Bayesian optimization (BO) is increasingly employed in critical applications such as materials design and drug discovery. An increasingly popular strategy in BO is to forgo the sole reliance on high-fidelity data and instead use an ensemble of information sources which provide inexpensive low-fidelity data. The overall premise of this strategy is to reduce the overall sampling costs by querying inexpensive low-fidelity sources whose data are correlated with high-fidelity samples. Here, we propose a multi-fidelity cost-aware BO framework that dramatically outperforms the state-of-the-art technologies in terms of efficiency, consistency, and robustness. We demonstrate the advantages of our framework on analytic and engineering problems and argue that these benefits stem from our two main contributions: (1) we develop a novel acquisition function for multi-fidelity cost-aware BO that safeguards the convergence against the biases of low-fidelity data, and (2) we tailor a newly developed emulator for multi-fidelity BO which enables us to not only simultaneously learn from an ensemble of multi-fidelity datasets, but also identify the severely biased low-fidelity sources that should be excluded from BO.

Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice, most lack guarantees on reductions in condition number. Moreover, the degree to which we can improve over existing heuristic preconditioners remains an important practical question. In this paper, we study the problem of optimal diagonal preconditioning that achieves maximal reduction in the condition number of any full-rank matrix by scaling its rows and/or columns. We first reformulate the problem as a quasi-convex problem and provide a simple algorithm based on bisection. Then we develop an interior point algorithm with $O(\log(1/\epsilon))$ iteration complexity, where each iteration consists of a Newton update based on the Nesterov-Todd direction. Next, we specialize to one-sided optimal diagonal preconditioning problems, and demonstrate that they can be formulated as standard dual SDP problems. We then develop efficient customized solvers and study the empirical performance of our optimal diagonal preconditioning procedures through extensive experiments on large matrices. Our findings suggest that optimal diagonal preconditioners can significantly improve upon existing heuristics-based diagonal preconditioners at reducing condition numbers and speeding up iterative methods. Moreover, our implementation of customized solvers, combined with a random row/column sampling step, can find near-optimal diagonal preconditioners for matrices up to size 200,000 in reasonable time, demonstrating their practical appeal.

Recently, Neural architecture search has achieved great success on classification tasks for mobile devices. The backbone network for object detection is usually obtained on the image classification task. However, the architecture which is searched through the classification task is sub-optimal because of the gap between the task of image and object detection. As while work focuses on backbone network architecture search for mobile device object detection is limited, mainly because the backbone always requires expensive ImageNet pre-training. Accordingly, it is necessary to study the approach of network architecture search for mobile device object detection without expensive pre-training. In this work, we propose a mobile object detection backbone network architecture search algorithm which is a kind of evolutionary optimized method based on non-dominated sorting for NAS scenarios. It can quickly search to obtain the backbone network architecture within certain constraints. It better solves the problem of suboptimal linear combination accuracy and computational cost. The proposed approach can search the backbone networks with different depths, widths, or expansion sizes via a technique of weight mapping, making it possible to use NAS for mobile devices detection tasks a lot more efficiently. In our experiments, we verify the effectiveness of the proposed approach on YoloX-Lite, a lightweight version of the target detection framework. Under similar computational complexity, the accuracy of the backbone network architecture we search for is 2.0% mAP higher than MobileDet. Our improved backbone network can reduce the computational effort while improving the accuracy of the object detection network. To prove its effectiveness, a series of ablation studies have been carried out and the working mechanism has been analyzed in detail.

Finding global optima in high-dimensional optimization problems is extremely challenging since the number of function evaluations required to sufficiently explore the search space increases exponentially with its dimensionality. Furthermore, multimodal cost functions render local gradient-based search techniques ineffective. To overcome these difficulties, we propose to trim uninteresting regions of the search space where global optima are unlikely to be found by means of autoencoders, exploiting the lower intrinsic dimensionality of certain cost functions; optima are then searched over lower-dimensional latent spaces. The methodology is tested on benchmark functions and on multiple variations of a structural topology optimization problem, where we show that we can estimate this intrinsic lower dimensionality and based thereon obtain the global optimum at best or superior results compared to established optimization procedures at worst.

Automated machine learning (AutoML) usually involves several crucial components, such as Data Augmentation (DA) policy, Hyper-Parameter Optimization (HPO), and Neural Architecture Search (NAS). Although many strategies have been developed for automating these components in separation, joint optimization of these components remains challenging due to the largely increased search dimension and the variant input types of each component. In parallel to this, the common practice of searching for the optimal architecture first and then retraining it before deployment in NAS often suffers from low performance correlation between the searching and retraining stages. An end-to-end solution that integrates the AutoML components and returns a ready-to-use model at the end of the search is desirable. In view of these, we propose DHA, which achieves joint optimization of Data augmentation policy, Hyper-parameter and Architecture. Specifically, end-to-end NAS is achieved in a differentiable manner by optimizing a compressed lower-dimensional feature space, while DA policy and HPO are regarded as dynamic schedulers, which adapt themselves to the update of network parameters and network architecture at the same time. Experiments show that DHA achieves state-of-the-art (SOTA) results on various datasets and search spaces. To the best of our knowledge, we are the first to efficiently and jointly optimize DA policy, NAS, and HPO in an end-to-end manner without retraining.

The Self-Optimization (SO) model is a useful computational model for investigating self-organization in "soft" Artificial life (ALife) as it has been shown to be general enough to model various complex adaptive systems. So far, existing work has been done on relatively small network sizes, precluding the investigation of novel phenomena that might emerge from the complexity arising from large numbers of nodes interacting in interconnected networks. This work introduces a novel implementation of the SO model that scales as $\mathcal{O}\left(N^{2}\right)$ with respect to the number of nodes $N$, and demonstrates the applicability of the SO model to networks with system sizes several orders of magnitude higher than previously was investigated. Removing the prohibitive computational cost of the naive $\mathcal{O}\left(N^{3}\right)$ algorithm, our on-the-fly computation paves the way for investigating substantially larger system sizes, allowing for more variety and complexity in future studies.

We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular policy parametrizations. For a variety of NPGs and reward functions we show that the trajectories in state-action space are solutions of gradient flows with respect to Hessian geometries, based on which we obtain global convergence guarantees and convergence rates. In particular, we show linear convergence for unregularized and regularized NPG flows with the metrics proposed by Kakade and Morimura and co-authors by observing that these arise from the Hessian geometries of conditional entropy and entropy respectively. Further, we obtain sublinear convergence rates for Hessian geometries arising from other convex functions like log-barriers. Finally, we interpret the discrete-time NPG methods with regularized rewards as inexact Newton methods if the NPG is defined with respect to the Hessian geometry of the regularizer. This yields local quadratic convergence rates of these methods for step size equal to the penalization strength.

Gradient compression is a popular technique for improving communication complexity of stochastic first-order methods in distributed training of machine learning models. However, the existing works consider only with-replacement sampling of stochastic gradients. In contrast, it is well-known in practice and recently confirmed in theory that stochastic methods based on without-replacement sampling, e.g., Random Reshuffling (RR) method, perform better than ones that sample the gradients with-replacement. In this work, we close this gap in the literature and provide the first analysis of methods with gradient compression and without-replacement sampling. We first develop a na\"ive combination of random reshuffling with gradient compression (Q-RR). Perhaps surprisingly, but the theoretical analysis of Q-RR does not show any benefits of using RR. Our extensive numerical experiments confirm this phenomenon. This happens due to the additional compression variance. To reveal the true advantages of RR in the distributed learning with compression, we propose a new method called DIANA-RR that reduces the compression variance and has provably better convergence rates than existing counterparts with with-replacement sampling of stochastic gradients. Next, to have a better fit to Federated Learning applications, we incorporate local computation, i.e., we propose and analyze the variants of Q-RR and DIANA-RR -- Q-NASTYA and DIANA-NASTYA that use local gradient steps and different local and global stepsizes. Finally, we conducted several numerical experiments to illustrate our theoretical results.

Simultaneous Localization & Mapping (SLAM) is the process of building a mutual relationship between localization and mapping of the subject in its surrounding environment. With the help of different sensors, various types of SLAM systems have developed to deal with the problem of building the relationship between localization and mapping. A limitation in the SLAM process is the lack of consideration of dynamic objects in the mapping of the environment. We propose the Dynamic Object Tracking SLAM (DyOb-SLAM), which is a Visual SLAM system that can localize and map the surrounding dynamic objects in the environment as well as track the dynamic objects in each frame. With the help of a neural network and a dense optical flow algorithm, dynamic objects and static objects in an environment can be differentiated. DyOb-SLAM creates two separate maps for both static and dynamic contents. For the static features, a sparse map is obtained. For the dynamic contents, a trajectory global map is created as output. As a result, a frame to frame real-time based dynamic object tracking system is obtained. With the pose calculation of the dynamic objects and camera, DyOb-SLAM can estimate the speed of the dynamic objects with time. The performance of DyOb-SLAM is observed by comparing it with a similar Visual SLAM system, VDO-SLAM and the performance is measured by calculating the camera and object pose errors as well as the object speed error.

Metasurfaces (MTSs) are increasingly emerging as enabling technologies to meet the demands for multi-functional, small form-factor, efficient, reconfigurable, tunable, and low-cost radio-frequency (RF) components because of their ability to manipulate waves in a sub-wavelength thickness through modified boundary conditions. They enable the design of reconfigurable intelligent surfaces (RISs) for adaptable wireless channels and smart radio environments, wherein the inherently stochastic nature of the wireless environment is transformed into a programmable propagation channel. In particular, space-limited RF applications, such as communications and radar, that have strict radiation requirements are currently being investigated for potential RIS deployment. The RIS comprises sub-wavelength units or meta-atoms, which are independently controlled and whose geometry and material determine the spectral response of the RIS. Conventionally, designing RIS to yield the desired EM response requires trial and error by iteratively investigating a large possibility of various geometries and materials through thousands of full-wave EM simulations. In this context, machine/deep learning (ML/DL) techniques are proving critical in reducing the computational cost and time of RIS inverse design. Instead of explicitly solving Maxwell's equations, DL models learn physics-based relationships through supervised training data. The ML/DL techniques also aid in RIS deployment for numerous wireless applications, which requires dealing with multiple channel links between the base station (BS) and the users. As a result, the BS and RIS beamformers require a joint design, wherein the RIS elements must be rapidly reconfigured. This chapter provides a synopsis of DL techniques for both inverse RIS design and RIS-assisted wireless systems.