Intelligent agents in real-world applications must adapt their behavior to changing contexts and user preferences. For example, planning a road trip requires considering both travel time and cost. Multi-objective reinforcement learning (MORL) provides a principled approach to navigate such trade-offs. However, most existing approaches require predefined preference weights during training and jointly optimize the model for all objectives. In this paper, we introduce TORA (Train Once, Realign Anytime), a novel framework that defers preference integration to inference time, enabling flexible adaptation to user preferences without retraining. TORA independently trains diffusion planning models for each objective and combines them at inference time using user-specified preferences to generate behavior aligned with desired trade-offs. Furthermore, new objectives can be added seamlessly by training additional models without modifying existing ones. Empirical evaluations on standard offline MORL benchmarks demonstrate that TORA achieves competitive and consistent performance compared to methods that require fixed preference weights.

Deep learning-based methods have achieved a breakthrough in image anomaly detection, but their complexity introduces a considerable challenge to understanding why an instance is predicted to be anomalous. We introduce a novel explanation method that generates multiple alternative modifications for each anomaly, capturing diverse concepts of anomalousness. Each modification is trained to be perceived as normal by the anomaly detector. The method provides a semantic explanation of the mechanism that triggered the detector, allowing users to explore ``what-if scenarios.'' Qualitative and quantitative analyses across various image datasets demonstrate that applying this method to state-of-the-art detectors provides high-quality semantic explanations.

Modern deep learning techniques focus on extracting intricate information from data to achieve accurate predictions. However, the training datasets may be crowdsourced and include sensitive information, such as personal contact details, financial data, and medical records. As a result, there is a growing emphasis on developing privacy-preserving training algorithms for neural networks that maintain good performance while preserving privacy. In this paper, we investigate the generalization and privacy performances of the differentially private gradient descent (DP-GD) algorithm, which is a private variant of the gradient descent (GD) by incorporating additional noise into the gradients during each iteration. Moreover, we identify a concrete learning task where DP-GD can achieve superior generalization performance compared to GD in training two-layer Huberized ReLU convolutional neural networks (CNNs). Specifically, we demonstrate that, under mild conditions, a small signal-to-noise ratio can result in GD producing training models with poor test accuracy, whereas DP-GD can yield training models with good test accuracy and privacy guarantees if the signal-to-noise ratio is not too small. This indicates that DP-GD has the potential to enhance model performance while ensuring privacy protection in certain learning tasks. Numerical simulations are further conducted to support our theoretical results.

Understanding the generalization and optimization of neural networks is a longstanding problem in modern learning theory. The prior analysis often leads to risk bounds of order $1/\sqrt{n}$ for ReLU networks, where $n$ is the sample size. In this paper, we present a general optimization and generalization analysis for gradient descent applied to shallow ReLU networks. We develop convergence rates of the order $1/T$ for gradient descent with $T$ iterations, and show that the gradient descent iterates fall inside local balls around either an initialization point or a reference point. Then we develop improved Rademacher complexity estimates by using the activation pattern of the ReLU function in these local balls. We apply our general result to NTK-separable data with a margin $\gamma$, and develop an almost optimal risk bound of the order $1/(n\gamma^2)$ for the ReLU network with a polylogarithmic width.

Deep learning algorithms excel at extracting fine-grained patterns from data to enable accurate predictions. However, this capability can conflict with the goal of protecting the privacy of individuals. This paper addresses both the practical and theoretical challenges of developing privacy-preserving deep learning algorithms that maintain strong predictive performance. Specifically, we propose a differentially private GD algorithm for three-layer neural networks with gradient perturbation. Both privacy and utility guarantees of the proposed method are presented, attaining-up to constants-an optimal excess population risk of order$\mathcal{O}\left(\frac{1}{\sqrt{n}}+\frac{\sqrt{d \log (1 / \delta)}}{n \epsilon}\right)$, where$s$is the data dimension,$\epsilon$is the privacy budget, and$\delta$is the failure probability. To our knowledge, this is the first utility analysis achieving optimal rates, on par with their counterparts in the convex setting, for differentially private GD algorithms in multi-laver neural networks.

Significant progress has been made recently in understanding the generalization of neural networks (NNs) trained by gradient descent (GD) using the algorithmic stability approach. However, most of the existing research has focused on one-hidden-layer NNs and has not addressed the impact of different network scaling. Here, network scaling corresponds to the normalization of the layers. In this article, we greatly extend the previous work (Lei et al., 2022; Richards & Kuzborskij, 2021) by conducting a comprehensive stability and generalization analysis of GD for two-layer and three-layer NNs. For two-layer NNs, our results are established under general network scaling, relaxing previous conditions. In the case of three-layer NNs, our technical contribution lies in demonstrating its nearly co-coercive property by utilizing a novel induction strategy that thoroughly explores the effects of overparameterization. As a direct application of our general findings, we derive the excess risk rate of O(1/n) for GD in both two-layer and three-layer NNs. This sheds light on sufficient or necessary conditions for underparameterized and overparameterized NNs trained by GD to attain the desired risk rate of O(1/n). Moreover, we demonstrate that as the scaling factor increases or the network complexity decreases, less overparameterization is required for GD to achieve the desired error rates. Additionally, under a low-noise condition, we obtain a fast risk rate of O(1/n) for GD in both two-layer and three-layer NNs.

Adversarial examples are manipulated samples used to deceive machine learning models, posing a serious threat in safety-critical applications. Existing safety certificates for machine learning models are limited to individual input examples, failing to capture generalization to unseen data. To address this limitation, we propose novel generalization bounds based on the PAC-Bayesian and randomized smoothing frameworks, providing certificates that predict the model’s performance and robustness on unseen test samples based solely on the training data. We present an effective procedure to train and compute the first non-vacuous generalization bounds for neural networks in adversarial settings. Experimental results on the widely recognized MNIST and CIFAR-10 datasets demonstrate the efficacy of our approach, yielding the first robust risk certificates for stochastic convolutional neural networks under the $L_2$ threat model. Our method offers valuable tools for evaluating model susceptibility to real-world adversarial risks.

Modern machine learning algorithms aim to extract fine-grained information from data to provide accurate predictions, which often conflicts with the goal of privacy protection. This paper addresses the practical and theoretical importance of developing privacy-preserving machine learning algorithms that ensure good performance while preserving privacy. In this paper, we focus on the privacy and utility (measured by excess risk bounds) performances of differentially private stochastic gradient descent (SGD) algorithms in the setting of stochastic convex optimization. Specifically, we examine the pointwise problem in the low-noise setting for which we derive sharper excess risk bounds for the differentially private SGD algorithm. In the pairwise learning setting, we propose a simple differentially private SGD algorithm based on gradient perturbation. Furthermore, we develop novel utility bounds for the proposed algorithm, proving that it achieves optimal excess risk rates even for non-smooth losses. Notably, we establish fast learning rates for privacy-preserving pairwise learning under the low-noise condition, which is the first of its kind.

Recently there is a large amount of work devoted to the study of Markov chain stochastic gradient methods (MC-SGMs) which mainly focus on their convergence analysis for solving minimization problems. In this paper, we provide a comprehensive generalization analysis of MC-SGMs for both minimization and minimax problems through the lens of algorithmic stability in the framework of statistical learning theory. For empirical risk minimization (ERM) problems, we establish the optimal excess population risk bounds for both smooth and non-smooth cases by introducing on-average argument stability. For minimax problems, we develop a quantitative connection between on-average argument stability and generalization error which extends the existing results for uniform stability (Lei et al., 2021). We further develop the first nearly optimal convergence rates for convex-concave problems both in expectation and with high probability, which, combined with our stability results, show that the optimal generalization bounds can be attained for both smooth and non-smooth cases. To the best of our knowledge, this is the first generalization analysis of SGMs when the gradients are sampled from a Markov process.

Randomized coordinate descent (RCD) is a popular optimization algorithm with wide applications in various machine learning problems, which motivates a lot of theoretical analysis on its convergence behavior. As a comparison, there is no work studying how the models trained by RCD would generalize to test examples. In this paper, we initialize the generalization analysis of RCD by leveraging the powerful tool of algorithmic stability. We establish argument stability bounds of RCD for both convex and strongly convex objectives, from which we develop optimal generalization bounds by showing how to early-stop the algorithm to tradeoff the estimation and optimization. Our analysis shows that RCD enjoys better stability as compared to stochastic gradient descent.

Pairwise learning refers to learning tasks where the loss function depends on a pair of instances. It instantiates many important machine learning tasks such as bipartite ranking and metric learning. A popular approach to handle streaming data in pairwise learning is an online gradient descent (OGD) algorithm, where one needs to pair the current instance with a buffering set of previous instances with a sufficiently large size and therefore suffers from a scalability issue. In this paper, we propose simple stochastic and online gradient descent methods for pairwise learning. A notable difference from the existing studies is that we only pair the current instance with the previous one in building a gradient direction, which is efficient in both the storage and computational complexity. We develop novel stability results, optimization, and generalization error bounds for both convex and nonconvex as well as both smooth and nonsmooth problems. We introduce novel techniques to decouple the dependency of models and the previous instance in both the optimization and generalization analysis. Our study resolves an open question on developing meaningful generalization bounds for OGD using a buffering set with a very small fixed size. We also extend our algorithms and stability analysis to develop differentially private SGD algorithms for pairwise learning which significantly improves the existing results.