Collaborative and Distributed Bayesian Optimization via Consensus: Showcasing the Power of Collaboration for Optimal Design

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.

Federated Data Analytics: A Study on Linear Models

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.

Self-scalable Tanh (Stan): Faster Convergence and Better Generalization in Physics-informed Neural Networks

Physics-informed Neural Networks (PINNs) are gaining attention in the engineering and scientific literature for solving a range of differential equations with applications in weather modeling, healthcare, manufacturing, etc. Poor scalability is one of the barriers to utilizing PINNs for many real-world problems. To address this, a Self-scalable tanh (Stan) activation function is proposed for the PINNs. The proposed Stan function is smooth, non-saturating, and has a trainable parameter. During training, it can allow easy flow of gradients to compute the required derivatives and also enable systematic scaling of the input-output mapping. It is shown theoretically that the PINNs with the proposed Stan function have no spurious stationary points when using gradient descent algorithms. The proposed Stan is tested on a number of numerical studies involving general regression problems. It is subsequently used for solving multiple forward problems, which involve second-order derivatives and multiple dimensions, and an inverse problem where the thermal diffusivity of a rod is predicted with heat conduction data. These case studies establish empirically that the Stan activation function can achieve better training and more accurate predictions than the existing activation functions in the literature.

Federated Gaussian Process: Convergence, Automatic Personalization and Multi-fidelity Modeling

In this paper, we propose \texttt{FGPR}: a Federated Gaussian process ($\mathcal{GP}$) regression framework that uses an averaging strategy for model aggregation and stochastic gradient descent for local client computations. Notably, the resulting global model excels in personalization as \texttt{FGPR} jointly learns a global $\mathcal{GP}$ prior across all clients. The predictive posterior then is obtained by exploiting this prior and conditioning on local data which encodes personalized features from a specific client. Theoretically, we show that \texttt{FGPR} converges to a critical point of the full log-likelihood function, subject to statistical error. Through extensive case studies we show that \texttt{FGPR} excels in a wide range of applications and is a promising approach for privacy-preserving multi-fidelity data modeling.

The Internet of Federated Things (IoFT): A Vision for the Future and In-depth Survey of Data-driven Approaches for Federated Learning

The Internet of Things (IoT) is on the verge of a major paradigm shift. In the IoT system of the future, IoFT, the cloud will be substituted by the crowd where model training is brought to the edge, allowing IoT devices to collaboratively extract knowledge and build smart analytics/models while keeping their personal data stored locally. This paradigm shift was set into motion by the tremendous increase in computational power on IoT devices and the recent advances in decentralized and privacy-preserving model training, coined as federated learning (FL). This article provides a vision for IoFT and a systematic overview of current efforts towards realizing this vision. Specifically, we first introduce the defining characteristics of IoFT and discuss FL data-driven approaches, opportunities, and challenges that allow decentralized inference within three dimensions: (i) a global model that maximizes utility across all IoT devices, (ii) a personalized model that borrows strengths across all devices yet retains its own model, (iii) a meta-learning model that quickly adapts to new devices or learning tasks. We end by describing the vision and challenges of IoFT in reshaping different industries through the lens of domain experts. Those industries include manufacturing, transportation, energy, healthcare, quality & reliability, business, and computing.

GIFAIR-FL: An Approach for Group and Individual Fairness in Federated Learning

In this paper we propose \texttt{GIFAIR-FL}: an approach that imposes group and individual fairness to federated learning settings. By adding a regularization term, our algorithm penalizes the spread in the loss of client groups to drive the optimizer to fair solutions. Theoretically, we show convergence in non-convex and strongly convex settings. Our convergence guarantees hold for both $i.i.d.$ and non-$i.i.d.$ data. To demonstrate the empirical performance of our algorithm, we apply our method on image classification and text prediction tasks. Compared to existing algorithms, our method shows improved fairness results while retaining superior or similar prediction accuracy.

SALR: Sharpness-aware Learning Rates for Improved Generalization

In an effort to improve generalization in deep learning, we propose SALR: a sharpness-aware learning rate update technique designed to recover flat minimizers. Our method dynamically updates the learning rate of gradient-based optimizers based on the local sharpness of the loss function. This allows optimizers to automatically increase learning rates at sharp valleys to increase the chance of escaping them. We demonstrate the effectiveness of SALR when adopted by various algorithms over a broad range of networks. Our experiments indicate that SALR improves generalization, converges faster, and drives solutions to significantly flatter regions.

Lookahead Bayesian Optimization via Rollout: Guarantees and Sequential Rolling Horizons

Lookahead, also known as non-myopic, Bayesian optimization (BO) aims to find optimal sampling policies through solving a dynamic programming (DP) formulation that maximizes a long-term reward over a rolling horizon. Though promising, lookahead BO faces the risk of error propagation through its increased dependence on a possibly mis-specified model. In this work we focus on the rollout approximation for solving the intractable DP. We first prove the improving nature of rollout in tackling lookahead BO. We then provide both a theoretical and practical guideline to decide on the rolling horizon stagewise. This guideline is built on quantifying the negative effect of a mis-specified model. To illustrate our idea, we provide case studies on both single and multi-information source BO. Empirical results show the advantageous properties of our method over several myopic and non-myopic BO algorithms.

The Rényi Gaussian Process

In this article we introduce an alternative closed form lower bound on the Gaussian process ($\mathcal{GP}$) likelihood based on the R\'enyi $\alpha$-divergence. This new lower bound can be viewed as a convex combination of the Nystr\"om approximation and the exact $\mathcal{GP}$. The key advantage of this bound, is its capability to control and tune the enforced regularization on the model and thus is a generalization of the traditional sparse variational $\mathcal{GP}$ regression. From the theoretical perspective, we show that with probability at least $1-\delta$, the R\'enyi $\alpha$-divergence between the variational distribution and the true posterior becomes arbitrarily small as the number of data points increase.

Variational Inference of Joint Models using Multivariate Gaussian Convolution Processes

We present a non-parametric prognostic framework for individualized event prediction based on joint modeling of both longitudinal and time-to-event data. Our approach exploits a multivariate Gaussian convolution process (MGCP) to model the evolution of longitudinal signals and a Cox model to map time-to-event data with longitudinal data modeled through the MGCP. Taking advantage of the unique structure imposed by convolved processes, we provide a variational inference framework to simultaneously estimate parameters in the joint MGCP-Cox model. This significantly reduces computational complexity and safeguards against model overfitting. Experiments on synthetic and real world data show that the proposed framework outperforms state-of-the art approaches built on two-stage inference and strong parametric assumptions.