Related papers: Learning without Concentration

Muon is a recently proposed optimizer that enforces orthogonality in parameter updates by projecting gradients onto the Stiefel manifold, leading to stable and efficient training in large-scale deep neural networks. Meanwhile, the…

We study fast learning rates when the losses are not necessarily bounded and may have a distribution with heavy tails. To enable such analyses, we introduce two new conditions: (i) the envelope function $\sup_{f \in \mathcal{F}}|\ell \circ…

Score-based diffusion models have become a powerful framework for generative modeling, with score estimation as a central statistical bottleneck. Existing guarantees for score estimation largely focus on light-tailed targets or rely on…

In standard reinforcement learning (RL), a learning agent seeks to optimize the overall reward. However, many key aspects of a desired behavior are more naturally expressed as constraints. For instance, the designer may want to limit the…

Ensemble learning has achieved remarkable success in machine learning, but its reliance on numerous base learners limits its application in resource-constrained environments. This paper introduces an innovative "Margin-Maximizing…

We study the sample complexity of the best-case Empirical Risk Minimizer in the setting of stochastic convex optimization. We show that there exists an instance in which the sample size is linear in the dimension, learning is possible, but…

We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach…

In order to circumvent statistical and computational hardness results in sequential decision-making, recent work has considered smoothed online learning, where the distribution of data at each time is assumed to have bounded likeliehood…

Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a…

We develop in this paper a framework of empirical gain maximization (EGM) to address the robust regression problem where heavy-tailed noise or outliers may present in the response variable. The idea of EGM is to approximate the density…

Here we propose a general theoretical method for analyzing the risk bound in the presence of adversaries. Specifically, we try to fit the adversarial learning problem into the minimax framework. We first show that the original adversarial…

We address the problem of minimizing a convex smooth function $f(x)$ over a compact polyhedral set $D$ given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as…

Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the…

Deep neural networks frequently suffer from performance degradation when the training data is long-tailed because several majority classes dominate the training, resulting in a biased model. Recent studies have made a great effort in…

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 propose a reinforcement learning (RL) framework under a broad class of risk objectives, characterized by convex scoring functions. This class covers many common risk measures, such as variance, Expected Shortfall, entropic Value-at-Risk,…

For a convex class of functions $F$, a regularization functions $\Psi(\cdot)$ and given the random data $(X_i, Y_i)_{i=1}^N$, we study estimation properties of regularization procedures of the form \begin{equation*} \hat f \in {\rm…

Recently, several studies consider the stochastic optimization problem but in a heavy-tailed noise regime, i.e., the difference between the stochastic gradient and the true gradient is assumed to have a finite $p$-th moment (say being upper…

We develop a distributed algorithm for convex Empirical Risk Minimization, the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order…

A new risk bound is presented for the problem of convex/concave function estimation, using the least squares estimator. The best known risk bound, as had appeared in \citet{GSvex}, scaled like $\log(en) n^{-4/5}$ under the mean squared…