Bayesian optimization is a powerful tool for optimizing an expensive-to-evaluate black-box function. In particular, the effectiveness of expected improvement (EI) has been demonstrated in a wide range of applications. However, theoretical analyses of EI are limited compared with other theoretically established algorithms. This paper analyzes a randomized variant of EI, which evaluates the EI from the maximum of the posterior sample path. We show that this posterior sampling-based random EI achieves the sublinear Bayesian cumulative regret bounds under the assumption that the black-box function follows a Gaussian process. Finally, we demonstrate the effectiveness of the proposed method through numerical experiments.

In multi-source learning with discrete labels, distributional heterogeneity across domains poses a central challenge to developing predictive models that transfer reliably to unseen domains. We study multi-source unsupervised domain adaptation, where labeled data are drawn from multiple source domains and only unlabeled data from a target domain. To address potential distribution shifts, we propose a novel Conditional Group Distributionally Robust Optimization (CG-DRO) framework that learns a classifier by minimizing the worst-case cross-entropy loss over the convex combinations of the conditional outcome distributions from the sources. To solve the resulting minimax problem, we develop an efficient Mirror Prox algorithm, where we employ a double machine learning procedure to estimate the risk function. This ensures that the errors of the machine learning estimators for the nuisance models enter only at higher-order rates, thereby preserving statistical efficiency under covariate shift. We establish fast statistical convergence rates for the estimator by constructing two surrogate minimax optimization problems that serve as theoretical bridges. A distinguishing challenge for CG-DRO is the emergence of nonstandard asymptotics: the empirical estimator may fail to converge to a standard limiting distribution due to boundary effects and system instability. To address this, we introduce a perturbation-based inference procedure that enables uniformly valid inference, including confidence interval construction and hypothesis testing.

We introduce a new framework of episodic tabular Markov decision processes (MDPs) with adversarial preferences, which we refer to as preference-based MDPs (PbMDPs). Unlike standard episodic MDPs with adversarial losses, where the numerical value of the loss is directly observed, in PbMDPs the learner instead observes preferences between two candidate arms, which represent the choices being compared. In this work, we focus specifically on the setting where the reward functions are determined by Borda scores. We begin by establishing a regret lower bound for PbMDPs with Borda scores. As a preliminary step, we present a simple instance to prove a lower bound of $Ω(\sqrt{HSAT})$ for episodic MDPs with adversarial losses, where $H$ is the number of steps per episode, $S$ is the number of states, $A$ is the number of actions, and $T$ is the number of episodes. Leveraging this construction, we then derive a regret lower bound of $Ω( (H^2 S K)^{1/3} T^{2/3} )$ for PbMDPs with Borda scores, where $K$ is the number of arms. Next, we develop algorithms that achieve a regret bound of order $T^{2/3}$. We first propose a global optimization approach based on online linear optimization over the set of all occupancy measures, achieving a regret bound of $\tilde{O}((H^2 S^2 K)^{1/3} T^{2/3} )$ under known transitions. However, this approach suffers from suboptimal dependence on the potentially large number of states $S$ and computational inefficiency. To address this, we propose a policy optimization algorithm whose regret is roughly bounded by $\tilde{O}( (H^6 S K^5)^{1/3} T^{2/3} )$ under known transitions, and further extend the result to the unknown-transition setting.

Automating the formulation of decision-making problems represents a major step toward fully autonomous decision-support systems. Traditionally, solving such problems involves two sequential stages: first, translating real-world scenarios into well-defined mathematical models-an essential skill emphasized in operations research education-and second, applying computational tools to find optimal or near-optimal solutions. While substantial research in recent decades has primarily focused on the second stage-enhancing algorithms and improving solver efficiency-advancements span a wide range, from foundational developments such as reinforcement learning (RL) frameworks (e.g., Sutton and Barto 2018) and approximate dynamic programming techniques (e.g., Powell 2011), to powerful solvers like COPT, CPLEX, and Gurobi. Such innovations coupled with increasing computational power have led to high-impact real-world applications, exemplified by AlphaGo, which leveraged deep learning and RL to solve complex, large-scale decision-making problems (Silver et al. 2016). That said, while these advancements have shifted many computational tasks to automated software, the initial problem formulation step has largely remained manual and dependent on expert knowledge. The recent rapid progress in large language models (LLMs) provides a promising opportunity to automate this crucial first step. LLMs excel in natural language processing and have demonstrated significant potential for effectively automating the formulation of mathematical models directly from plain English descriptions. Leveraging LLMs can substantially reduce the human expertise required, simplify the problem formulation process, and make advanced optimization methods accessible to a broader audience. Among various optimization problems, dynamic programming (DP) represents a particularly important yet challenging category for formulation automation.

Highway on-ramp merging areas are common bottlenecks to traffic congestion and accidents. Currently, a cooperative control strategy based on connected and automated vehicles (CAVs) is a fundamental solution to this problem. While CAVs are not fully widespread, it is necessary to propose a hierarchical cooperative on-ramp merging control (HCOMC) framework for heterogeneous traffic flow on two-lane highways to address this gap. This paper extends longitudinal car-following models based on the intelligent driver model and lateral lane-changing models using the quintic polynomial curve to account for human-driven vehicles (HDVs) and CAVs, comprehensively considering human factors and cooperative adaptive cruise control. Besides, this paper proposes a HCOMC framework, consisting of a hierarchical cooperative planning model based on the modified virtual vehicle model, a discretionary lane-changing model based on game theory, and a multi-objective optimization model using the elitist non-dominated sorting genetic algorithm to ensure the safe, smooth, and efficient merging process. Then, the performance of our HCOMC is analyzed under different traffic densities and CAV penetration rates through simulation. The findings underscore our HCOMC's pronounced comprehensive advantages in enhancing the safety of group vehicles, stabilizing and expediting merging process, optimizing traffic efficiency, and economizing fuel consumption compared with benchmarks.

Text-to-audio models have recently emerged as a powerful technology for generating sound from textual descriptions. However, their high computational demands raise concerns about energy consumption and environmental impact. In this paper, we conduct an analysis of the energy usage of 7 state-of-the-art text-to-audio diffusion-based generative models, evaluating to what extent variations in generation parameters affect energy consumption at inference time. We also aim to identify an optimal balance between audio quality and energy consumption by considering Pareto-optimal solutions across all selected models. Our findings provide insights into the trade-offs between performance and environmental impact, contributing to the development of more efficient generative audio models.

Trajectory planning involving multi-agent interactions has been a long-standing challenge in the field of robotics, primarily burdened by the inherent yet intricate interactions among agents. While game-theoretic methods are widely acknowledged for their effectiveness in managing multi-agent interactions, significant impediments persist when it comes to accommodating the intentional uncertainties of agents. In the context of intentional uncertainties, the heavy computational burdens associated with existing game-theoretic methods are induced, leading to inefficiencies and poor scalability. In this paper, we propose a novel game-theoretic interactive trajectory planning method to effectively address the intentional uncertainties of agents, and it demonstrates both high efficiency and enhanced scalability. As the underpinning basis, we model the interactions between agents under intentional uncertainties as a general Bayesian game, and we show that its agent-form equivalence can be represented as a potential game under certain minor assumptions. The existence and attainability of the optimal interactive trajectories are illustrated, as the corresponding Bayesian Nash equilibrium can be attained by optimizing a unified optimization problem. Additionally, we present a distributed algorithm based on the dual consensus alternating direction method of multipliers (ADMM) tailored to the parallel solving of the problem, thereby significantly improving the scalability. The attendant outcomes from simulations and experiments demonstrate that the proposed method is effective across a range of scenarios characterized by general forms of intentional uncertainties. Its scalability surpasses that of existing centralized and decentralized baselines, allowing for real-time interactive trajectory planning in uncertain game settings.

In this paper, we present enhanced analysis for sign-based optimization algorithms with momentum updates. Traditional sign-based methods, under the separable smoothness assumption, guarantee a convergence rate of $\mathcal{O}(T^{-1/4})$, but they either require large batch sizes or assume unimodal symmetric stochastic noise. To address these limitations, we demonstrate that signSGD with momentum can achieve the same convergence rate using constant batch sizes without additional assumptions. Our analysis, under the standard $l_2$-smoothness condition, improves upon the result of the prior momentum-based signSGD method by a factor of $\mathcal{O}(d^{1/2})$, where $d$ is the problem dimension. Furthermore, we explore sign-based methods with majority vote in distributed settings and show that the proposed momentum-based method yields convergence rates of $\mathcal{O}\left( d^{1/2}T^{-1/2} + dn^{-1/2} \right)$ and $\mathcal{O}\left( \max \{ d^{1/4}T^{-1/4}, d^{1/10}T^{-1/5} \} \right)$, which outperform the previous results of $\mathcal{O}\left( dT^{-1/4} + dn^{-1/2} \right)$ and $\mathcal{O}\left( d^{3/8}T^{-1/8} \right)$, respectively. Numerical experiments further validate the effectiveness of the proposed methods.

This thesis addresses challenges related to data and parameter efficiency in neural language models, with a focus on representation analysis and the introduction of new optimization techniques. The first part examines the properties and dynamics of language representations within neural models, emphasizing their significance in enhancing robustness and generalization. It proposes innovative approaches based on representation smoothness, including regularization strategies that utilize Jacobian and Hessian matrices to stabilize training and mitigate sensitivity to input perturbations. The second part focuses on methods to significantly enhance data and parameter efficiency by integrating active learning strategies with parameter-efficient fine-tuning, guided by insights from representation smoothness analysis. It presents smoothness-informed early-stopping techniques designed to eliminate the need for labeled validation sets and proposes innovative combinations of active learning and parameter-efficient fine-tuning to reduce labeling efforts and computational resources. Extensive experimental evaluations across various NLP tasks demonstrate that these combined approaches substantially outperform traditional methods in terms of performance, stability, and efficiency. The third part explores weak supervision techniques enhanced by in-context learning to effectively utilize unlabeled data, further reducing dependence on extensive labeling. It shows that using in-context learning as a mechanism for weak supervision enables models to better generalize from limited labeled data by leveraging unlabeled examples more effectively during training. Comprehensive empirical evaluations confirm significant gains in model accuracy, adaptability, and robustness, especially in low-resource settings and dynamic data environments.

A methodology is developed, based on nonparametric Bayesian dictionary learning, for joint space-time wind field data extrapolation and estimation of related statistics by relying on limited/incomplete measurements. Specifically, utilizing sparse/incomplete measured data, a time-dependent optimization problem is formulated for determining the expansion coefficients of an associated low-dimensional representation of the stochastic wind field. Compared to an alternative, standard, compressive sampling treatment of the problem, the developed methodology exhibits the following advantages. First, the Bayesian formulation enables also the quantification of the uncertainty in the estimates. Second, the requirement in standard CS-based applications for an a priori selection of the expansion basis is circumvented. Instead, this is done herein in an adaptive manner based on the acquired data. Overall, the methodology exhibits enhanced extrapolation accuracy, even in cases of high-dimensional data of arbitrary form, and of relatively large extrapolation distances. Thus, it can be used, potentially, in a wide range of wind engineering applications where various constraints dictate the use of a limited number of sensors. The efficacy of the methodology is demonstrated by considering two case studies. The first relates to the extrapolation of simulated wind velocity records consistent with a prescribed joint wavenumber-frequency power spectral density in a three-dimensional domain (2D and time). The second pertains to the extrapolation of four-dimensional (3D and time) boundary layer wind tunnel experimental data that exhibit significant spatial variability and non-Gaussian characteristics.