Related papers: Excess Risk Bounds for Exponentially Concave Losse…
There have been extensive studies on solving differential equations using physics-informed neural networks. While this method has proven advantageous in many cases, a major criticism lies in its lack of analytical error bounds. Therefore,…
We study the problem of deleting user data from machine learning models trained using empirical risk minimization. Our focus is on learning algorithms which return the empirical risk minimizer and approximate unlearning algorithms that…
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…
We introduce an online mathematical framework for survival analysis, allowing real time adaptation to dynamic environments and censored data. This framework enables the estimation of event time distributions through an optimal second order…
We propose a general approach for supervised learning with structured output spaces, such as combinatorial and polyhedral sets, that is based on minimizing estimated conditional risk functions. Given a loss function defined over pairs of…
Weighted empirical risk minimization is a common approach to prediction under distribution drift. This article studies its out-of-sample prediction error under nonstationarity. We provide a general decomposition of the excess risk into a…
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
In this paper, we investigate the framework of Online Convex Optimization (OCO) for online learning. OCO offers a very powerful online learning framework for many applications. In this context, we study a specific framework of OCO called…
Risk-bounded motion planning is an important yet difficult problem for safety-critical tasks. While existing mathematical programming methods offer theoretical guarantees in the context of constrained Markov decision processes, they either…
We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…
We consider Constrained Online Convex Optimization (COCO) with adversarially chosen constraints. At each round, the learner chooses an action before observing the loss and constraint function for that round. The goal is to achieve small…
We study the problem of excess risk evaluation for empirical risk minimization (ERM) under convex losses. We show that by leveraging the idea of wild refitting, one can upper bound the excess risk through the so-called "wild optimism,"…
We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
Loss functions are at the heart of deep learning, shaping how models learn and perform across diverse tasks. They are used to quantify the difference between predicted outputs and ground truth labels, guiding the optimization process to…
Consider the problem of learning a large number of response functions simultaneously based on the same input variables. The training data consist of a single independent random sample of the input variables drawn from a common distribution…
We formalize the problem of machine unlearning as design of efficient unlearning algorithms corresponding to learning algorithms which perform a selection of adaptive queries from structured query classes. We give efficient unlearning…
Understanding the fundamental limits of robust supervised learning has emerged as a problem of immense interest, from both practical and theoretical standpoints. In particular, it is critical to determine classifier-agnostic bounds on the…
Trace norm regularization is a popular method of multitask learning. We give excess risk bounds with explicit dependence on the number of tasks, the number of examples per task and properties of the data distribution. The bounds are…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…