We develop an algorithmic framework for solving convex optimization problems using no-regret game dynamics. By converting the problem of minimizing a convex function into an auxiliary problem of solving a min-max game in a sequential fashion, we can consider a range of strategies for each of the two-players who must select their actions one after the other. A common choice for these strategies are so-called no-regret learning algorithms, and we describe a number of such and prove bounds on their regret. We then show that many classical first-order methods for convex optimization -- including average-iterate gradient descent, the Frank-Wolfe algorithm, Nesterov's acceleration methods, and the accelerated proximal method -- can be interpreted as special cases of our framework as long as each player makes the correct choice of no-regret strategy. Proving convergence rates in this framework becomes very straightforward, as they follow from plugging in the appropriate known regret bounds. Our framework also gives rise to a number of new first-order methods for special cases of convex optimization that were not previously known.

In this work, we consider the problem of imbalanced data in a regression framework when the imbalanced phenomenon concerns continuous or discrete covariates. Such a situation can lead to biases in the estimates. In this case, we propose a data augmentation algorithm that combines a weighted resampling (WR) and a data augmentation (DA) procedure. In a first step, the DA procedure permits exploring a wider support than the initial one. In a second step, the WR method drives the exogenous distribution to a target one. We discuss the choice of the DA procedure through a numerical study that illustrates the advantages of this approach. Finally, an actuarial application is studied.

The minimax optimization over Riemannian manifolds (possibly nonconvex constraints) has been actively applied to solve many problems, such as robust dimensionality reduction and deep neural networks with orthogonal weights (Stiefel manifold). Although many optimization algorithms for minimax problems have been developed in the Euclidean setting, it is difficult to convert them into Riemannian cases, and algorithms for nonconvex minimax problems with nonconvex constraints are even rare. On the other hand, to address the big data challenges, decentralized (serverless) training techniques have recently been emerging since they can reduce communications overhead and avoid the bottleneck problem on the server node. Nonetheless, the algorithm for decentralized Riemannian minimax problems has not been studied. In this paper, we study the distributed nonconvex-strongly-concave minimax optimization problem over the Stiefel manifold and propose both deterministic and stochastic minimax methods. The Steifel manifold is a non-convex set. The global function is represented as the finite sum of local functions. For the deterministic setting, we propose DRGDA and prove that our deterministic method achieves a gradient complexity of $O( \epsilon^{-2})$ under mild conditions. For the stochastic setting, we propose DRSGDA and prove that our stochastic method achieves a gradient complexity of $O(\epsilon^{-4})$. The DRGDA and DRSGDA are the first algorithms for distributed minimax optimization with nonconvex constraints with exact convergence. Extensive experimental results on the Deep Neural Networks (DNNs) training over the Stiefel manifold demonstrate the efficiency of our algorithms.

In many bandit problems, the maximal reward achievable by a policy is often unknown in advance. We consider the problem of estimating the optimal policy value in the sublinear data regime before the optimal policy is even learnable. We refer to this as $V^*$ estimation. It was recently shown that fast $V^*$ estimation is possible but only in disjoint linear bandits with Gaussian covariates. Whether this is possible for more realistic context distributions has remained an open and important question for tasks such as model selection. In this paper, we first provide lower bounds showing that this general problem is hard. However, under stronger assumptions, we give an algorithm and analysis proving that $\widetilde{\mathcal{O}}(\sqrt{d})$ sublinear estimation of $V^*$ is indeed information-theoretically possible, where $d$ is the dimension. We then present a more practical, computationally efficient algorithm that estimates a problem-dependent upper bound on $V^*$ that holds for general distributions and is tight when the context distribution is Gaussian. We prove our algorithm requires only $\widetilde{\mathcal{O}}(\sqrt{d})$ samples to estimate the upper bound. We use this upper bound and the estimator to obtain novel and improved guarantees for several applications in bandit model selection and testing for treatment effects.

Clustering is a technique used in machine learning and data analysis to group similar data points together. The goal of clustering is to identify patterns and relationships in the data without any prior knowledge of the underlying structure. Clustering is commonly used in unsupervised learning, where the algorithm is not given any labeled data and must find its own structure in the data. There are numerous applications of clustering in various fields such as finance, marketing, biology, social networks, image and video processing, and many more. There are several different algorithms that can be used for clustering, including k-means, hierarchical clustering, and DBSCAN.

Future AI applications require performance, reliability and privacy that the existing, cloud-dependant system architectures cannot provide. In this article, we study orchestration in the device-edge-cloud continuum, and focus on edge AI for resource orchestration. We claim that to support the constantly growing requirements of intelligent applications in the device-edge-cloud computing continuum, resource orchestration needs to embrace edge AI and emphasize local autonomy and intelligence. To justify the claim, we provide a general definition for continuum orchestration, and look at how current and emerging orchestration paradigms are suitable for the computing continuum. We describe certain major emerging research themes that may affect future orchestration, and provide an early vision of an orchestration paradigm that embraces those research themes. Finally, we survey current key edge AI methods and look at how they may contribute into fulfilling the vision of future continuum orchestration.

In this paper, we present a novel model-agnostic machine learning technique to extract a reduced thermochemical model for reacting hypersonic flows simulation. A first simulation gathers all relevant thermodynamic states and the corresponding gas properties via a given model. The states are embedded in a low-dimensional space and clustered to identify regions with different levels of thermochemical (non)-equilibrium. Then, a surrogate surface from the reduced cluster-space to the output space is generated using radial-basis-function networks. The method is validated and benchmarked on a simulation of a hypersonic flat-plate boundary layer with finite-rate chemistry. The gas properties of the reactive air mixture are initially modeled using the open-source Mutation++ library. Substituting Mutation++ with the light-weight, machine-learned alternative improves the performance of the solver by 50% while maintaining overall accuracy.

Let $(x_{i}, y_{i})_{i=1,\dots,n}$ denote independent samples from a general mixture distribution $\sum_{c\in\mathcal{C}}\rho_{c}P_{c}^{x}$, and consider the hypothesis class of generalized linear models $\hat{y} = F(\Theta^{\top}x)$. In this work, we investigate the asymptotic joint statistics of the family of generalized linear estimators $(\Theta_{1}, \dots, \Theta_{M})$ obtained either from (a) minimizing an empirical risk $\hat{R}_{n}(\Theta;X,y)$ or (b) sampling from the associated Gibbs measure $\exp(-\beta n \hat{R}_{n}(\Theta;X,y))$. Our main contribution is to characterize under which conditions the asymptotic joint statistics of this family depends (on a weak sense) only on the means and covariances of the class conditional features distribution $P_{c}^{x}$. In particular, this allow us to prove the universality of different quantities of interest, such as the training and generalization errors, redeeming a recent line of work in high-dimensional statistics working under the Gaussian mixture hypothesis. Finally, we discuss the applications of our results to different machine learning tasks of interest, such as ensembling and uncertainty

Depression is the most common psychological disorder and is considered as a leading cause of disability and suicide worldwide. An automated system capable of detecting signs of depression in human speech can contribute to ensuring timely and effective mental health care for individuals suffering from the disorder. Developing such automated system requires accurate machine learning models, capable of capturing signs of depression. However, state-of-the-art models based on deep acoustic representations require abundant data, meticulous selection of features, and rigorous training; the procedure involves enormous computational resources. In this work, we explore the effectiveness of two different acoustic feature groups - conventional hand-curated and deep representation features, for predicting the severity of depression from speech. We explore the relevance of possible contributing factors to the models' performance, including gender of the individual, severity of the disorder, content and length of speech. Our findings suggest that models trained on conventional acoustic features perform equally well or better than the ones trained on deep representation features at significantly lower computational cost, irrespective of other factors, e.g. content and length of speech, gender of the speaker and severity of the disorder. This makes such models a better fit for deployment where availability of computational resources is restricted, such as real time depression monitoring applications in smart devices.

In-context learning (ICL) suffers from oversensitivity to the prompt, making it unreliable in real-world scenarios. We study the sensitivity of ICL with respect to multiple perturbation types. First, we find that label bias obscures the true sensitivity, and therefore prior work may have significantly underestimated ICL sensitivity. Second, we observe a strong negative correlation between ICL sensitivity and accuracy: predictions sensitive to perturbations are less likely to be correct. Motivated by these findings, we propose \textsc{SenSel}, a few-shot selective prediction method that abstains from sensitive predictions. Experiments on ten classification datasets show that \textsc{SenSel} consistently outperforms two commonly used confidence-based and entropy-based baselines on abstention decisions.