Federated Learning (FL) is a learning paradigm that protects privacy by keeping client data on edge devices. However, optimizing FL in practice can be difficult due to the diversity and heterogeneity of the learning system. Despite recent research efforts to improve the optimization of heterogeneous data, the impact of time-evolving heterogeneous data in real-world scenarios, such as changing client data or intermittent clients joining or leaving during training, has not been studied well. In this work, we propose Continual Federated Learning (CFL), a flexible framework for capturing the time-evolving heterogeneity of FL. CFL can handle complex and realistic scenarios, which are difficult to evaluate in previous FL formulations, by extracting information from past local data sets and approximating local objective functions. We theoretically demonstrate that CFL methods have a faster convergence rate than FedAvg in time-evolving scenarios, with the benefit depending on approximation quality. Through experiments, we show that our numerical findings match the convergence analysis and that CFL methods significantly outperform other state-of-the-art FL baselines.

The sole aim of this book is to give a self-contained introduction to concepts and mathematical tools in Bayesian matrix decomposition in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning Bayesian matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of variational inference for conducting the optimization. We refer the reader to literature in the field of Bayesian analysis for a more detailed introduction to the related fields. This book is primarily a summary of purpose, significance of important Bayesian matrix decomposition methods, e.g., real-valued decomposition, nonnegative matrix factorization, Bayesian interpolative decomposition, and the origin and complexity of the methods which shed light on their applications. The mathematical prerequisite is a first course in statistics and linear algebra. Other than this modest background, the development is self-contained, with rigorous proof provided throughout.

Policy optimization methods are popular reinforcement learning algorithms in practice. Recent works have built theoretical foundation for them by proving $\sqrt{T}$ regret bounds even when the losses are adversarial. Such bounds are tight in the worst case but often overly pessimistic. In this work, we show that in tabular Markov decision processes (MDPs), by properly designing the regularizer, the exploration bonus and the learning rates, one can achieve a more favorable polylog$(T)$ regret when the losses are stochastic, without sacrificing the worst-case guarantee in the adversarial regime. To our knowledge, this is also the first time a gap-dependent polylog$(T)$ regret bound is shown for policy optimization. Specifically, we achieve this by leveraging a Tsallis entropy or a Shannon entropy regularizer in the policy update. Then we show that under known transitions, we can further obtain a first-order regret bound in the adversarial regime by leveraging the log-barrier regularizer.

Bilevel optimization recently has attracted increased interest in machine learning due to its many applications such as hyper-parameter optimization and meta learning. Although many bilevel methods recently have been proposed, these methods do not consider using adaptive learning rates. It is well known that adaptive learning rates can accelerate optimization algorithms. To fill this gap, in the paper, we propose a novel fast adaptive bilevel framework to solve stochastic bilevel optimization problems that the outer problem is possibly nonconvex and the inner problem is strongly convex. Our framework uses unified adaptive matrices including many types of adaptive learning rates, and can flexibly use the momentum and variance reduced techniques. In particular, we provide a useful convergence analysis framework for the bilevel optimization. Specifically, we propose a fast single-loop adaptive bilevel optimization (BiAdam) algorithm, which achieves a sample complexity of $\tilde{O}(\epsilon^{-4})$ for finding an $\epsilon$-stationary solution. Meanwhile, we propose an accelerated version of BiAdam algorithm (VR-BiAdam), which reaches the best known sample complexity of $\tilde{O}(\epsilon^{-3})$. To the best of our knowledge, we first study the adaptive bilevel optimization methods with adaptive learning rates. Experimental results on data hyper-cleaning and hyper-representation learning tasks demonstrate the efficiency of our algorithms.

We develop an algorithmic framework for solving convex optimization problems using no-regret game dynamics. By converting the problem of minimizing a convex function into an auxiliary problem of solving a min-max game in a sequential fashion, we can consider a range of strategies for each of the two-players who must select their actions one after the other. A common choice for these strategies are so-called no-regret learning algorithms, and we describe a number of such and prove bounds on their regret. We then show that many classical first-order methods for convex optimization -- including average-iterate gradient descent, the Frank-Wolfe algorithm, Nesterov's acceleration methods, and the accelerated proximal method -- can be interpreted as special cases of our framework as long as each player makes the correct choice of no-regret strategy. Proving convergence rates in this framework becomes very straightforward, as they follow from plugging in the appropriate known regret bounds. Our framework also gives rise to a number of new first-order methods for special cases of convex optimization that were not previously known.

A basic task in the design of an industrial robot application is the relative placement of robot and workpiece. Process points are defined in Cartesian coordinates relative to the workpiece coordinate system, and the workpiece has to be located such that the robot can reach all points. Finding such a location is still an iterative procedure based on the developers' intuition. One difficulty is the choice of one of the several solutions of the backward transform of a typical 6R robot. We present a novel algorithm that simultaneously optimizes the workpiece location and the robot configuration at all process points using higher order optimization algorithms. A key ingredient is the extension of the robot with a virtual prismatic axis. The practical feasibility of the approach is shown with an example using a commercial industrial robot.

The choice of optimization algorithm can depend on several factors, including the specific problem you're trying to solve, the size and complexity of your dataset, and the resources (such as computational power and memory) that you have available.

Future AI applications require performance, reliability and privacy that the existing, cloud-dependant system architectures cannot provide. In this article, we study orchestration in the device-edge-cloud continuum, and focus on edge AI for resource orchestration. We claim that to support the constantly growing requirements of intelligent applications in the device-edge-cloud computing continuum, resource orchestration needs to embrace edge AI and emphasize local autonomy and intelligence. To justify the claim, we provide a general definition for continuum orchestration, and look at how current and emerging orchestration paradigms are suitable for the computing continuum. We describe certain major emerging research themes that may affect future orchestration, and provide an early vision of an orchestration paradigm that embraces those research themes. Finally, we survey current key edge AI methods and look at how they may contribute into fulfilling the vision of future continuum orchestration.

Data-driven materials design often encounters challenges where systems require or possess qualitative (categorical) information. Metal-organic frameworks (MOFs) are an example of such material systems. The representation of MOFs through different building blocks makes it a challenge for designers to incorporate qualitative information into design optimization. Furthermore, the large number of potential building blocks leads to a combinatorial challenge, with millions of possible MOFs that could be explored through time consuming physics-based approaches. In this work, we integrated Latent Variable Gaussian Process (LVGP) and Multi-Objective Batch-Bayesian Optimization (MOBBO) to identify top-performing MOFs adaptively, autonomously, and efficiently without any human intervention. Our approach provides three main advantages: (i) no specific physical descriptors are required and only building blocks that construct the MOFs are used in global optimization through qualitative representations, (ii) the method is application and property independent, and (iii) the latent variable approach provides an interpretable model of qualitative building blocks with physical justification. To demonstrate the effectiveness of our method, we considered a design space with more than 47,000 MOF candidates. By searching only ~1% of the design space, LVGP-MOBBO was able to identify all MOFs on the Pareto front and more than 97% of the 50 top-performing designs for the CO$_2$ working capacity and CO$_2$/N$_2$ selectivity properties. Finally, we compared our approach with the Random Forest algorithm and demonstrated its efficiency, interpretability, and robustness.

Learning the underlying Bayesian Networks (BNs), represented by directed acyclic graphs (DAGs), of the concerned events from purely-observational data is a crucial part of evidential reasoning. This task remains challenging due to the large and discrete search space. A recent flurry of developments followed NOTEARS[1] recast this combinatorial problem into a continuous optimization problem by leveraging an algebraic equality characterization of acyclicity. However, the continuous optimization methods suffer from obtaining non-spare graphs after the numerical optimization, which leads to the inflexibility to rule out the potentially cycle-inducing edges or false discovery edges with small values. To address this issue, in this paper, we develop a completely data-driven DAG structure learning method without a predefined value to post-threshold small values. We name our method NOTEARS with adaptive Lasso (NOTEARS-AL), which is achieved by applying the adaptive penalty method to ensure the sparsity of the estimated DAG. Moreover, we show that NOTEARS-AL also inherits the oracle properties under some specific conditions. Extensive experiments on both synthetic and a real-world dataset demonstrate that our method consistently outperforms NOTEARS.