Advancements in materials play a crucial role in technological progress. However, the process of discovering and developing materials with desired properties is often impeded by substantial experimental costs, extensive resource utilization, and lengthy development periods. To address these challenges, modern approaches often employ machine learning (ML) techniques such as Bayesian Optimization (BO), which streamline the search for optimal materials by iteratively selecting experiments that are most likely to yield beneficial results. However, traditional BO methods, while beneficial, often struggle with balancing the trade-off between exploration and exploitation, leading to sub-optimal performance in material discovery processes. This paper introduces a novel Threshold-Driven UCB-EI Bayesian Optimization (TDUE-BO) method, which dynamically integrates the strengths of Upper Confidence Bound (UCB) and Expected Improvement (EI) acquisition functions to optimize the material discovery process. Unlike the classical BO, our method focuses on efficiently navigating the high-dimensional material design space (MDS). TDUE-BO begins with an exploration-focused UCB approach, ensuring a comprehensive initial sweep of the MDS. As the model gains confidence, indicated by reduced uncertainty, it transitions to the more exploitative EI method, focusing on promising areas identified earlier. The UCB-to-EI switching policy dictated guided through continuous monitoring of the model uncertainty during each step of sequential sampling results in navigating through the MDS more efficiently while ensuring rapid convergence. The effectiveness of TDUE-BO is demonstrated through its application on three different material datasets, showing significantly better approximation and optimization performance over the EI and UCB-based BO methods in terms of the RMSE scores and convergence efficiency, respectively.

Hyperdimensional computing (HDC) is an emerging computing paradigm with significant promise for efficient and robust learning. In HDC, objects are encoded with high-dimensional vector symbolic sequences called hypervectors. The quality of hypervectors, defined by their distribution and independence, directly impacts the performance of HDC systems. Despite a large body of work on the processing parts of HDC systems, little to no attention has been paid to data encoding and the quality of hypervectors. Most prior studies have generated hypervectors using inherent random functions, such as MATLAB`s or Python`s random function. This work introduces an optimization technique for generating hypervectors by employing quasi-random sequences. These sequences have recently demonstrated their effectiveness in achieving accurate and low-discrepancy data encoding in stochastic computing systems. The study outlines the optimization steps for utilizing Sobol sequences to produce high-quality hypervectors in HDC systems. An optimization algorithm is proposed to select the most suitable Sobol sequences for generating minimally correlated hypervectors, particularly in applications related to symbol-oriented architectures. The performance of the proposed technique is evaluated in comparison to two traditional approaches of generating hypervectors based on linear-feedback shift registers and MATLAB random function. The evaluation is conducted for two applications: (i) language and (ii) headline classification. Our experimental results demonstrate accuracy improvements of up to 10.79%, depending on the vector size. Additionally, the proposed encoding hardware exhibits reduced energy consumption and a superior area-delay product.

Mathematically, a set of causal relations can be represented with a directed acyclic graph (DAG) where nodes are variables, and directed edges indicate direct causal effects. The goal of causal discovery is to recover the graph from the observed data. The data can either be interventional, where some variables were purposely manipulated, or purely observational, where there has been no manipulation. The challenge of causal discovery is the search for the true DAGs is NP-hard. Exact methods are intractable, even for modest numbers of variables [Chi96]. Yet datasets in fields like biology routinely involve thousands of variables [Dix+16]. To address this problem, Zheng et al. [Zhe+18] introduced Differentiable Causal Discovery (DCD), which formulates the DAG search as a continuous optimization over the space of all graph adjacency matrices. An essential element of this strategy is an acyclicity constraint, in the form of a penalty, that guides an otherwise unconstrained search toward acyclic graphs.

The performance of state-of-the-art machine learning models often deteriorates when testing on demographics that are under-represented in the training dataset. This problem has predominately been studied in a supervised learning setting where the data distribution is static. However, real-world applications often involve distribution shifts caused by the deployed models. For instance, the performance disparity against monitory users can lead to a high customer churn rate, thus the available data provided by active users are skewed due to the lack of minority users. This feedback effect further exacerbates the disparity among different demographic groups in future steps. To address this issue, we propose asymptotically fair participation as a condition to maintain long-term model performance over all demographic groups. In this work, we aim to address the problem of achieving asymptotically fair participation via optimal control formulation. Moreover, we design a surrogate retention system based on existing literature on evolutionary population dynamics to approximate the dynamics of distribution shifts on active user counts, from which the objective of achieving asymptotically fair participation is formulated as an optimal control problem, and the control variables are considered as the model parameters. We apply an efficient implementation of Pontryagin's maximum principle to estimate the optimal control solution. To evaluate the effectiveness of the proposed method, we design a generic simulation environment that simulates the population dynamics of the feedback effect between user retention and model performance. When we deploy the resulting models to the simulation environment, the optimal control solution accounts for long-term planning and leads to superior performance compared with existing baseline methods.

Machine learning assumes a pivotal role in our data-driven world. The increasing scale of models and datasets necessitates quick and reliable algorithms for model training. This dissertation investigates adaptivity in machine learning optimizers. The ensuing chapters are dedicated to various facets of adaptivity, including: 1. personalization and user-specific models via personalized loss, 2. provable post-training model adaptations via meta-learning, 3. learning unknown hyperparameters in real time via hyperparameter variance reduction, 4. fast O(1/k^2) global convergence of second-order methods via stepsized Newton method regardless of the initialization and choice basis, 5. fast and scalable second-order methods via low-dimensional updates. This thesis contributes novel insights, introduces new algorithms with improved convergence guarantees, and improves analyses of popular practical algorithms.

We propose integrating the edge-computing paradigm into the multi-robot collaborative scheduling to maximize resource utilization for complex collaborative tasks, which many robots must perform together. Examples include collaborative map-merging to produce a live global map during exploration instead of traditional approaches that schedule tasks on centralized cloud-based systems to facilitate computing. Our decentralized approach to a consensus-based scheduling strategy benefits a multi-robot-edge collaboration system by adapting to dynamic computation needs and communication-changing statistics as the system tries to optimize resources while maintaining overall performance objectives. Before collaborative task offloading, continuous device, and network profiling are performed at the computing resources, and the distributed scheduling scheme then selects the resource with maximum utility derived using a utility maximization approach. Thorough evaluations with and without edge servers on simulation and real-world multi-robot systems demonstrate that a lower task latency, a large throughput gain, and better frame rate processing may be achieved compared to the conventional edge-based systems.

The development of 6G/B5G wireless networks, which have requirements that go beyond current 5G networks, is gaining interest from academia and industry. However, to increase 6G/B5G network quality, conventional cellular networks that rely on terrestrial base stations are constrained geographically and economically. Meanwhile, NOMA allows multiple users to share the same resources, which improves the spectral efficiency of the system and has the advantage of supporting a larger number of users. Additionally, by intelligently manipulating the phase and amplitude of both the reflected and transmitted signals, STAR-RISs can achieve improved coverage, increased spectral efficiency, and enhanced communication reliability. However, STAR-RISs must simultaneously optimize the amplitude and phase shift corresponding to reflection and transmission, which makes the existing terrestrial networks more complicated and is considered a major challenging issue. Motivated by the above, we study the joint user pairing for NOMA and beamforming design of Multi-STAR-RISs in an indoor environment. Then, we formulate the optimization problem with the objective of maximizing the total throughput of MUs by jointly optimizing the decoding order, user pairing, active beamforming, and passive beamforming. However, the formulated problem is a MINLP. To address this challenge, we first introduce the decoding order for NOMA networks. Next, we decompose the original problem into two subproblems, namely: 1) MU pairing and 2) Beamforming optimization under the optimal decoding order. For the first subproblem, we employ correlation-based K-means clustering to solve the user pairing problem. Then, to jointly deal with beamforming vector optimizations, we propose MAPPO, which can make quick decisions in the given environment owing to its low complexity.

We prove an upper bound on the covering number of real algebraic varieties, images of polynomial maps and semialgebraic sets. The bound remarkably improves the best known general bound by Yomdin-Comte, and its proof is much more straightforward. As a consequence, our result gives new bounds on the volume of the tubular neighborhood of the image of a polynomial map and a semialgebraic set, where results for varieties by Lotz and Basu-Lerario are not directly applicable. We apply our theory to three main application domains. Firstly, we derive a near-optimal bound on the covering number of low rank CP tensors. Secondly, we prove a bound on the sketching dimension for (general) polynomial optimization problems. Lastly, we deduce generalization error bounds for deep neural networks with rational or ReLU activations, improving or matching the best known results in the literature.

The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. In this study, we delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on probability spaces. Our particular focus centers on the Wasserstein distance function, which serves as a relevant example. In contrast to the existing body of literature focused on approximating efficiently pointwise evaluations, we chart a new course to define functional approximants by adopting three machine learning-based approaches: 1. Solving a finite number of optimal transport problems and computing the corresponding Wasserstein potentials. 2. Employing empirical risk minimization with Tikhonov regularization in Wasserstein Sobolev spaces. 3. Addressing the problem through the saddle point formulation that characterizes the weak form of the Tikhonov functional's Euler-Lagrange equation. As a theoretical contribution, we furnish explicit and quantitative bounds on generalization errors for each of these solutions. In the proofs, we leverage the theory of metric Sobolev spaces and we combine it with techniques of optimal transport, variational calculus, and large deviation bounds. In our numerical implementation, we harness appropriately designed neural networks to serve as basis functions. These networks undergo training using diverse methodologies. This approach allows us to obtain approximating functions that can be rapidly evaluated after training. Consequently, our constructive solutions significantly enhance at equal accuracy the evaluation speed, surpassing that of state-of-the-art methods by several orders of magnitude.

The advent of predictive methodologies has catalyzed the emergence of data-driven decision support across various domains. However, developing models capable of effectively handling input time series data presents an enduring challenge. This study presents novel preference learning approaches to multiple criteria sorting problems in the presence of temporal criteria. We first formulate a convex quadratic programming model characterized by fixed time discount factors, operating within a regularization framework. To enhance scalability and accommodate learnable time discount factors, we introduce a novel monotonic Recurrent Neural Network (mRNN). It is designed to capture the evolving dynamics of preferences over time while upholding critical properties inherent to MCS problems, including criteria monotonicity, preference independence, and the natural ordering of classes. The proposed mRNN can describe the preference dynamics by depicting marginal value functions and personalized time discount factors along with time, effectively amalgamating the interpretability of traditional MCS methods with the predictive potential offered by deep preference learning models. Comprehensive assessments of the proposed models are conducted, encompassing synthetic data scenarios and a real-case study centered on classifying valuable users within a mobile gaming app based on their historical in-app behavioral sequences. Empirical findings underscore the notable performance improvements achieved by the proposed models when compared to a spectrum of baseline methods, spanning machine learning, deep learning, and conventional multiple criteria sorting approaches.