In this work, we provide a fundamental unified convergence theorem used for deriving expected and almost sure convergence results for a series of stochastic optimization methods. Our unified theorem only requires to verify several representative conditions and is not tailored to any specific algorithm. As a direct application, we recover expected and almost sure convergence results of the stochastic gradient method (SGD) and random reshuffling (RR) under more general settings. Moreover, we establish new expected and almost sure convergence results for the stochastic proximal gradient method (prox-SGD) and stochastic model-based methods (SMM) for nonsmooth nonconvex optimization problems. These applications reveal that our unified theorem provides a plugin-type convergence analysis and strong convergence guarantees for a wide class of stochastic optimization methods.

Co-administration of two or more drugs simultaneously can result in adverse drug reactions. Identifying drug-drug interactions (DDIs) is necessary, especially for drug development and for repurposing old drugs. DDI prediction can be viewed as a matrix completion task, for which matrix factorization (MF) appears as a suitable solution. This paper presents a novel Graph Regularized Probabilistic Matrix Factorization (GRPMF) method, which incorporates expert knowledge through a novel graph-based regularization strategy within an MF framework. An efficient and sounded optimization algorithm is proposed to solve the resulting non-convex problem in an alternating fashion. The performance of the proposed method is evaluated through the DrugBank dataset, and comparisons are provided against state-of-the-art techniques. The results demonstrate the superior performance of GRPMF when compared to its counterparts.

We systematically study the spectrum of kernel-based graph Laplacian (GL) constructed from high-dimensional and noisy random point cloud in the nonnull setup. The problem is motived by studying the model when the clean signal is sampled from a manifold that is embedded in a low-dimensional Euclidean subspace, and corrupted by high-dimensional noise. We quantify how the signal and noise interact over different regions of signal-to-noise ratio (SNR), and report the resulting peculiar spectral behavior of GL. In addition, we explore the impact of chosen kernel bandwidth on the spectrum of GL over different regions of SNR, which lead to an adaptive choice of kernel bandwidth that coincides with the common practice in real data. This result paves the way to a theoretical understanding of how practitioners apply GL when the dataset is noisy.

Multiple pre-training objectives fill the vacancy of the understanding capability of single-objective language modeling, which serves the ultimate purpose of pre-trained language models (PrLMs), generalizing well on a mass of scenarios. However, learning multiple training objectives in a single model is challenging due to the unknown relative significance as well as the potential contrariety between them. Empirical studies have shown that the current objective sampling in an ad-hoc manual setting makes the learned language representation barely converge to the desired optimum. Thus, we propose \textit{MOMETAS}, a novel adaptive sampler based on meta-learning, which learns the latent sampling pattern on arbitrary pre-training objectives. Such a design is lightweight with negligible additional training overhead. To validate our approach, we adopt five objectives and conduct continual pre-training with BERT-base and BERT-large models, where MOMETAS demonstrates universal performance gain over other rule-based sampling strategies on 14 natural language processing tasks.

Decentralized optimization is increasingly popular in machine learning for its scalability and efficiency. Intuitively, it should also provide better privacy guarantees, as nodes only observe the messages sent by their neighbors in the network graph. But formalizing and quantifying this gain is challenging: existing results are typically limited to Local Differential Privacy (LDP) guarantees that overlook the advantages of decentralization. In this work, we introduce pairwise network differential privacy, a relaxation of LDP that captures the fact that the privacy leakage from a node $u$ to a node $v$ may depend on their relative position in the graph. We then analyze the combination of local noise injection with (simple or randomized) gossip averaging protocols on fixed and random communication graphs. We also derive a differentially private decentralized optimization algorithm that alternates between local gradient descent steps and gossip averaging. Our results show that our algorithms amplify privacy guarantees as a function of the distance between nodes in the graph, matching the privacy-utility trade-off of the trusted curator, up to factors that explicitly depend on the graph topology. Finally, we illustrate our privacy gains with experiments on synthetic and real-world datasets.

A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data, in part due to spurious correlations. To tackle this challenge, we first formalize the OOD generalization problem as constrained optimization, called Disentanglement-constrained Domain Generalization (DDG). We relax this non-trivial constrained optimization problem to a tractable form with finite-dimensional parameterization and empirical approximation. Then a theoretical analysis of the extent to which the above transformations deviates from the original problem is provided. Based on the transformation, we propose a primal-dual algorithm for joint representation disentanglement and domain generalization. In contrast to traditional approaches based on domain adversarial training and domain labels, DDG jointly learns semantic and variation encoders for disentanglement, enabling flexible manipulation and augmentation on training data. DDG aims to learn intrinsic representations of semantic concepts that are invariant to nuisance factors and generalizable across domains. Comprehensive experiments on popular benchmarks show that DDG can achieve competitive OOD performance and uncover interpretable salient structures within data.

There is a recent proliferation of research on the integration of machine learning and optimization. One expansive area within this research stream is predictive-model embedded optimization, which proposes the use of pre-trained predictive models as surrogates for uncertain or highly complex objective functions. In this setting, features of the predictive models become decision variables in the optimization problem. Despite a recent surge in publications in this area, only a few papers note the importance of incorporating trust region considerations in this decision-making pipeline, i.e., enforcing solutions to be similar to the data used to train the predictive models. Without such constraints, the evaluation of the predictive model at solutions obtained from optimization cannot be trusted and the practicality of the solutions may be unreasonable. In this paper, we provide an overview of the approaches appearing in the literature to construct a trust region, and propose three alternative approaches. Our numerical evaluation highlights that trust-region constraints learned through isolation forests, one of the newly proposed approaches, outperform all previously suggested approaches, both in terms of solution quality and computational time.

Despite the impressive performance of Artificial Intelligence (AI) systems, their robustness remains elusive and constitutes a key issue that impedes large-scale adoption. Robustness has been studied in many domains of AI, yet with different interpretations across domains and contexts. In this work, we systematically survey the recent progress to provide a reconciled terminology of concepts around AI robustness. We introduce three taxonomies to organize and describe the literature both from a fundamental and applied point of view: 1) robustness by methods and approaches in different phases of the machine learning pipeline; 2) robustness for specific model architectures, tasks, and systems; and in addition, 3) robustness assessment methodologies and insights, particularly the trade-offs with other trustworthiness properties. Finally, we identify and discuss research gaps and opportunities and give an outlook on the field. We highlight the central role of humans in evaluating and enhancing AI robustness, considering the necessary knowledge humans can provide, and discuss the need for better understanding practices and developing supportive tools in the future.

Learning rate adaptation is a popular topic in machine learning. Gradient Descent trains neural nerwork with a fixed learning rate. Learning rate adaptation is proposed to accelerate the training process through adjusting the step size in the training session. Famous works include Momentum, Adam and Hypergradient. Hypergradient is the most special one. Hypergradient achieved adaptation by calculating the derivative of learning rate with respect to cost function and utilizing gradient descent for learning rate. However, Hypergradient is still not perfect. In practice, Hypergradient fail to decrease training loss after learning rate adaptation with a large probability. Apart from that, evidence has been found that Hypergradient are not suitable for dealing with large datesets in the form of minibatch training. Most unfortunately, Hypergradient always fails to get a good accuracy on the validation dataset although it could reduce training loss to a very tiny value. To solve Hypergradient's problems, we propose a novel adaptation algorithm, where learning rate is parameter specific and internal structured. We conduct extensive experiments on multiple network models and datasets compared with various benchmark optimizers. It is shown that our algorithm can achieve faster and higher qualified convergence than those state-of-art optimizers.

Applications of Structural Health Monitoring (SHM) combined with Machine Learning (ML) techniques enhance real-time performance tracking and increase structural integrity awareness of civil, aerospace and automotive infrastructures. This SHM-ML synergy has gained popularity in the last years thanks to the anticipation of maintenance provided by arising ML algorithms and their ability of handling large quantities of data and considering their influence in the problem. In this paper we develop a novel ML nearest-neighbors-alike algorithm based on the principle of maximum entropy to predict fatigue damage (Palmgren-Miner index) in composite materials by processing the signals of Lamb Waves -- a non-destructive SHM technique -- with other meaningful features such as layup parameters and stiffness matrices calculated from the Classical Laminate Theory (CLT). The full data analysis cycle is applied to a dataset of delamination experiments in composites. The predictions achieve a good level of accuracy, similar to other ML algorithms, e.g. Neural Networks or Gradient-Boosted Trees, and computation times are of the same order of magnitude. The key advantages of our proposal are: (1) The automatic determination of all the parameters involved in the prediction, so no hyperparameters have to be set beforehand, which saves time devoted to hypertuning the model and also represents an advantage for autonomous, self-supervised SHM. (2) No training is required, which, in an \textit{online learning} context where streams of data are fed continuously to the model, avoids repeated training -- essential for reliable real-time, continuous monitoring.