We focus on collaborative and federated black-box optimization (BBOpt), where agents optimize their heterogeneous black-box functions through collaborative sequential experimentation. From a Bayesian optimization perspective, we address the fundamental challenges of distributed experimentation, heterogeneity, and privacy within BBOpt, and propose three unifying frameworks to tackle these issues: (i) a global framework where experiments are centrally coordinated, (ii) a local framework that allows agents to make decisions based on minimal shared information, and (iii) a predictive framework that enhances local surrogates through collaboration to improve decision-making. We categorize existing methods within these frameworks and highlight key open questions to unlock the full potential of federated BBOpt. Our overarching goal is to shift federated learning from its predominantly descriptive/predictive paradigm to a prescriptive one, particularly in the context of BBOpt - an inherently sequential decision-making problem.

This paper introduces a framework for Bayesian Optimization (BO) with metric movement costs, addressing a critical challenge in practical applications where input alterations incur varying costs. Our approach is a convenient plug-in that seamlessly integrates with the existing literature on batched algorithms, where designs within batches are observed following the solution of a Traveling Salesman Problem. The proposed method provides a theoretical guarantee of convergence in terms of movement costs for BO. Empirically, our method effectively reduces average movement costs over time while maintaining comparable regret performance to conventional BO methods. This framework also shows promise for broader applications in various bandit settings with movement costs.

Online learning has demonstrated notable potential to dynamically allocate limited resources to monitor a large population of processes, effectively balancing the exploitation of processes yielding high rewards, and the exploration of uncertain processes. However, most online learning algorithms were designed under 1) a centralized setting that requires data sharing across processes to obtain an accurate prediction or 2) a homogeneity assumption that estimates a single global model from the decentralized data. To facilitate the online learning of heterogeneous processes from the decentralized data, we propose a federated collaborative online monitoring method, which captures the latent representative models inherent in the population through representation learning and designs a novel federated collaborative UCB algorithm to estimate the representative models from sequentially observed decentralized data. The efficiency of our method is illustrated through theoretical analysis, simulation studies, and decentralized cognitive degradation monitoring in Alzheimer's disease. Monitoring a large population of dynamic processes within the constraints of monitoring resources poses a significant challenge across various industrial sectors, including healthcare and engineering systems [1], [2]. The complexity arises from two key factors: 1) the inherent disparity between the limited monitoring resources available and the large population of processes to be monitored, and 2) the uncertain and heterogeneous dynamics in the progression of these processes. In tackling this intricate problem, online learning from bandit feedback has demonstrated notable potential [2], [3].

Building a predictive model that rapidly adapts to real-time condition monitoring (CM) signals is critical for engineering systems/units. Unfortunately, many current methods suffer from a trade-off between representation power and agility in online settings. For instance, parametric methods that assume an underlying functional form for CM signals facilitate efficient online prediction updates. However, this simplification leads to vulnerability to model specifications and an inability to capture complex signals. On the other hand, approaches based on over-parameterized or non-parametric models can excel at explaining complex nonlinear signals, but real-time updates for such models pose a challenging task. In this paper, we propose a neural process-based approach that addresses this trade-off. It encodes available observations within a CM signal into a representation space and then reconstructs the signal's history and evolution for prediction. Once trained, the model can encode an arbitrary number of observations without requiring retraining, enabling on-the-spot real-time predictions along with quantified uncertainty and can be readily updated as more online data is gathered. Furthermore, our model is designed to incorporate qualitative information (i.e., labels) from individual units. This integration not only enhances individualized predictions for each unit but also enables joint inference for both signals and their associated labels. Numerical studies on both synthetic and real-world data in reliability engineering highlight the advantageous features of our model in real-time adaptation, enhanced signal prediction with uncertainty quantification, and joint prediction for labels and signals.

In this work, we study the problem of common and unique feature extraction from noisy data. When we have N observation matrices from N different and associated sources corrupted by sparse and potentially gross noise, can we recover the common and unique components from these noisy observations? This is a challenging task as the number of parameters to estimate is approximately thrice the number of observations. Despite the difficulty, we propose an intuitive alternating minimization algorithm called triple component matrix factorization (TCMF) to recover the three components exactly. TCMF is distinguished from existing works in literature thanks to two salient features. First, TCMF is a principled method to separate the three components given noisy observations provably. Second, the bulk of the computation in TCMF can be distributed. On the technical side, we formulate the problem as a constrained nonconvex nonsmooth optimization problem. Despite the intricate nature of the problem, we provide a Taylor series characterization of its solution by solving the corresponding Karush-Kuhn-Tucker conditions. Using this characterization, we can show that the alternating minimization algorithm makes significant progress at each iteration and converges into the ground truth at a linear rate. Numerical experiments in video segmentation and anomaly detection highlight the superior feature extraction abilities of TCMF.

Current techniques for Out-of-Distribution (OoD) detection predominantly rely on quantifying predictive uncertainty and incorporating model regularization during the training phase, using either real or synthetic OoD samples. However, methods that utilize real OoD samples lack exploration and are prone to overfit the OoD samples at hand. Whereas synthetic samples are often generated based on features extracted from training data, rendering them less effective when the training and OoD data are highly overlapped in the feature space. In this work, we propose a Wasserstein-score-based generative adversarial training scheme to enhance OoD detection accuracy, which, for the first time, performs data augmentation and exploration simultaneously under the supervision of limited OoD samples. Specifically, the generator explores OoD spaces and generates synthetic OoD samples using feedback from the discriminator, while the discriminator exploits both the observed and synthesized samples for OoD detection using a predefined Wasserstein score. We provide theoretical guarantees that the optimal solutions of our generative scheme are statistically achievable through adversarial training in empirical settings. We then demonstrate that the proposed method outperforms state-of-the-art techniques on various computer vision datasets and exhibits superior generalizability to unseen OoD data.

Optimal design is a critical yet challenging task within many applications. This challenge arises from the need for extensive trial and error, often done through simulations or running field experiments. Fortunately, sequential optimal design, also referred to as Bayesian optimization when using surrogates with a Bayesian flavor, has played a key role in accelerating the design process through efficient sequential sampling strategies. However, a key opportunity exists nowadays. The increased connectivity of edge devices sets forth a new collaborative paradigm for Bayesian optimization. A paradigm whereby different clients collaboratively borrow strength from each other by effectively distributing their experimentation efforts to improve and fast-track their optimal design process. To this end, we bring the notion of consensus to Bayesian optimization, where clients agree (i.e., reach a consensus) on their next-to-sample designs. Our approach provides a generic and flexible framework that can incorporate different collaboration mechanisms. In lieu of this, we propose transitional collaborative mechanisms where clients initially rely more on each other to maneuver through the early stages with scant data, then, at the late stages, focus on their own objectives to get client-specific solutions. Theoretically, we show the sub-linear growth in regret for our proposed framework. Empirically, through simulated datasets and a real-world collaborative material discovery experiment, we show that our framework can effectively accelerate and improve the optimal design process and benefit all participants.

We introduce a relevant yet challenging problem named Personalized Dictionary Learning (PerDL), where the goal is to learn sparse linear representations from heterogeneous datasets that share some commonality. In PerDL, we model each dataset's shared and unique features as global and local dictionaries. Challenges for PerDL not only are inherited from classical dictionary learning (DL), but also arise due to the unknown nature of the shared and unique features. In this paper, we rigorously formulate this problem and provide conditions under which the global and local dictionaries can be provably disentangled. Under these conditions, we provide a meta-algorithm called Personalized Matching and Averaging (PerMA) that can recover both global and local dictionaries from heterogeneous datasets. PerMA is highly efficient; it converges to the ground truth at a linear rate under suitable conditions. Moreover, it automatically borrows strength from strong learners to improve the prediction of weak learners. As a general framework for extracting global and local dictionaries, we show the application of PerDL in different learning tasks, such as training with imbalanced datasets and video surveillance.

As edge devices become increasingly powerful, data analytics are gradually moving from a centralized to a decentralized regime where edge compute resources are exploited to process more of the data locally. This regime of analytics is coined as federated data analytics (FDA). In spite of the recent success stories of FDA, most literature focuses exclusively on deep neural networks. In this work, we take a step back to develop an FDA treatment for one of the most fundamental statistical models: linear regression. Our treatment is built upon hierarchical modeling that allows borrowing strength across multiple groups. To this end, we propose two federated hierarchical model structures that provide a shared representation across devices to facilitate information sharing. Notably, our proposed frameworks are capable of providing uncertainty quantification, variable selection, hypothesis testing and fast adaptation to new unseen data. We validate our methods on a range of real-life applications including condition monitoring for aircraft engines. The results show that our FDA treatment for linear models can serve as a competing benchmark model for future development of federated algorithms.

Recent development of advanced sensing and high computing technologies has enabled the wide adoption of machine vision to automatically inspect products' dimensional quality for efficient process control and reducing the manual inspection cost. The process control procedure requires effective data analysis methods to provide reliable inspection results. In this paper, we consider a high-volume manufacturing system that uses machine vision at the quality inspection station for automatic classification of product defects. Here classification implies both; identifying a defect and classifying its corresponding type. As a motivating example, we consider the scenario where batches of three-dimensional (3D) point cloud data are independently collected from a manufacturing process. The 3D point cloud data is obtained by measuring the 3D location of points on the product surface using a 3D scanner. The location measurements can then be used for fast classification of surface defects, and thus provide timely feedback for process control. Figure 1 (right) shows some exemplar surface defects on a wood product and the corresponding 3D point cloud measurements. The 3D point cloud measurements have a set of defining characteristics that should be considered in the development of defect classification techniques.