Related papers: Optimistic Rates for Learning with a Smooth Loss

We study prediction and estimation problems using empirical risk minimization, relative to a general convex loss function. We obtain sharp error rates even when concentration is false or is very restricted, for example, in heavy-tailed…

Popular machine learning estimators involve regularization parameters that can be challenging to tune, and standard strategies rely on grid search for this task. In this paper, we revisit the techniques of approximating the regularization…

In this paper, we study an online learning algorithm with a robust loss function $\mathcal{L}_{\sigma}$ for regression over a reproducing kernel Hilbert space (RKHS). The loss function $\mathcal{L}_{\sigma}$ involving a scaling parameter…

Recent advances in randomized incremental methods for minimizing $L$-smooth $\mu$-strongly convex finite sums have culminated in tight complexity of $\tilde{O}((n+\sqrt{n L/\mu})\log(1/\epsilon))$ and $O(n+\sqrt{nL/\epsilon})$, where…

In this paper we study the differentially private Empirical Risk Minimization (ERM) problem in different settings. For smooth (strongly) convex loss function with or without (non)-smooth regularization, we give algorithms that achieve…

In statistical learning theory, convex surrogates of the 0-1 loss are highly preferred because of the computational and theoretical virtues that convexity brings in. This is of more importance if we consider smooth surrogates as witnessed…

Hoffman's classical result gives a bound on the distance of a point from a convex and compact polytope in terms of the magnitude of violation of the constraints. Recently, several results showed that Hoffman's bound can be used to derive…

We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function…

Theoretical analysis of the divide-and-conquer based distributed learning with least square loss in the reproducing kernel Hilbert space (RKHS) have recently been explored within the framework of learning theory. However, the studies on…

We prove the tightest-known upper bounds on the sample complexity of multi-group learning. Our algorithm extends the one-inclusion graph prediction strategy using a generalization of bipartite $b$-matching. In the group-realizable setting,…

We present a novel notion of complexity that interpolates between and generalizes some classic existing complexity notions in learning theory: for estimators like empirical risk minimization (ERM) with arbitrary bounded losses, it is upper…

Convex risk measures play a foundational role in the area of stochastic optimization. However, in contrast to risk neutral models, their applications are still limited due to the lack of efficient solution methods. In particular, the mean…

Consider nonparametric function estimation under $L^p$-loss. The minimax rate for estimation of the regression function over a H\"older ball with smoothness index $\beta$ is $n^{-\beta/(2\beta+1)}$ if $1\leq p<\infty$ and $(n/\log…

We define an online learning and optimization problem with discrete and irreversible decisions contributing toward a coverage target. In each period, a decision-maker selects facilities to open, receives information on the success of each…

Optimization of convex functions under stochastic zeroth-order feedback has been a major and challenging question in online learning. In this work, we consider the problem of optimizing second-order smooth and strongly convex functions…

In this paper, an online learning algorithm is proposed as sequential stochastic approximation of a regularization path converging to the regression function in reproducing kernel Hilbert spaces (RKHSs). We show that it is possible to…

This paper presents a new statistical analysis aiming to explain the recent superior achievements of the pre-training techniques in natural language processing (NLP). We prove that when the classes of the pre-training task (e.g., different…

Adjusting the learning rate schedule in stochastic gradient methods is an important unresolved problem which requires tuning in practice. If certain parameters of the loss function such as smoothness or strong convexity constants are known,…

Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are…

We study the generalization properties of ridge regression with random features in the statistical learning framework. We show for the first time that $O(1/\sqrt{n})$ learning bounds can be achieved with only $O(\sqrt{n}\log n)$ random…