相关论文: On the Fine-Grained Complexity of Empirical Risk M…

We derive bounds on the sample complexity of empirical risk minimization (ERM) in the context of minimizing non-convex risks that admit the strict saddle property. Recent progress in non-convex optimization has yielded efficient algorithms…

Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…

Theoretical analyses of Empirical Risk Minimization (ERM) are standardly framed within the Real-RAM model of computation. In this setting, training even simple neural networks is known to be $\exists \mathbb{R}$-complete -- a complexity…

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 this paper, we consider the problem of empirical risk minimization (ERM) of smooth, strongly convex loss functions using iterative gradient-based methods. A major goal of this literature has been to compare different algorithms, such as…

We study the minimal error of the Empirical Risk Minimization (ERM) procedure in the task of regression, both in the random and the fixed design settings. Our sharp lower bounds shed light on the possibility (or impossibility) of adapting…

Empirical risk minimization is the main tool for prediction problems, but its extension to relational data remains unsolved. We solve this problem using recent ideas from graph sampling theory to (i) define an empirical risk for relational…

Empirical risk minimization (ERM) can be computationally expensive, with standard solvers scaling poorly even in the convex setting. We propose a novel lossless compression framework for convex ERM based on color refinement, extending prior…

The theoretical and empirical performance of Empirical Risk Minimization (ERM) often suffers when loss functions are poorly behaved with large Lipschitz moduli and spurious sharp minimizers. We propose and analyze a counterpart to ERM…

Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical…

We address the problem of algorithmic fairness: ensuring that sensitive variables do not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint…

Many modern computational approaches to classical problems in quantitative finance are formulated as empirical loss minimization (ERM), allowing direct applications of classical results from statistical machine learning. These methods,…

Currently, machine learning plays an important role in the lives and individual activities of numerous people. Accordingly, it has become necessary to design machine learning algorithms to ensure that discrimination, biased views, or unfair…

Networked data, in which every training example involves two objects and may share some common objects with others, is used in many machine learning tasks such as learning to rank and link prediction. A challenge of learning from networked…

Developing simple, sample-efficient learning algorithms for robust classification is a pressing issue in today's tech-dominated world, and current theoretical techniques requiring exponential sample complexity and complicated improper…

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…

Given a collection of feature maps indexed by a set $\mathcal{T}$, we study the performance of empirical risk minimization (ERM) on regression problems with square loss over the union of the linear classes induced by these feature maps.…

Empirical risk minimization (ERM) is the workhorse of machine learning, whether for classification and regression or for off-policy policy learning, but its model-agnostic guarantees can fail when we use adaptively collected data, such as…

The well-known empirical risk minimization (ERM) principle is the basis of many widely used machine learning algorithms, and plays an essential role in the classical PAC theory. A common description of a learning algorithm's performance is…

We study the high-dimensional asymptotics of empirical risk minimization (ERM) in over-parametrized two-layer neural networks with quadratic activations trained on synthetic data. We derive sharp asymptotics for both training and test…