Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian manifold structure and performing optimization intrinsically on the manifold. This approach typically involves computing a search direction in the tangent space and updating variables via a retraction operation. However, as the size of the variables increases, the computational cost of the retraction can become prohibitively high, limiting the applicability of Riemannian optimization to large-scale problems. To address this challenge and enhance scalability, we propose a novel approach that restricts each update on a random submanifold, thereby significantly reducing the per-iteration complexity. We introduce two sampling strategies for selecting the random submanifolds and theoretically analyze the convergence of the proposed methods. We provide convergence results for general nonconvex functions and functions that satisfy Riemannian Polyak-Lojasiewicz condition as well as for stochastic optimization settings. Additionally, we demonstrate how our approach can be generalized to quotient manifolds derived from the orthogonal manifold. Extensive experiments verify the benefits of the proposed method, across a wide variety of problems.

Fairness in machine learning has become a critical concern, particularly in high-stakes applications. Existing approaches often focus on achieving full fairness across all score ranges generated by predictive models, ensuring fairness in both high and low-scoring populations. However, this stringent requirement can compromise predictive performance and may not align with the practical fairness concerns of stakeholders. In this work, we propose a novel framework for building partially fair machine learning models, which enforce fairness within a specific score range of interest, such as the middle range where decisions are most contested, while maintaining flexibility in other regions. We introduce two statistical metrics to rigorously evaluate partial fairness within a given score range, such as the top 20%-40% of scores. To achieve partial fairness, we propose an in-processing method by formulating the model training problem as constrained optimization with difference-of-convex constraints, which can be solved by an inexact difference-of-convex algorithm (IDCA). We provide the complexity analysis of IDCA for finding a nearly KKT point. Through numerical experiments on real-world datasets, we demonstrate that our framework achieves high predictive performance while enforcing partial fairness where it matters most.

High-stakes decisions in domains such as healthcare, energy, and public policy are often made by human experts using domain knowledge and heuristics, yet are increasingly supported by predictive and optimization-based tools. A dominant approach in operations research is the predict-then-optimize paradigm, where a predictive model estimates uncertain inputs, and an optimization model recommends a decision. However, this approach often lacks interpretability and can fail under distributional uncertainty -- particularly when the outcome distribution is multi-modal or complex -- leading to brittle or misleading decisions. In this paper, we introduce CREDO, a novel framework that quantifies, for any candidate decision, a distribution-free upper bound on the probability that the decision is suboptimal. By combining inverse optimization geometry with conformal prediction and generative modeling, CREDO produces risk certificates that are both statistically rigorous and practically interpretable. This framework enables human decision-makers to audit and validate their own decisions under uncertainty, bridging the gap between algorithmic tools and real-world judgment.

Accurately modeling the friction torque in robotic joints has long been challenging due to the request for a robust mathematical description. Traditional model-based approaches are often labor-intensive, requiring extensive experiments and expert knowledge, and they are difficult to adapt to new scenarios and dependencies. On the other hand, data-driven methods based on neural networks are easier to implement but often lack robustness, interpretability, and trustworthiness--key considerations for robotic hardware and safety-critical applications such as human-robot interaction. To address the limitations of both approaches, we propose the use of symbolic regression (SR) to estimate the friction torque. SR generates interpretable symbolic formulas similar to those produced by model-based methods while being flexible to accommodate various dynamic effects and dependencies. In this work, we apply SR algorithms to approximate the friction torque using collected data from a KUKA LWR-IV+ robot. Our results show that SR not only yields formulas with comparable complexity to model-based approaches but also achieves higher accuracy. Moreover, SR-derived formulas can be seamlessly extended to include load dependencies and other dynamic factors.

Meta-Black-Box Optimization (MetaBBO) garners attention due to its success in automating the configuration and generation of black-box optimizers, significantly reducing the human effort required for optimizer design and discovering optimizers with higher performance than classic human-designed optimizers. However, existing MetaBBO methods conduct one-off training under the assumption that a stationary problem distribution with extensive and representative training problem samples is pre-available. This assumption is often impractical in real-world scenarios, where diverse problems following shifting distribution continually arise. Consequently, there is a pressing need for methods that can continuously learn from new problems encountered on-the-fly and progressively enhance their capabilities. In this work, we explore a novel paradigm of lifelong learning in MetaBBO and introduce LiBOG, a novel approach designed to learn from sequentially encountered problems and generate high-performance optimizers for Black-Box Optimization (BBO). LiBOG consolidates knowledge both across tasks and within tasks to mitigate catastrophic forgetting. Extensive experiments demonstrate LiBOG's effectiveness in learning to generate high-performance optimizers in a lifelong learning manner, addressing catastrophic forgetting while maintaining plasticity to learn new tasks.

This thesis delves into the forefront of wireless communication by exploring the synergistic integration of three transformative technologies: STAR-RIS, CoMP, and NOMA. Driven by the ever-increasing demand for higher data rates, improved spectral efficiency, and expanded coverage in the evolving landscape of 6G development, this research investigates the potential of these technologies to revolutionize future wireless networks. The thesis analyzes the performance gains achievable through strategic deployment of STAR-RIS, focusing on mitigating inter-cell interference, enhancing signal strength, and extending coverage to cell-edge users. Resource sharing strategies for STAR-RIS elements are explored, optimizing both transmission and reflection functionalities. Analytical frameworks are developed to quantify the benefits of STAR-RIS assisted CoMP-NOMA networks under realistic channel conditions, deriving key performance metrics such as ergodic rates and outage probabilities. Additionally, the research delves into energy-efficient design approaches for CoMP-NOMA networks incorporating RIS, proposing novel RIS configurations and optimization algorithms to achieve a balance between performance and energy consumption. Furthermore, the application of Deep Reinforcement Learning (DRL) techniques for intelligent and adaptive optimization in aerial RIS-assisted CoMP-NOMA networks is explored, aiming to maximize network sum rate while meeting user quality of service requirements. Through a comprehensive investigation of these technologies and their synergistic potential, this thesis contributes valuable insights into the future of wireless communication, paving the way for the development of more efficient, reliable, and sustainable networks capable of meeting the demands of our increasingly connected world.

--Nowadays, Generative AI (GenAI) reshapes numerous domains by enabling machines to create content across modalities. As GenAI evolves into autonomous agents capable of reasoning, collaboration, and interaction, they are increasingly deployed on network infrastructures to serve humans automatically. This emerging paradigm, known as the agentic network, presents new optimization challenges due to the demand to incorporate subjective intents of human users expressed in natural language. Traditional generic Deep Reinforcement Learning (DRL) struggles to capture intent semantics and adjust policies dynamically, thus leading to suboptimality. First, we propose Intent-oriented Knowledge Distillation (IoKD), which efficiently distills intent-understanding capabilities from resource-intensive LAMs to lightweight edge LAMs (E-LAMs) to serve end users. Second, we develop Symbiotic Reinforcement Learning (SRL), integrating E-LAMs with a policy-based DRL framework. In SRL, E-LAMs translate natural language user intents into structured preference vectors that guide both state representation and reward design. The DRL, in turn, optimizes the generative service function chain composition and E-LAM selection based on real-time network conditions, thus optimizing the subjective Quality-of-Experience (QoE). Extensive experiments conducted in an agentic network with 81 agents demonstrate that IoKD reduces mean squared error in intent prediction by up to 22.5%, while SRL outperforms conventional generic DRL by up to 23.5% in maximizing intent-aware QoE. Generative AI (GenAI) has revolutionized the technological landscape, enabling machines to create content across multiple modalities, including text, images, and videos [1]. Moreover, GenAI is rapidly evolving from basic content generation to complex reasoning and decision-making, transforming how machines interact with and serve humans. G. Sun is with the College of Computer Science and Technology, Jilin University, China, and also with the College of Computing and Data Science, Nanyang Technological University, Singapore (e-mail: sungeng@jlu.edu.cn).

Constrained Bayesian optimization (CBO) methods have seen significant success in black-box optimization with constraints, and one of the most commonly used CBO methods is the constrained expected improvement (CEI) algorithm. CEI is a natural extension of the expected improvement (EI) when constraints are incorporated. However, the theoretical convergence rate of CEI has not been established. In this work, we study the convergence rate of CEI by analyzing its simple regret upper bound. First, we show that when the objective function $f$ and constraint function $c$ are assumed to each lie in a reproducing kernel Hilbert space (RKHS), CEI achieves the convergence rates of $\mathcal{O} \left(t^{-\frac{1}{2}}\log^{\frac{d+1}{2}}(t) \right) \ \text{and }\ \mathcal{O}\left(t^{\frac{-ν}{2ν+d}} \log^{\fracν{2ν+d}}(t)\right)$ for the commonly used squared exponential and Matérn kernels, respectively. Second, we show that when $f$ and $c$ are assumed to be sampled from Gaussian processes (GPs), CEI achieves the same convergence rates with a high probability. Numerical experiments are performed to validate the theoretical analysis.

Preferential Bayesian optimization (PBO) is a variant of Bayesian optimization that observes relative preferences (e.g., pairwise comparisons) instead of direct objective values, making it especially suitable for human-in-the-loop scenarios. However, real-world optimization tasks often involve inequality constraints, which existing PBO methods have not yet addressed. To fill this gap, we propose constrained preferential Bayesian optimization (CPBO), an extension of PBO that incorporates inequality constraints for the first time. Specifically, we present a novel acquisition function for this purpose. Our technical evaluation shows that our CPBO method successfully identifies optimal solutions by focusing on exploring feasible regions. As a practical application, we also present a designer-in-the-loop system for banner ad design using CPBO, where the objective is the designer's subjective preference, and the constraint ensures a target predicted click-through rate. We conducted a user study with professional ad designers, demonstrating the potential benefits of our approach in guiding creative design under real-world constraints.

End-to-end learning has become a widely applicable and studied problem in training predictive ML models to be aware of their impact on downstream decision-making tasks. These end-to-end models often outperform traditional methods that separate training from the optimization and only myopically focus on prediction error. However, the computational complexity of end-to-end frameworks poses a significant challenge, particularly for large-scale problems. While training an ML model using gradient descent, each time we need to compute a gradient we must solve an expensive optimization problem. We present a meta-optimization method that learns efficient algorithms to approximate optimization problems, dramatically reducing computational overhead of solving the decision problem in general, an aspect we leverage in the training within the end-to-end framework. Our approach introduces a neural network architecture that near-optimally solves optimization problems while ensuring feasibility constraints through alternate projections. We prove exponential convergence, approximation guarantees, and generalization bounds for our learning method. This method offers superior computational efficiency, producing high-quality approximations faster and scaling better with problem size compared to existing techniques. Our approach applies to a wide range of optimization problems including deterministic, single-stage as well as two-stage stochastic optimization problems. We illustrate how our proposed method applies to (1) an electricity generation problem using real data from an electricity routing company coordinating the movement of electricity throughout 13 states, (2) a shortest path problem with a computer vision task of predicting edge costs from terrain maps, (3) a two-stage multi-warehouse cross-fulfillment newsvendor problem, as well as a variety of other newsvendor-like problems.