Federated learning algorithms, such as FedAvg, are negatively affected by data heterogeneity and partial client participation. To mitigate the latter problem, global variance reduction methods, like FedVARP, leverage stale model updates for non-participating clients. These methods are effective under homogeneous client participation. Y et, this paper shows that, when some clients participate much less than others, aggregating updates with different levels of staleness can detrimentally affect the training process. Motivated by this observation, we introduce FedStale, a novel algorithm that updates the global model in each round through a convex combination of "fresh" updates from participating clients and "stale" updates from non-participating ones. By adjusting the weight in the convex combination, FedStale interpolates between FedAvg, which only uses fresh updates, and FedVARP, which treats fresh and stale updates equally. Our analysis of FedStale convergence yields the following novel findings: i) it integrates and extends previous FedAvg and FedVARP analyses to heterogeneous client participation; ii) it underscores how the least participating client influences convergence error; iii) it provides practical guidelines to best exploit stale updates, showing that their usefulness diminishes as data heterogeneity decreases and participation heterogeneity increases. Extensive experiments featuring diverse levels of client data and participation heterogeneity not only confirm these findings but also show that FedStale outperforms both FedAvg and FedVARP in many settings.

We propose Test-Time Augmentation (TTA) as an effective technique for addressing combinatorial optimization problems, including the Traveling Salesperson Problem. In general, deep learning models possessing the property of invariance, where the output is uniquely determined regardless of the node indices, have been proposed to learn graph structures efficiently. In contrast, we interpret the permutation of node indices, which exchanges the elements of the distance matrix, as a TTA scheme. The results demonstrate that our method is capable of obtaining shorter solutions than the latest models. Furthermore, we show that the probability of finding a solution closer to an exact solution increases depending on the augmentation size.

This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms significantly enhances the accuracy of the results. Simple modifications to the loss function may also improve precision, offering an additional avenue for enhancement. Despite optimization algorithms having a greater impact on convergence than adjustments to the loss function, practical considerations often favor tweaking the latter due to ease of implementation. On a global scale, the integration of an enhanced optimizer and a marginally adjusted loss function enables a reduction in the loss function by several orders of magnitude across diverse physical problems. Consequently, our results obtained using compact networks (typically comprising 2 or 3 layers of 20-30 neurons) achieve accuracies comparable to finite difference schemes employing thousands of grid points. This study encourages the continued advancement of PINNs and associated optimization techniques for broader applications across various fields.

Preserving and encouraging mobility in the elderly and adults with chronic conditions is of paramount importance. However, existing walking aids are either inadequate to provide sufficient support to users' stability or too bulky and poorly maneuverable to be used outside hospital environments. In addition, they all lack adaptability to individual requirements. To address these challenges, this paper introduces WANDER, a novel Walking Assistive omNi-Directional Exo-Robot. It consists of an omnidirectional platform and a robust aluminum structure mounted on top of it, which provides partial body weight support. A comfortable and minimally restrictive coupling interface embedded with a force/torque sensor allows to detect users' intentions, which are translated into command velocities by means of a variable admittance controller. An optimization technique based on users' preferences, i.e., Preference-Based Optimization (PBO) guides the choice of the admittance parameters (i.e., virtual mass and damping) to better fit subject-specific needs and characteristics. Experiments with twelve healthy subjects exhibited a significant decrease in energy consumption and jerk when using WANDER with PBO parameters as well as improved user performance and comfort. The great interpersonal variability in the optimized parameters highlights the importance of personalized control settings when walking with an assistive device, aiming to enhance users' comfort and mobility while ensuring reliable physical support.

Stochastic optimization algorithms, particularly stochastic policy gradient (SPG), report significant success in reinforcement learning (RL). Nevertheless, up to now, that how to speedily acquire an optimal solution for RL is still a challenge. To tackle this issue, this work develops a fast SPG algorithm from the perspective of utilizing a momentum, coined SPG-NM. Specifically, in SPG-NM, a novel type of the negative momentum (NM) technique is applied into the classical SPG algorithm. Different from the existing NM techniques, we have adopted a few hyper-parameters in our SPG-NM algorithm. Moreover, the computational complexity is nearly same as the modern SPG-type algorithms, e.g., accelerated policy gradient (APG), which equips SPG with Nesterov's accelerated gradient (NAG). We evaluate the resulting algorithm on two classical tasks, bandit setting and Markov decision process (MDP). Numerical results in different tasks demonstrate faster convergence rate of the resulting algorithm by comparing state-of-the-art algorithms, which confirm the positive impact of NM in accelerating SPG for RL. Also, numerical experiments under different settings confirm the robustness of our SPG-NM algorithm for some certain crucial hyper-parameters, which ride the user feel free in practice.

There has been a longstanding trade-off between the accuracy of a candidate machine learning (ML) model and its Our previous work developed a methodology that addresses interpretability. This is evident in the extreme example of some of these concerns by combining vectorization deep neural networks (DNNs), which can offer excellent methods to image data with EBMs. The possibility of using accuracy for many problems but are limited in their interpretability EBMs as models for image data poses numerous challenges, due to the number of inaccessible layers. Alternatively, the principal of which is the mapping from images there are simple techniques, such as linear models or to a vector representation that could then be used directly decision trees, that offer the user full comprehension of the with EBMs. In our previous work, we used the Gabor internal weights. However, these are often unable to model Wavelet transform in conjunction with a constrained optimization the complex relationships seen in modern datasets. For tabular procedure to extract key image features from the data, there has been considerable progress toward finding data (Schug et al. 2024). We also applied a highly custom a middle ground, typically through explaining complex feature engineering to tailor this process to the particular models with surrogates such as LIME (Ribeiro, Singh, and dataset (Schug et al. 2023). In both cases, we relied on domain Guestrin 2016) and Shapley (Lundberg and Lee 2017).

Abstract--Library-based methods are known to be very effective for fast motion planning by adapting an experience retrieved from a precomputed library. This article presents CoverLib, a principled approach for constructing and utilizing such a library. CoverLib iteratively adds an experience-classifier-pair to the library, where each classifier corresponds to an adaptable region of the experience within the problem space. This iterative process is an active procedure, as it selects the next experience based on its ability to effectively cover the uncovered region. During the query phase, these classifiers are utilized to select an experience that is expected to be adaptable for a given problem. Experimental results demonstrate that CoverLib effectively mitigates the trade-off between plannability and speed observed in global (e.g. As a result, it achieves both fast planning and high success rates over the problem domain. Similarly, in home service OTION planning has been studied from two ends of the spectrum: global and local methods. Global robotics, although the tasks are diverse, the tasks that act as methods, such as sampling-based motion planners (SBMP) bottlenecks are often known in advance (e.g., reaching into a like Probabilistic Roadmap (PRM) [1] and Rapidly-exploring narrow container). Random Tree (RRT) [2], are expected to find a solution if one exists, given enough time. However, these methods often A promising approach to this end is to use a library of require long and varying amount of computational time to experiences [5]-[10] reviewed in Section II-A.

Quadratically-constrained unbounded integer programs hold the distinction of being undecidable, suggesting a possible soft-spot for Mathematical Programming (MP) techniques, which otherwise constitute a good choice to treat integer or mixed-integer (MI) problems. We consider the challenge of minimizing MI convex quadratic objective functions subject to unbounded decision variables and quadratic constraints. Given the theoretical weakness of white-box MP solvers to handle such models, we turn to black-box meta-heuristics of the Evolution Strategies (ESs) family, and question their capacity to solve this challenge. Through an empirical assessment of quadratically-constrained quadratic objective functions, across varying Hessian forms and condition numbers, we compare the performance of the CPLEX solver to state-of-the-art MI ESs, which handle constraints by penalty. Our systematic investigation begins where the CPLEX solver encounters difficulties (timeouts as the search-space dimensionality increases, (D>=30), on which we report by means of detailed analyses. Overall, the empirical observations confirm that black-box and white-box solvers can be competitive, especially when the constraint function is separable, and that two common ESs' mutation operators can effectively handle the integer unboundedness. We also conclude that conditioning and separability are not intuitive factors in determining the complexity of this class of MI problems, where regular versus rough landscape structures can pose mirrored degrees of challenge for MP versus ESs.

Determining the optimal configuration of adsorbates on a slab (adslab) is pivotal in the exploration of novel catalysts across diverse applications. Traditionally, the quest for the lowest energy adslab configuration involves placing the adsorbate onto the slab followed by an optimization process. Prior methodologies have relied on heuristics, problem-specific intuitions, or brute-force approaches to guide adsorbate placement. In this work, we propose a novel framework for adsorbate placement using denoising diffusion. The model is designed to predict the optimal adsorbate site and orientation corresponding to the lowest energy configuration. Further, we have an end-to-end evaluation framework where diffusion-predicted adslab configuration is optimized with a pretrained machine learning force field and finally evaluated with Density Functional Theory (DFT). Our findings demonstrate an acceleration of up to 5x or 3.5x improvement in accuracy compared to the previous best approach. Given the novelty of this framework and application, we provide insights into the impact of pre-training, model architectures, and conduct extensive experiments to underscore the significance of this approach.

In the task of differentially private (DP) continual counting, we receive a stream of increments and our goal is to output an approximate running total of these increments, without revealing too much about any specific increment. Despite its simplicity, differentially private continual counting has attracted significant attention both in theory and in practice. Existing algorithms for differentially private continual counting are either inefficient in terms of their space usage or add an excessive amount of noise, inducing suboptimal utility. The most practical DP continual counting algorithms add carefully correlated Gaussian noise to the values. The task of choosing the covariance for this noise can be expressed in terms of factoring the lower-triangular matrix of ones (which computes prefix sums). We present two approaches from this class (for different parameter regimes) that achieve near-optimal utility for DP continual counting and only require logarithmic or polylogarithmic space (and time). Our first approach is based on a space-efficient streaming matrix multiplication algorithm for a class of Toeplitz matrices. We show that to instantiate this algorithm for DP continual counting, it is sufficient to find a low-degree rational function that approximates the square root on a circle in the complex plane. We then apply and extend tools from approximation theory to achieve this. We also derive efficient closed-forms for the objective function for arbitrarily many steps, and show direct numerical optimization yields a highly practical solution to the problem. Our second approach combines our first approach with a recursive construction similar to the binary tree mechanism.