In this monograph, I introduce the basic concepts of Online Learning through a modern view
of Online Convex Optimization. Here, online learning refers to the framework of regret …

We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical
problem of estimating a bounded mean. Our approach generalizes and improves on the …

A classic problem in statistics is the estimation of the expectation of random variables from
samples. This gives rise to the tightly connected problems of deriving concentration …

We consider the problem of estimating the mean of a sequence of random elements $ f
(\theta, X_1) $$,\ldots, $$ f (\theta, X_n) $ where $ f $ is a fixed scalar function …

Self-normalized processes arise naturally in many statistical tasks. While self-normalized
concentration has been extensively studied for scalar-valued processes, there is less work …

We present new algorithms for online convex optimization over unbounded domains that
obtain parameter-free regret in high-probability given access only to potentially heavy-tailed …

We consider a variant of the classical online linear optimization problem in which at every
step, the online player receives a “hint” vector before choosing the action for that round …

We provide practical, efficient, and nonparametric methods for auditing the fairness of
deployed classification and regression models. Whereas previous work relies on a fixed …

Existing concentration bounds for bounded vector-valued random variables include
extensions of the scalar Hoeffding and Bernstein inequalities. While the latter is typically …

Logistic bandit is a ubiquitous framework of modeling users' choices, eg, click vs. no click for
advertisement recommender system. We observe that the prior works overlook or neglect …