In sparse linear bandits, a learning agent sequentially selects an action and receive reward feedback, and the reward function depends linearly on a few coordinates of the covariates of the actions. This has applications in many real-world sequential decision making problems. In this paper, we propose a simple and computationally efficient sparse linear estimation method called PopArt that enjoys a tighter $\ell_1$ recovery guarantee compared to Lasso (Tibshirani, 1996) in many problems. Our bound naturally motivates an experimental design criterion that is convex and thus computationally efficient to solve. Based on our novel estimator and design criterion, we derive sparse linear bandit algorithms that enjoy improved regret upper bounds upon the state of the art (Hao et al., 2020), especially w.r.t. the geometry of the given action set. Finally, we prove a matching lower bound for sparse linear bandits in the data-poor regime, which closes the gap between upper and lower bounds in prior work.

Federated Learning (FL) enables many resource-limited devices to train a model collaboratively without data sharing. However, many existing works focus on model-homogeneous FL, where the global and local models are the same size, ignoring the inherently heterogeneous computational capabilities of different devices and restricting resource-constrained devices from contributing to FL. In this paper, we consider model-heterogeneous FL and propose Federated Partial Model Training (FedPMT), where devices with smaller computational capabilities work on partial models (subsets of the global model) and contribute to the global model. Different from Dropout-based partial model generation, which removes neurons in hidden layers at random, model training in FedPMT is achieved from the back-propagation perspective. As such, all devices in FedPMT prioritize the most crucial parts of the global model. Theoretical analysis shows that the proposed partial model training design has a similar convergence rate to the widely adopted Federated Averaging (FedAvg) algorithm, $\mathcal{O}(1/T)$, with the sub-optimality gap enlarged by a constant factor related to the model splitting design in FedPMT. Empirical results show that FedPMT significantly outperforms the existing benchmark FedDrop. Meanwhile, compared to the popular model-homogeneous benchmark, FedAvg, FedPMT reaches the learning target in a shorter completion time, thus achieving a better trade-off between learning accuracy and completion time.

The central question of ensemble learning has been: what factors make an ensemble system good or bad? It has We propose a fundamental theory on ensemble been widely believed that accurate and diverse models lead learning that answers the central question: what to better performance for ensemble systems. Guided by factors make an ensemble system good or bad? this intuition, many heuristical metrics have been proposed Previous studies used a variant of Fano's inequality to measure accuracy and diversity (Kohavi et al., 1996; of information theory and derived a lower Skalak et al., 1996; Cunningham & Carney, 2000; Shipp bound of the classification error rate on the basis & Kuncheva, 2002). However, these metrics lack theoretical of the accuracy and diversity of models. We grounding, and indeed, Kuncheva & Whitaker (2003) revisit the original Fano's inequality and argue empirically showed that there are no connections between that the studies did not take into account the information the metrics and system performance through a broad range lost when multiple model predictions of experiments. Turning to theoretical viewpoints, Geman are combined into a final prediction. To address et al. (1992) decomposed the squared error loss used in regression this issue, we generalize the previous theory to tasks into the bias and covariance of models. Bias incorporate the information loss, which we name here corresponds to accuracy and covariance diversity.

Advancements in materials play a crucial role in technological progress. However, the process of discovering and developing materials with desired properties is often impeded by substantial experimental costs, extensive resource utilization, and lengthy development periods. To address these challenges, modern approaches often employ machine learning (ML) techniques such as Bayesian Optimization (BO), which streamline the search for optimal materials by iteratively selecting experiments that are most likely to yield beneficial results. However, traditional BO methods, while beneficial, often struggle with balancing the trade-off between exploration and exploitation, leading to sub-optimal performance in material discovery processes. This paper introduces a novel Threshold-Driven UCB-EI Bayesian Optimization (TDUE-BO) method, which dynamically integrates the strengths of Upper Confidence Bound (UCB) and Expected Improvement (EI) acquisition functions to optimize the material discovery process. Unlike the classical BO, our method focuses on efficiently navigating the high-dimensional material design space (MDS). TDUE-BO begins with an exploration-focused UCB approach, ensuring a comprehensive initial sweep of the MDS. As the model gains confidence, indicated by reduced uncertainty, it transitions to the more exploitative EI method, focusing on promising areas identified earlier. The UCB-to-EI switching policy dictated guided through continuous monitoring of the model uncertainty during each step of sequential sampling results in navigating through the MDS more efficiently while ensuring rapid convergence. The effectiveness of TDUE-BO is demonstrated through its application on three different material datasets, showing significantly better approximation and optimization performance over the EI and UCB-based BO methods in terms of the RMSE scores and convergence efficiency, respectively.

Case-based planning is an approach to planning where previous planning experience provides guidance to solving new problems. Such a guidance can be extremely useful, or even necessary, when the new problem is very hard to solve, or the stored previous experience is highly valuable, because, e.g., it was provided or validated by human experts, and the system should try to reuse it as much as possible. To do so, a case-based planning system stores in a library previous planning experience in the form of already encountered problems and their solutions. The quality of such a plan library critically influences the performance of the planner, and therefore it needs to be carefully designed and created. For this reason, it is also important to update the library during the lifetime of the system, as the type of problems being addressed may evolve or differ from the ones the library was originally designed for. Moreover, like in general case-based reasoning, the library needs to be maintained at a manageable size, otherwise the computational cost of querying it grows excessively, making the entire approach ineffective. In this paper, we formally define the problem of maintaining a library of cases, discuss which criteria should drive the maintenance, study the computational complexity of the maintenance problem, and propose offline techniques to reduce an oversized library that optimize different criteria. Moreover, we introduce a complementary online approach that attempts to limit the growth of the library, and we consider the combination of offline and online techniques to ensure the best performance of the case-based planner. Finally, we experimentally show the practical effectiveness of the offline and online methods for reducing the library.

Non-negative matrix factorization (NMF) is an important technique for obtaining low dimensional representations of datasets. However, classical NMF does not take into account data that is collected at different times or in different locations, which may exhibit heterogeneity. We resolve this problem by solving a modified NMF objective, Stratified-NMF, that simultaneously learns strata-dependent statistics and a shared topics matrix. We develop multiplicative update rules for this novel objective and prove convergence of the objective. Then, we experiment on synthetic data to demonstrate the efficiency and accuracy of the method. Lastly, we apply our method to three real world datasets and empirically investigate their learned features.

According to the literature, Product reviews are an important source of information for customers to support their buying decision. Product reviews improve customer trust and loyalty. Reviews help customers in understanding what other customers think about a particular product and helps in driving purchase decisions. Therefore, for an e-commerce platform it is important to understand the sentiments in customer reviews to understand their products and services, and it also allows them to potentially create positive consumer interaction as well as long lasting relationships. Reviews also provide innovative ways to market the products for an ecommerce company. One such approach is Nudge Marketing. Nudge marketing is a subtle way for an ecommerce company to help their customers make better decisions without hesitation.

Incorporating prior knowledge into a data-driven modeling problem can drastically improve performance, reliability, and generalization outside of the training sample. The stronger the structural properties, the more effective these improvements become. Manifolds are a powerful nonlinear generalization of Euclidean space for modeling finite dimensions. Structural impositions in constrained systems increase when applying group structure, converting them into Lie manifolds. The range of their applications is very wide and includes the important case of robotic tasks. Canonical Correlation Analysis (CCA) can construct a hierarchical sequence of maximal correlations of up to two paired data sets in these Euclidean spaces. We present a method to generalize this concept to Lie Manifolds and demonstrate its efficacy through the substantial improvements it achieves in making structure-consistent predictions about changes in the state of a robotic hand.

Abstract: In Robust Control and Data Driven Robust Control design methodologies, multiple plant transfer functions or a family of transfer functions are considered and a common controller is designed such that all the plants that fall into this family are stabilized. Though the plants are stabilized, the controller might be sub-optimal for each of the plants when the variations in the plants are large. This paper presents a way of clustering stable linear dynamical systems for the design of robust controllers within each of the clusters such that the controllers are optimal for each of the clusters. First a k-medoids algorithm for hard clustering will be presented for stable Linear Time Invariant (LTI) systems and then a Gaussian Mixture Models (GMM) clustering for a special class of LTI systems, common for Hard Disk Drive plants, will be presented. Keywords: Robust Control, Clustering, k-medoids, Gaussian Mixture Models, Hard Disk Drives 1. INTRODUCTION Recently, in most of the personal computers, Solid State Drives (SSD) have replaced HDDs as the data transfer rate of SSDs is much higher than that of HDDs.

We study the problem of teaching multiple learners simultaneously in the nonparametric iterative teaching setting, where the teacher iteratively provides examples to the learner for accelerating the acquisition of a target concept. This problem is motivated by the gap between current single-learner teaching setting and the real-world scenario of human instruction where a teacher typically imparts knowledge to multiple students. Under the new problem formulation, we introduce a novel framework -- Multi-learner Nonparametric Teaching (MINT). In MINT, the teacher aims to instruct multiple learners, with each learner focusing on learning a scalar-valued target model. To achieve this, we frame the problem as teaching a vector-valued target model and extend the target model space from a scalar-valued reproducing kernel Hilbert space used in single-learner scenarios to a vector-valued space. Furthermore, we demonstrate that MINT offers significant teaching speed-up over repeated single-learner teaching, particularly when the multiple learners can communicate with each other. Lastly, we conduct extensive experiments to validate the practicality and efficiency of MINT.