We investigate the in-distribution generalization of machine learning algorithms. We depart from traditional complexity-based approaches by analyzing information-theoretic bounds that quantify the dependence between a learning algorithm and the training data. We consider two categories of generalization guarantees: 1) Guarantees in expectation: These bounds measure performance in the average case. Here, the dependence between the algorithm and the data is often captured by information measures. While these measures offer an intuitive interpretation, they overlook the geometry of the algorithm's hypothesis class. Here, we introduce bounds using the Wasserstein distance to incorporate geometry, and a structured, systematic method to derive bounds capturing the dependence between the algorithm and an individual datum, and between the algorithm and subsets of the training data. 2) PAC-Bayesian guarantees: These bounds measure the performance level with high probability. Here, the dependence between the algorithm and the data is often measured by the relative entropy. We establish connections between the Seeger--Langford and Catoni's bounds, revealing that the former is optimized by the Gibbs posterior. We introduce novel, tighter bounds for various types of loss functions. To achieve this, we introduce a new technique to optimize parameters in probabilistic statements. To study the limitations of these approaches, we present a counter-example where most of the information-theoretic bounds fail while traditional approaches do not. Finally, we explore the relationship between privacy and generalization. We show that algorithms with a bounded maximal leakage generalize. For discrete data, we derive new bounds for differentially private algorithms that guarantee generalization even with a constant privacy parameter, which is in contrast to previous bounds in the literature.

Recent studies show that well-devised perturbations on graph structures or node features can mislead trained Graph Neural Network (GNN) models. However, these methods often overlook practical assumptions, over-rely on heuristics, or separate vital attack components. In response, we present GAIM, an integrated adversarial attack method conducted on a node feature basis while considering the strict black-box setting. Specifically, we define an adversarial influence function to theoretically assess the adversarial impact of node perturbations, thereby reframing the GNN attack problem into the adversarial influence maximization problem. In our approach, we unify the selection of the target node and the construction of feature perturbations into a single optimization problem, ensuring a unique and consistent feature perturbation for each target node. We leverage a surrogate model to transform this problem into a solvable linear programming task, streamlining the optimization process. Moreover, we extend our method to accommodate label-oriented attacks, broadening its applicability. Thorough evaluations on five benchmark datasets across three popular models underscore the effectiveness of our method in both untargeted and label-oriented targeted attacks. Through comprehensive analysis and ablation studies, we demonstrate the practical value and efficacy inherent to our design choices.

Recent research in Meta-Black-Box Optimization (MetaBBO) have shown that meta-trained neural networks can effectively guide the design of black-box optimizers, significantly reducing the need for expert tuning and delivering robust performance across complex problem distributions. Despite their success, a paradox remains: MetaBBO still rely on human-crafted Exploratory Landscape Analysis features to inform the meta-level agent about the low-level optimization progress. To address the gap, this paper proposes Neural Exploratory Landscape Analysis (NeurELA), a novel framework that dynamically profiles landscape features through a two-stage, attention-based neural network, executed in an entirely end-to-end fashion. NeurELA is pre-trained over a variety of MetaBBO algorithms using a multi-task neuroevolution strategy. Extensive experiments show that NeurELA achieves consistently superior performance when integrated into different and even unseen MetaBBO tasks and can be efficiently fine-tuned for further performance boost. This advancement marks a pivotal step in making MetaBBO algorithms more autonomous and broadly applicable.

Motion planning is a key aspect of robotics. A common approach to address motion planning problems is trajectory optimization. Trajectory optimization can represent the high-level behaviors of robots through mathematical formulations. However, current trajectory optimization approaches have two main challenges. Firstly, their solution heavily depends on the initial guess, and they are prone to get stuck in local minima. Secondly, they face scalability limitations by increasing the number of constraints. This thesis endeavors to tackle these challenges by introducing four innovative trajectory optimization algorithms to improve reliability, scalability, and computational efficiency. There are two novel aspects of the proposed algorithms. The first key innovation is remodeling the kinematic constraints and collision avoidance constraints. Another key innovation lies in the design of algorithms that effectively utilize parallel computation on GPU accelerators. By using reformulated constraints and leveraging the computational power of GPUs, the proposed algorithms of this thesis demonstrate significant improvements in efficiency and scalability compared to the existing methods. Parallelization enables faster computation times, allowing for real-time decision-making in dynamic environments. Moreover, the algorithms are designed to adapt to changes in the environment, ensuring robust performance. Extensive benchmarking for each proposed optimizer validates their efficacy. Overall, this thesis makes a significant contribution to the field of trajectory optimization algorithms. It introduces innovative solutions that specifically address the challenges faced by existing methods. The proposed algorithms pave the way for more efficient and robust motion planning solutions in robotics by leveraging parallel computation and specific mathematical structures.

Speech modeling methods learn one embedding for a fixed segment of speech, typically in between 10-25 ms. The information present in speech can be divided into two categories: "what is being said" (content) and "how it is expressed" (other) and these two are orthogonal in nature causing the optimization algorithm to find a sub-optimal solution if forced to optimize together. This leads to sub-optimal performance in one or all downstream tasks as shown by previous studies. Current self-supervised learning (SSL) methods such as HuBERT are very good at modeling the content information present in speech. Data augmentation improves the performance on tasks which require effective modeling of other information but this leads to a divided capacity of the model. In this work, we conduct a preliminary study to understand the importance of modeling other information using separate learnable parameters. We propose a modified version of HuBERT, termed Other HuBERT (O-HuBERT), to test our hypothesis. Our findings are twofold: first, the O-HuBERT method is able to utilize all layers to build complex features to encode other information; second, a robust data augmentation strategy is essential for learning the information required by tasks that depend on other information and to achieve state-of-the-art (SOTA) performance on the SUPERB benchmark with a similarly sized model (100 million parameters) and pre-training data (960 hours).

Quantum Artificial Intelligence (QAI) is the intersection of quantum computing and AI, a technological synergy with expected significant benefits for both. In this paper, we provide a brief overview of what has been achieved in QAI so far and point to some open questions for future research. In particular, we summarize some major key findings on the feasability and the potential of using quantum computing for solving computationally hard problems in various subfields of AI, and vice versa, the leveraging of AI methods for building and operating quantum computing devices.

This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest due to their potential impact on advancing scientific research and industrial practices by improving predictive models with small- or large-scale datasets and expressive predictive models with useful inductive biases. The survey has two parts. The first considers incorporating physics knowledge on an architectural level through objective functions, structured predictive models, and data augmentation. The second considers data as physics knowledge, which motivates looking at multi-task, meta, and contextual learning as an alternative approach to incorporating physics knowledge in a data-driven fashion. Finally, we also provide an industrial perspective on the application of these methods and a survey of the open-source ecosystem for physics-informed machine learning.

The imbalance of exploration and exploitation has long been a significant challenge in reinforcement learning. In policy optimization, excessive reliance on exploration reduces learning efficiency, while over-dependence on exploitation might trap agents in local optima. This paper revisits the exploration-exploitation dilemma from the perspective of entropy by revealing the relationship between entropy and the dynamic adaptive process of exploration and exploitation. Based on this theoretical insight, we establish an end-to-end adaptive framework called AdaZero, which automatically determines whether to explore or to exploit as well as their balance of strength. Experiments show that AdaZero significantly outperforms baseline models across various Atari and MuJoCo environments with only a single setting. Especially in the challenging environment of Montezuma, AdaZero boosts the final returns by up to fifteen times. Moreover, we conduct a series of visualization analyses to reveal the dynamics of our self-adaptive mechanism, demonstrating how entropy reflects and changes with respect to the agent's performance and adaptive process.

Fairness in clustering has been considered extensively in the past; however, the trade-off between the two objectives -- e.g., can we sacrifice just a little in the quality of the clustering to significantly increase fairness, or vice-versa? -- has rarely been addressed. We introduce novel algorithms for tracing the complete trade-off curve, or Pareto front, between quality and fairness in clustering problems; that is, computing all clusterings that are not dominated in both objectives by other clusterings. Unlike previous work that deals with specific objectives for quality and fairness, we deal with all objectives for fairness and quality in two general classes encompassing most of the special cases addressed in previous work. Our algorithm must take exponential time in the worst case as the Pareto front itself can be exponential. Even when the Pareto front is polynomial, our algorithm may take exponential time, and we prove that this is inevitable unless P = NP. However, we also present a new polynomial-time algorithm for computing the entire Pareto front when the cluster centers are fixed, and for perhaps the most natural fairness objective: minimizing the sum, over all clusters, of the imbalance between the two groups in each cluster.

Multi-Objective Optimization (MOO) is an important problem in real-world applications. However, for a non-trivial problem, no single solution exists that can optimize all the objectives simultaneously. In a typical MOO problem, the goal is to find a set of optimum solutions (Pareto set) that trades off the preferences among objectives. Scalarization in MOO is a well-established method for finding a finite set approximation of the whole Pareto set (PS). However, in real-world experimental design scenarios, it's beneficial to obtain the whole PS for flexible exploration of the design space. Recently Pareto set learning (PSL) has been introduced to approximate the whole PS. PSL involves creating a manifold representing the Pareto front of a multi-objective optimization problem. A naive approach includes finding discrete points on the Pareto front through randomly generated preference vectors and connecting them by regression. However, this approach is computationally expensive and leads to a poor PS approximation. We propose to optimize the preference points to be distributed evenly on the Pareto front. Our formulation leads to a bilevel optimization problem that can be solved by e.g. differentiable cross-entropy methods. We demonstrated the efficacy of our method for complex and difficult black-box MOO problems using both synthetic and real-world benchmark data.