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We consider statistical learning question for $\psi$-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,$\cdots$ The consistency of the empirical risk minimization algorithm is…

Although there exist plentiful theories of empirical risk minimization (ERM) for supervised learning, current theoretical understandings of ERM for a related problem---stochastic convex optimization (SCO), are limited. In this work, we…

We consider the online convex optimization problem. In the setting of arbitrary sequences and finite set of parameters, we establish a new fast-rate quantile regret bound. Then we investigate the optimization into the L1-ball by…

The theory of reinforcement learning has focused on two fundamental problems: achieving low regret, and identifying $\epsilon$-optimal policies. While a simple reduction allows one to apply a low-regret algorithm to obtain an…

Given finite-dimensional random vectors $Y$, $X$, and $Z$ that form a Markov chain in that order (i.e., $Y \to X \to Z$), we derive upper bounds on the excess minimum risk using generalized information divergence measures. Here, $Y$ is a…

In this paper we consider the problem of Learning from Satisfying Assignments introduced by \cite{1} of finding a distribution that is a close approximation to the uniform distribution over the satisfying assignments of a low complexity…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

We study episodic reinforcement learning with fixed reward and transition functions, but with episode-dependent admissible action sets that are observed at the start of each episode. Performance is measured by cumulative regret against the…

We consider the problem of decision-making with side information and unbounded loss functions. Inspired by probably approximately correct learning model, we use a slightly different model that incorporates the notion of side information in…

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs,…

This paper provides a comprehensive error analysis of learning with vector-valued random features (RF). The theory is developed for RF ridge regression in a fully general infinite-dimensional input-output setting, but nonetheless applies to…

The nonparametric regression with a random design model is considered. We want to recover the regression function at a point x where the design density is vanishing or exploding. Depending on assumptions on the regression function local…

Recently many first and second order variants of SGD have been proposed to facilitate training of Deep Neural Networks (DNNs). A common limitation of these works stem from the fact that they use the same learning rate across all instances…

Recent research shows the susceptibility of machine learning models to adversarial attacks, wherein minor but maliciously chosen perturbations of the input can significantly degrade model performance. In this paper, we theoretically analyse…

Representation learning has been widely studied in the context of meta-learning, enabling rapid learning of new tasks through shared representations. Recent works such as MAML have explored using fine-tuning-based metrics, which measure the…

We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. When the input…

This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…

In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…

Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding of…

Nonparametric regression with random design is considered. Estimates are defined by minimzing a penalized empirical $L_2$ risk over a suitably chosen class of neural networks with one hidden layer via gradient descent. Here, the gradient…