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 sensor design experiment, we show that our framework can effectively accelerate and improve the optimal design process and benefit all participants. Note to Practitioners—The proposed algorithm allows multiple clients to collaboratively distribute their trial-and-error efforts to fast-track and improve the optimal design process. In the algorithm, each client performs a test locally and then shares the results with an orchestrator. Using the information from all clients, the orchestrator then finds the best new experiment that each client should undertake and sends those back for the next round of experiments. Through this process, all clients can leverage each other’s strengths and optimize their designs with far fewer experiments than each client operating in isolation. This is confirmed through many simulation examples, along with a real-life sensor design experiment where multiple collaborating agents seqeuntially coordinate their experimentation efforts. The goal is to rapidly discover the biosensor design and measurement format parameters that find the maximum amount of captured target analyte.

In this paper, we propose FGPR: a Federated Gaussian process ( GP) regression framework that uses an averaging strategy for model aggregation and stochastic gradient descent for local computations. Notably, the resulting global model excels in personalization as FGPR jointly learns a shared prior across all devices. The predictive posterior is then obtained by exploiting this shared prior and conditioning on local data, which encodes personalized features from a specific dataset. Theoretically, we show that FGPR converges to a critical point of the full log-marginal likelihood function, subject to statistical errors. This result offers standalone value as it brings federated learning theoretical results to correlated paradigms. Through extensive case studies on several regression tasks, we show that FGPR excels in a wide range of applications and is a promising approach for privacy-preserving multi-fidelity data modeling.

In an effort to improve generalization in deep learning and automate the process of learning rate scheduling, 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.

Differential equations are fundamental in modeling numerous physical systems, including thermal, manufacturing, and meteorological systems. Traditionally, numerical methods often approximate the solutions of complex systems modeled by differential equations. With the advent of modern deep learning, Physics-informed Neural Networks (PINNs) are evolving as a new paradigm for solving differential equations with a pseudo-closed form solution. Unlike numerical methods, the PINNs can solve the differential equations mesh-free, integrate the experimental data, and resolve challenging inverse problems. However, one of the limitations of PINNs is the poor training caused by using the activation functions designed typically for purely data-driven problems. This work proposes a scalable tanh-based activation function for PINNs to improve learning the solutions of differential equations. The proposed Self-scalable tanh (Stan) function is smooth, non-saturating, and has a trainable parameter. It can allow an easy flow of gradients and enable systematic scaling of the input-output mapping during training. Various forward problems to solve differential equations and inverse problems to find the parameters of differential equations demonstrate that the Stan activation function can achieve better training and more accurate predictions than the existing activation functions for PINN in the literature.

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 and provide a sufficient condition for the used heuristic to be rollout improving. 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.