consider a dynamic assortment selection problem where a seller has a fixed inventory of $N$ substitutable products and faces an unknown demand that arrives sequentially over $T$ periods. In each period, the seller needs to decide on the assortment of products (of cardinality at most $K$) to offer to the customers. The customer's response follows an unknown multinomial logit model (MNL) with parameters $v$. The goal of the seller is to maximize the total expected revenue given the fixed initial inventory of $N$ products. We give a policy that achieves a regret of $\tilde O\Big(K \sqrt{KN T}\Big(\sqrt{v_{\text{max}}} + \frac{1}{q_{\text{min}}}\text{OPT}\Big)\Big)$, where $v_{\text{max}}\leq 1$ is the maximum utility for any product and $q_{\text{min}}$ the minimum inventory level, under a mild assumption on the model parameters. In particular, our policy achieves a near-optimal $\tilde O(\sqrt{T})$ regret in a large-inventory setting. Our policy builds upon the UCB-based approach for MNL-bandit without inventory constraints in [1] and addresses the inventory constraints through an exponentially sized LP for which we present a tractable approximation while keeping the $\tilde O(\sqrt{T})$ regret bound.

Dynamic algorithm selection aims to exploit the complementarity of multiple optimization algorithms by switching between them during the search. While these kinds of dynamic algorithms have been shown to have potential to outperform their component algorithms, it is still unclear how this potential can best be realized. One promising approach is to make use of landscape features to enable a per-run trajectory-based switch. Here, the samples seen by the first algorithm are used to create a set of features which describe the landscape from the perspective of the algorithm. These features are then used to predict what algorithm to switch to. In this work, we extend this per-run trajectory-based approach to consider a wide variety of potential points at which to perform the switch. We show that using a sliding window to capture the local landscape features contains information which can be used to predict whether a switch at that point would be beneficial to future performance. By analyzing the resulting models, we identify what features are most important to these predictions. Finally, by evaluating the importance of features and comparing these values between multiple algorithms, we show clear differences in the way the second algorithm interacts with the local landscape features found before the switch.

Homomorphic Encryption (HE) is a set of powerful properties of certain cryptosystems that allow for privacy-preserving operation over the encrypted text. Still, HE is not widespread due to limitations in terms of efficiency and usability. Among the challenges of HE, scheme parametrization (i.e., the selection of appropriate parameters within the algorithms) is a relevant multi-faced problem. First, the parametrization needs to comply with a set of properties to guarantee the security of the underlying scheme. Second, parametrization requires a deep understanding of the low-level primitives since the parameters have a confronting impact on the precision, performance, and security of the scheme. Finally, the circuit to be executed influences, and it is influenced by, the parametrization. Thus, there is no general optimal selection of parameters, and this selection depends on the circuit and the scenario of the application. Currently, most of the existing HE frameworks require cryptographers to address these considerations manually. It requires a minimum of expertise acquired through a steep learning curve. In this paper, we propose a unified solution for the aforementioned challenges. Concretely, we present an expert system combining Fuzzy Logic and Linear Programming. The Fuzzy Logic Modules receive a user selection of high-level priorities for the security, efficiency, and performance of the cryptosystem. Based on these preferences, the expert system generates a Linear Programming Model that obtains optimal combinations of parameters by considering those priorities while preserving a minimum level of security for the cryptosystem. We conduct an extended evaluation where we show that an expert system generates optimal parameter selections that maintain user preferences without undergoing the inherent complexity of analyzing the circuit.

It is often unnoticed that the predominant way to use collocation methods is fundamentally flawed when applied to optimal control in robotics. Such methods assume that the system dynamics is given by a first order ODE, whereas robots are often governed by a second or higher order ODE involving configuration variables and their time derivatives. To apply a collocation method, therefore, the usual practice is to resort to the well known procedure of casting an M th order ODE into M first order ones. This manipulation, which in the continuous domain is perfectly valid, leads to inconsistencies when the problem is discretized. Since the configuration variables and their time derivatives are approximated with polynomials of the same degree, their differential dependencies cannot be fulfilled, and the actual dynamics is not satisfied, not even at the collocation points. This paper draws attention to this problem, and develops improved versions of the trapezoidal and Hermite-Simpson collocation methods that do not present these inconsistencies. In many cases, the new methods reduce the dynamic transcription error in one order of magnitude, or even more, without noticeably increasing the cost of computing the solutions.

Direct multiple shooting (DMS) and direct collocation (DC) are two common transcription methods for solving optimal control problems (OCP) in biomechanics and robotics. They have rarely been compared in terms of solution and speed. Through five examples of predictive simulations solved using five transcription methods and 100 initial guesses in the Bioptim software, we showed that not a single method outperformed systematically better. All methods converged to almost the same solution (cost, states, and controls) in all but one OCP, with several local minima being found in the latter. Nevertheless, DC based on fourth-order Legendre polynomials provided overall better results, especially in terms of dynamic consistency compared to DMS based on a fourth-order Runge-Kutta method. Furthermore, expressing the rigid-body constraints using inverse dynamics was usually faster than forward dynamics. DC with dynamics constraints based on inverse dynamics converged to better and less variable solutions. Consequently, we recommend starting with this transcription to solve OCPs but keep testing other methods.

This paper is concerned with data clustering to separate clusters based on the connectivity principle for categorizing similar and dissimilar data into different groups. Although classical clustering algorithms such as K-means are efficient techniques, they often trap in local optima and have a slow convergence rate in solving high-dimensional problems. To address these issues, many successful meta-heuristic optimization algorithms and intelligence-based methods have been introduced to attain the optimal solution in a reasonable time. They are designed to escape from a local optimum problem by allowing flexible movements or random behaviors. In this study, we attempt to conceptualize a powerful approach using the three main components: Chimp Optimization Algorithm (ChOA), Generalized Normal Distribution Algorithm (GNDA), and Opposition-Based Learning (OBL) method. Firstly, two versions of ChOA with two different independent groups' strategies and seven chaotic maps, entitled ChOA(I) and ChOA(II), are presented to achieve the best possible result for data clustering purposes. Secondly, a novel combination of ChOA and GNDA algorithms with the OBL strategy is devised to solve the major shortcomings of the original algorithms. Lastly, the proposed ChOAGNDA method is a Selective Opposition (SO) algorithm based on ChOA and GNDA, which can be used to tackle large and complex real-world optimization problems, particularly data clustering applications. The results are evaluated against seven popular meta-heuristic optimization algorithms and eight recent state-of-the-art clustering techniques. Experimental results illustrate that the proposed work significantly outperforms other existing methods in terms of the achievement in minimizing the Sum of Intra-Cluster Distances (SICD), obtaining the lowest Error Rate (ER), accelerating the convergence speed, and finding the optimal cluster centers.