In online learning, a decision maker repeatedly selects one of a set of actions, with the goal of minimizing the overall loss incurred. Following the recent line of research on algorithms endowed with additional predictive features, we revisit this problem by allowing the decision maker to acquire additional information on the actions to be selected. In particular, we study the power of \emph{best-action queries}, which reveal beforehand the identity of the best action at a given time step. In practice, predictive features may be expensive, so we allow the decision maker to issue at most $k$ such queries. We establish tight bounds on the performance any algorithm can achieve when given access to $k$ best-action queries for different types of feedback models. In particular, we prove that in the full feedback model, $k$ queries are enough to achieve an optimal regret of $\Theta(\min\{\sqrt T, \frac{T}{k}\})$. This finding highlights the significant multiplicative advantage in the regret rate achievable with even a modest (sublinear) number $k \in \Omega(\sqrt{T})$ of queries. Additionally, we study the challenging setting in which the only available feedback is obtained during the time steps corresponding to the $k$ best-action queries. There, we provide a tight regret rate of $\Theta(\min\{\frac{T}{\sqrt k},\frac{T^2}{k^2}\})$, which improves over the standard $\Theta(\frac{T}{\sqrt k})$ regret rate for label efficient prediction for $k \in \Omega(T^{2/3})$.

We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty value. These training methods are particularly relevant for active learning and data subset selection problems. For SGD with a constant step size update, we present convergence results for linear classifiers and linearly separable datasets using squared hinge loss and similar training loss functions. Additionally, we extend our analysis to more general classifiers and datasets, considering a wide range of loss-based sampling strategies and smooth convex training loss functions. We propose a novel algorithm called Adaptive-Weight Sampling (AWS) that utilizes SGD with an adaptive step size that achieves stochastic Polyak's step size in expectation. We establish convergence rate results for AWS for smooth convex training loss functions. Our numerical experiments demonstrate the efficiency of AWS on various datasets by using either exact or estimated loss values.

Predicting the popularity of social media content in real time requires approaches that efficiently operate at global scale. Popularity prediction is important for many applications, including detection of harmful viral content to enable timely content moderation. The prediction task is difficult because views result from interactions between user interests, content features, resharing, feed ranking, and network structure. We consider the problem of accurately predicting popularity both at any given prediction time since a content item's creation and for arbitrary time horizons into the future. In order to achieve high accuracy for different prediction time horizons, it is essential for models to use static features (of content and user) as well as observed popularity growth up to prediction time. We propose a feature-based approach based on a self-excited Hawkes point process model, which involves prediction of the content's popularity at one or more reference horizons in tandem with a point predictor of an effective growth parameter that reflects the timescale of popularity growth. This results in a highly scalable method for popularity prediction over arbitrary prediction time horizons that also achieves a high degree of accuracy, compared to several leading baselines, on a dataset of public page content on Facebook over a two-month period, covering billions of content views and hundreds of thousands of distinct content items. The model has shown competitive prediction accuracy against a strong baseline that consists of separately trained models for specific prediction time horizons.