We provide an online learning algorithm that obtains regret $G\|w_\star\|\sqrt{T\log(\|w_\star\|G\sqrt{T})} + \|w_\star\|^2 + G^2$ on $G$-Lipschitz convex losses for any comparison point $w_\star$ without knowing either $G$ or $\|w_\star\|$. Importantly, this matches the optimal bound $G\|w_\star\|\sqrt{T}$ available with such knowledge (up to logarithmic factors), unless either $\|w_\star\|$ or $G$ is so large that even $G\|w_\star\|\sqrt{T}$ is roughly linear in $T$. Thus, it matches the optimal bound in all cases in which one can achieve sublinear regret, which arguably most "interesting" scenarios.

Follow-the-Regularized-Leader (FTRL) is a powerful framework for various online learning problems. By designing its regularizer and learning rate to be adaptive to past observations, FTRL is known to work adaptively to various properties of an underlying environment. However, most existing adaptive learning rates are for online learning problems with a minimax regret of $\Theta(\sqrt{T})$ for the number of rounds $T$, and there are only a few studies on adaptive learning rates for problems with a minimax regret of $\Theta(T^{2/3})$, which include several important problems dealing with indirect feedback. To address this limitation, we establish a new adaptive learning rate framework for problems with a minimax regret of $\Theta(T^{2/3})$. Our learning rate is designed by matching the stability, penalty, and bias terms that naturally appear in regret upper bounds for problems with a minimax regret of $\Theta(T^{2/3})$. As applications of this framework, we consider two major problems dealing with indirect feedback: partial monitoring and graph bandits. We show that FTRL with our learning rate and the Tsallis entropy regularizer improves existing Best-of-Both-Worlds (BOBW) regret upper bounds, which achieve simultaneous optimality in the stochastic and adversarial regimes. The resulting learning rate is surprisingly simple compared to the existing learning rates for BOBW algorithms for problems with a minimax regret of $\Theta(T^{2/3})$.

Clustering in education, particularly in large-scale online environments like MOOCs, is essential for understanding and adapting to diverse student needs. However, the effectiveness of clustering depends on its interpretability, which becomes challenging with high-dimensional data. Existing clustering approaches often neglect individual differences in feature importance and rely on a homogenized feature set. Addressing this gap, we introduce Interpret3C (Interpretable Conditional Computation Clustering), a novel clustering pipeline that incorporates interpretable neural networks (NNs) in an unsupervised learning context. This method leverages adaptive gating in NNs to select features for each student. Then, clustering is performed using the most relevant features per student, enhancing clusters' relevance and interpretability. We use Interpret3C to analyze the behavioral clusters considering individual feature importances in a MOOC with over 5, 000 students. This research contributes to the field by offering a scalable, robust clustering methodology and an educational case study that respects individual student differences and improves interpretability for high-dimensional data.

Knowledge tracing has been widely used in online learning systems to guide the students' future learning. However, most existing KT models primarily focus on extracting abundant information from the question sets and explore the relationships between them, but ignore the personalized student behavioral information in the learning process. This will limit the model's ability to accurately capture the personalized knowledge states of students and reasonably predict their performances. To alleviate this limitation, we explicitly models the personalized learning process by incorporating the emotions, a representative personalized behavior in the learning process, into KT framework. Specifically, we present a novel Dual-State Personalized Knowledge Tracing with Emotional Incorporation model to achieve this goal: Firstly, we incorporate emotional information into the modeling process of knowledge state, resulting in the Knowledge State Boosting Module. Secondly, we design an Emotional State Tracing Module to monitor students' personalized emotional states, and propose an emotion prediction method based on personalized emotional states. Finally, we apply the predicted emotions to enhance students' response prediction. Furthermore, to extend the generalization capability of our model across different datasets, we design a transferred version of DEKT, named Transfer Learning-based Self-loop model (T-DEKT). Extensive experiments show our method achieves the state-of-the-art performance.

In this article, we explore computer vision approaches to detect abnormal head pose during e-learning sessions and we introduce a study on the effects of mobile phone usage during these sessions. We utilize behavioral data collected from 120 learners monitored while participating in a MOOC learning sessions. Our study focuses on the influence of phone-usage events on behavior and physiological responses, specifically attention, heart rate, and meditation, before, during, and after phone usage. Additionally, we propose an approach for estimating head pose events using images taken by the webcam during the MOOC learning sessions to detect phone-usage events. Our hypothesis suggests that head posture undergoes significant changes when learners interact with a mobile phone, contrasting with the typical behavior seen when learners face a computer during e-learning sessions. We propose an approach designed to detect deviations in head posture from the average observed during a learner's session, operating as a semi-supervised method. This system flags events indicating alterations in head posture for subsequent human review and selection of mobile phone usage occurrences with a sensitivity over 90%.

We study the role of contextual information in the online learning problem of brokerage between traders. At each round, two traders arrive with secret valuations about an asset they wish to trade. The broker suggests a trading price based on contextual data about the asset. Then, the traders decide to buy or sell depending on whether their valuations are higher or lower than the brokerage price. We assume the market value of traded assets is an unknown linear function of a $d$-dimensional vector representing the contextual information available to the broker. Additionally, we model traders' valuations as independent bounded zero-mean perturbations of the asset's market value, allowing for potentially different unknown distributions across traders and time steps. Consistently with the existing online learning literature, we evaluate the performance of a learning algorithm with the regret with respect to the gain from trade. If the noise distributions admit densities bounded by some constant $L$, then, for any time horizon $T$: - If the agents' valuations are revealed after each interaction, we provide an algorithm achieving $O ( L d \ln T )$ regret, and show a corresponding matching lower bound of $\Omega( Ld \ln T )$. - If only their willingness to sell or buy at the proposed price is revealed after each interaction, we provide an algorithm achieving $O(\sqrt{LdT \ln T })$ regret, and show that this rate is optimal (up to logarithmic factors), via a lower bound of $\Omega(\sqrt{LdT})$. To complete the picture, we show that if the bounded density assumption is lifted, then the problem becomes unlearnable, even with full feedback.

We explore brokerage between traders in an online learning framework. At any round $t$, two traders meet to exchange an asset, provided the exchange is mutually beneficial. The broker proposes a trading price, and each trader tries to sell their asset or buy the asset from the other party, depending on whether the price is higher or lower than their private valuations. A trade happens if one trader is willing to sell and the other is willing to buy at the proposed price. Previous work provided guidance to a broker aiming at enhancing traders' total earnings by maximizing the gain from trade, defined as the sum of the traders' net utilities after each interaction. In contrast, we investigate how the broker should behave to maximize the trading volume, i.e., the total number of trades. We model the traders' valuations as an i.i.d. process with an unknown distribution. If the traders' valuations are revealed after each interaction (full-feedback), and the traders' valuations cumulative distribution function (cdf) is continuous, we provide an algorithm achieving logarithmic regret and show its optimality up to constant factors. If only their willingness to sell or buy at the proposed price is revealed after each interaction ($2$-bit feedback), we provide an algorithm achieving poly-logarithmic regret when the traders' valuations cdf is Lipschitz and show that this rate is near-optimal. We complement our results by analyzing the implications of dropping the regularity assumptions on the unknown traders' valuations cdf. If we drop the continuous cdf assumption, the regret rate degrades to $\Theta(\sqrt{T})$ in the full-feedback case, where $T$ is the time horizon. If we drop the Lipschitz cdf assumption, learning becomes impossible in the $2$-bit feedback case.

We study the task of online learning in the presence of Massart noise. Instead of assuming that the online adversary chooses an arbitrary sequence of labels, we assume that the context $\mathbf{x}$ is selected adversarially but the label $y$ presented to the learner disagrees with the ground-truth label of $\mathbf{x}$ with unknown probability at most $\eta$. We study the fundamental class of $\gamma$-margin linear classifiers and present a computationally efficient algorithm that achieves mistake bound $\eta T + o(T)$. Our mistake bound is qualitatively tight for efficient algorithms: it is known that even in the offline setting achieving classification error better than $\eta$ requires super-polynomial time in the SQ model. We extend our online learning model to a $k$-arm contextual bandit setting where the rewards -- instead of satisfying commonly used realizability assumptions -- are consistent (in expectation) with some linear ranking function with weight vector $\mathbf{w}^\ast$. Given a list of contexts $\mathbf{x}_1,\ldots \mathbf{x}_k$, if $\mathbf{w}^*\cdot \mathbf{x}_i > \mathbf{w}^* \cdot \mathbf{x}_j$, the expected reward of action $i$ must be larger than that of $j$ by at least $\Delta$. We use our Massart online learner to design an efficient bandit algorithm that obtains expected reward at least $(1-1/k)~ \Delta T - o(T)$ bigger than choosing a random action at every round.

As online courses become the norm in the higher-education landscape, investigations into student performance between students who take online vs on-campus versions of classes become necessary. While attention has been given to looking at differences in learning outcomes through comparisons of students' end performance, less attention has been given in comparing students' engagement patterns between different modalities. In this study, we analyze a heterogeneous knowledge graph consisting of students, course videos, formative assessments and their interactions to predict student performance via a Graph Convolutional Network (GCN). Using students' performance on the assessments, we attempt to determine a useful model for identifying at-risk students. We then compare the models generated between 5 on-campus and 2 fully-online MOOC-style instances of the same course. The model developed achieved a 70-90\% accuracy of predicting whether a student would pass a particular problem set based on content consumed, course instance, and modality.

Our ongoing development and deployment of an online robotics education platform highlighted a gap in providing an interactive, feedback-rich learning environment essential for mastering programming concepts in robotics, which they were not getting with the traditional code-simulate-turn in workflow. Since teaching resources are limited, students would benefit from feedback in real-time to find and fix their mistakes in the programming assignments. To address these concerns, this paper will focus on creating a system for unit testing while integrating it into the course workflow. We facilitate this real-time feedback by including unit testing in the design of programming assignments so students can understand and fix their errors on their own and without the prior help of instructors/TAs serving as a bottleneck. In line with the framework's personalized student-centered approach, this method makes it easier for students to revise, and debug their programming work, encouraging hands-on learning. The course workflow updated to include unit tests will strengthen the learning environment and make it more interactive so that students can learn how to program robots in a self-guided fashion.