Related papers: The Many Faces of Exponential Weights in Online Le…
Online learning algorithms are fast, memory-efficient, easy to implement, and applicable to many prediction problems, including classification, regression, and ranking. Several online algorithms were proposed in the past few decades, some…
This paper studies the Exponential Weights (EW) algorithm with an isotropic Gaussian prior for online logistic regression. We show that the near-optimal worst-case regret bound $O(d\log(Bn))$ for EW, established by Kakade and Ng (2005)…
We consider the online version of the isotonic regression problem. Given a set of linearly ordered points (e.g., on the real line), the learner must predict labels sequentially at adversarially chosen positions and is evaluated by her total…
We propose a Bayesian approach for recursively estimating the classifier weights in online learning of a classifier ensemble. In contrast with past methods, such as stochastic gradient descent or online boosting, our approach estimates the…
First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias, plays a critical role in…
On-line linear optimization on combinatorial action sets (d-dimensional actions) with bandit feedback, is known to have complexity in the order of the dimension of the problem. The exponential weighted strategy achieves the best known…
We revisit the sequential variants of linear regression with the squared loss, classification problems with hinge loss, and logistic regression, all characterized by unbounded losses in the setup where no assumptions are made on the…
This paper addresses the problem of online learning in metric spaces using exponential weights. We extend the analysis of the exponentially weighted average forecaster, traditionally studied in a Euclidean settings, to a more abstract…
In this paper, we investigate the online non-convex optimization problem which generalizes the classic {online convex optimization problem by relaxing the convexity assumption on the cost function. For this type of problem, the classic…
Learning and computation of equilibria are central problems in game theory, theory of computation, and artificial intelligence. In this work, we introduce proximal regret, a new notion of regret based on proximal operators that lies…
We analyze the inductive bias of gradient descent for weight normalized smooth homogeneous neural nets, when trained on exponential or cross-entropy loss. We analyse both standard weight normalization (SWN) and exponential weight…
This work focuses on the setting of dynamic regret in the context of online learning with full information. In particular, we analyze regret bounds with respect to the temporal variability of the loss functions. By assuming that the…
In this book, I introduce the basic concepts of Online Learning through the modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order…
Gradient-variation online learning aims to achieve regret guarantees that scale with variations in the gradients of online functions, which has been shown to be crucial for attaining fast convergence in games and robustness in stochastic…
We consider prediction with expert advice for strongly convex and bounded losses, and investigate trade-offs between regret and "variance" (i.e., squared difference of learner's predictions and best expert predictions). With $K$ experts,…
This paper shows that the implicit bias of gradient descent on linearly separable data is exactly characterized by the optimal solution of a dual optimization problem given by a smoothed margin, even for general losses. This is in contrast…
Online learning with limited information feedback (bandit) tries to solve the problem where an online learner receives partial feedback information from the environment in the course of learning. Under this setting, Flaxman et al.[8]…
Online learning constitutes a mathematical and compelling framework to analyze sequential decision making problems in adversarial environments. The learner repeatedly chooses an action, the environment responds with an outcome, and then the…
Weight averaging of Stochastic Gradient Descent (SGD) iterates is a popular method for training deep learning models. While it is often used as part of complex training pipelines to improve generalization or serve as a `teacher' model,…
We fix a fundamental issue in the stochastic extragradient method by providing a new sampling strategy that is motivated by approximating implicit updates. Since the existing stochastic extragradient algorithm, called Mirror-Prox, of…