Machine learning is widely used in various areas. However, the current machine learning framework remains vulnerable to issues such as adversarial attacks, fairness violations, and data leakage. These problems are not adequately captured by fitting models to collected data and focusing on test performance metrics alone, like accuracy or F1-score. In practice, machine learning tasks often involve additional quantities of interest, which turns an originally unconstrained optimisation problem (only optimising toward accuracy) into a constrained one. This thesis formally studies machine learning under different types of commonly concerning constraints, such as robustness, fairness, and privacy. I first focus on how the formal machine learning framework can be extended to incorporate robustness, which is a critical factor for safety. After that, I turn to more ethics-related aspects like fairness and privacy, to explore the possibility of formally fitting them into machine learning. My approach differs from empirically pushing up multiple metrics and instead emphasises fundamental ways to understand and address the underlying challenges.

The recent success of machine learning models, especially large-scale classifiers and language models, relies heavily on training with massive data. These data are often collected from online sources. This raises serious concerns about the protection of user data, as individuals may not have given consent for their data to be used in training. To address this concern, recent studies introduce the concept of unlearnable examples, i.e., data instances that appear natural but are intentionally altered to prevent models from effectively learning from them. While existing methods demonstrate empirical effectiveness, they typically rely on heuristic trials and lack formal guarantees. Besides, when unlearnable examples are mixed with clean data, as is often the case in practice, their unlearnability disappears. In this work, we propose a novel approach to constructing unlearnable examples by systematically maximising the Bayes error, a measurement of irreducible classification error. We develop an optimisation-based approach and provide an efficient solution using projected gradient ascent. Our method provably increases the Bayes error and remains effective when the unlearning examples are mixed with clean samples. Experimental results across multiple datasets and model architectures are consistent with our theoretical analysis and show that our approach can restrict data learnability, effectively in practice.

Fairness in machine learning is more important than ever as ethical concerns continue to grow. Individual fairness demands that individuals differing only in sensitive attributes receive the same outcomes. However, commonly used machine learning algorithms often fail to achieve such fairness. To improve individual fairness, various training methods have been developed, such as incorporating fairness constraints as optimisation objectives. While these methods have demonstrated empirical effectiveness, they lack formal guarantees of fairness. Existing approaches that aim to provide fairness guarantees primarily rely on verification techniques, which can sometimes fail to produce definitive results. Moreover, verification alone does not actively enhance individual fairness during training. To address this limitation, we propose a novel framework that formally guarantees individual fairness throughout training. Our approach consists of two parts, i.e., (1) provably fair initialisation that ensures the model starts in a fair state, and (2) a fairness-preserving training algorithm that maintains fairness as the model learns. A key element of our method is the use of randomised response mechanisms, which protect sensitive attributes while maintaining fairness guarantees. We formally prove that this mechanism sustains individual fairness throughout the training process. Experimental evaluations confirm that our approach is effective, i.e., producing models that are empirically fair and accurate. Furthermore, our approach is much more efficient than the alternative approach based on certified training (which requires neural network verification during training).

Face recognition is a widely used authentication technology in practice, where robustness is required. It is thus essential to have an efficient and easy-to-use method for evaluating the robustness of (possibly third-party) trained face recognition systems. Existing approaches to evaluating the robustness of face recognition systems are either based on empirical evaluation (e.g., measuring attacking success rate using state-of-the-art attacking methods) or formal analysis (e.g., measuring the Lipschitz constant). While the former demands significant user efforts and expertise, the latter is extremely time-consuming. In pursuit of a comprehensive, efficient, easy-to-use, and scalable estimation of the robustness of face recognition systems, we take an old-school alternative approach and introduceRobFace, i.e., evaluation using an optimized test suite. It contains transferable adversarial face images that are designed to comprehensively evaluate a face recognition system’s robustness along a variety of dimensions.RobFaceis system-agnostic and still consistent with system-specific empirical evaluation or formal analysis. We support this claim through extensive experimental results with various perturbations on multiple face recognition systems. To our knowledge,RobFaceis the first system-agnostic robustness estimation test suite.

Abstract Adversarial examples pose a security threat to many critical systems built on neural networks. While certified training improves robustness, it also decreases accuracy noticeably. Despite various proposals for addressing this issue, the significant accuracy drop remains. More importantly, it is not clear whether there is a certain fundamental limit on achieving robustness whilst maintaining accuracy. In this work, we offer a novel perspective based on Bayes errors. By adopting Bayes error to robustness analysis, we investigate the limit of certified robust accuracy, taking into account data distribution uncertainties. We first show that the accuracy inevitably decreases in the pursuit of robustness due to changed Bayes error in the altered data distribution. Subsequently, we establish an upper bound for certified robust accuracy, considering the distribution of individual classes and their boundaries. Our theoretical results are empirically evaluated on real-world datasets and are shown to be consistent with the limited success of existing certified training results, e.g., for CIFAR10, our analysis results in an upper bound (of certified robust accuracy) of 67.49%, meanwhile existing approaches are only able to increase it from 53.89% in 2017 to 62.84% in 2023.