We consider the problem of online learning where the sequence of actions played by the learner must adhere to an unknown safety constraint at every round. The goal is to minimize regret with respect to the best safe action in hindsight while simultaneously satisfying the safety constraint with high probability on each round. We provide a general meta-algorithm that leverages an online regression oracle to estimate the unknown safety constraint, and converts the predictions of an online learning oracle to predictions that adhere to the unknown safety constraint. On the theoretical side, our algorithm's regret can be bounded by the regret of the online regression and online learning oracles, the eluder dimension of the model class containing the unknown safety constraint, and a novel complexity measure that captures the difficulty of safe learning. We complement our result with an asymptotic lower bound that shows that the aforementioned complexity measure is necessary. When the constraints are linear, we instantiate our result to provide a concrete algorithm with $\sqrt{T}$ regret using a scaling transformation that balances optimistic exploration with pessimistic constraint satisfaction.

We study the problem of differentially-private (DP) stochastic (convex-concave) saddle-points in the polyhedral setting. We propose $(\varepsilon, \delta)$-DP algorithms based on stochastic mirror descent that attain nearly dimension-independent convergence rates for the expected duality gap, a type of guarantee that was known before only for bilinear objectives. For convex-concave and first-order-smooth stochastic objectives, our algorithms attain a rate of $\sqrt{\log(d)/n} + (\log(d)^{3/2}/[n\varepsilon])^{1/3}$, where $d$ is the dimension of the problem and $n$ the dataset size. Under an additional second-order-smoothness assumption, we improve the rate on the expected gap to $\sqrt{\log(d)/n} + (\log(d)^{3/2}/[n\varepsilon])^{2/5}$. Under this additional assumption, we also show, by using bias-reduced gradient estimators, that the duality gap is bounded by $\log(d)/\sqrt{n} + \log(d)/[n\varepsilon]^{1/2}$ with constant success probability. This result provides evidence of the near-optimality of the approach. Finally, we show that combining our methods with acceleration techniques from online learning leads to the first algorithm for DP Stochastic Convex Optimization in the polyhedral setting that is not based on Frank-Wolfe methods. For convex and first-order-smooth stochastic objectives, our algorithms attain an excess risk of $\sqrt{\log(d)/n} + \log(d)^{7/10}/[n\varepsilon]^{2/5}$, and when additionally assuming second-order-smoothness, we improve the rate to $\sqrt{\log(d)/n} + \log(d)/\sqrt{n\varepsilon}$. Instrumental to all of these results are various extensions of the classical Maurey Sparsification Lemma, which may be of independent interest.

ClickTree: A Tree-based Method for Predicting Math Students' Performance Based on Clickstream Data The prediction of student performance and the analysis of students' learning behavior play an important role in enhancing online courses. By analysing a massive amount of clickstream data that captures student behavior, educators can gain valuable insights into the factors that influence academic outcomes and identify areas of improvement in courses. In this study, we developed ClickTree, a tree-based methodology, to predict student performance in mathematical assignments based on students' clickstream data. We extracted a set of features, including problem-level, assignment-level and student-level features, from the extensive clickstream data and trained a CatBoost tree to predict whether a student successfully answers a problem in an assignment. The developed method achieved an AUC of 0.78844 in the Educational Data Mining Cup 2023 and ranked second in the competition. Furthermore, our results indicate that students encounter more difficulties in the problem types that they must select a subset of answers from a given set as well as problem subjects of Algebra II. Additionally, students who performed well in answering end-unit assignment problems engaged more with in-unit assignments and answered more problems correctly, while those who struggled had higher tutoring request rate. The proposed method can be utilized to improve students' learning experiences, and the above insights can be integrated into mathematical courses to enhance students' learning outcomes. In recent years, massive amounts of log data have been collected from students' interactions with online courses, providing researchers with valuable information to analyze student behavior and its impact on academic performance (Yi et al., 2018; Aljohani et al., 2019). By examining clickstream data, educators can gain deeper insights into students' study habits, navigation patterns, and levels of engagement (Wen and Rosé, 2014; Li et al., 2020; Matcha et al., 2020).

In this work, we investigate the online learning problem of revenue maximization in ad auctions, where the seller needs to learn the click-through rates (CTRs) of each ad candidate and charge the price of the winner through a pay-per-click manner. We focus on two models of the advertisers' strategic behaviors. First, we assume that the advertiser is completely myopic; i.e.~in each round, they aim to maximize their utility only for the current round. In this setting, we develop an online mechanism based on upper-confidence bounds that achieves a tight $O(\sqrt{T})$ regret in the worst-case and negative regret when the values are static across all the auctions and there is a gap between the highest expected value (i.e.~value multiplied by their CTR) and second highest expected value ad. Next, we assume that the advertiser is non-myopic and cares about their long term utility. This setting is much more complex since an advertiser is incentivized to influence the mechanism by bidding strategically in earlier rounds. In this setting, we provide an algorithm to achieve negative regret for the static valuation setting (with a positive gap), which is in sharp contrast with the prior work that shows $O(T^{2/3})$ regret when the valuation is generated by adversary.

We devise an online learning algorithm -- titled Switching via Monotone Adapted Regret Traces (SMART) -- that adapts to the data and achieves regret that is instance optimal, i.e., simultaneously competitive on every input sequence compared to the performance of the follow-the-leader (FTL) policy and the worst case guarantee of any other input policy. We show that the regret of the SMART policy on any input sequence is within a multiplicative factor $e/(e-1) \approx 1.58$ of the smaller of: 1) the regret obtained by FTL on the sequence, and 2) the upper bound on regret guaranteed by the given worst-case policy. This implies a strictly stronger guarantee than typical `best-of-both-worlds' bounds as the guarantee holds for every input sequence regardless of how it is generated. SMART is simple to implement as it begins by playing FTL and switches at most once during the time horizon to the worst-case algorithm. Our approach and results follow from an operational reduction of instance optimal online learning to competitive analysis for the ski-rental problem. We complement our competitive ratio upper bounds with a fundamental lower bound showing that over all input sequences, no algorithm can get better than a $1.43$-fraction of the minimum regret achieved by FTL and the minimax-optimal policy. We also present a modification of SMART that combines FTL with a ``small-loss" algorithm to achieve instance optimality between the regret of FTL and the small loss regret bound.

Personalized education, tailored to individual student needs, leverages educational technology and artificial intelligence (AI) in the digital age to enhance learning effectiveness. The integration of AI in educational platforms provides insights into academic performance, learning preferences, and behaviors, optimizing the personal learning process. Driven by data mining techniques, it not only benefits students but also provides educators and institutions with tools to craft customized learning experiences. To offer a comprehensive review of recent advancements in personalized educational data mining, this paper focuses on four primary scenarios: educational recommendation, cognitive diagnosis, knowledge tracing, and learning analysis. This paper presents a structured taxonomy for each area, compiles commonly used datasets, and identifies future research directions, emphasizing the role of data mining in enhancing personalized education and paving the way for future exploration and innovation.

Generative AI is expected to have a vast, positive impact on education; however, at present, this potential has not yet been demonstrated at scale at university level. In this study, we present first evidence that generative AI can increase the speed of learning substantially in university students. We tested whether using the AI-powered teaching assistant Syntea affected the speed of learning of hundreds of distance learning students across more than 40 courses at the IU International University of Applied Sciences. Our analysis suggests that using Syntea reduced their study time substantially--by about 27\% on average--in the third month after the release of Syntea. Taken together, the magnitude of the effect and the scalability of the approach implicate generative AI as a key lever to significantly improve and accelerate learning by personalisation.

The integration of artificial intelligence (AI) into daily life, particularly through information retrieval and recommender systems, has necessitated advanced user modeling and profiling techniques to deliver personalized experiences. These techniques aim to construct accurate user representations based on the rich amounts of data generated through interactions with these systems. This paper presents a comprehensive survey of the current state, evolution, and future directions of user modeling and profiling research. We provide a historical overview, tracing the development from early stereotype models to the latest deep learning techniques, and propose a novel taxonomy that encompasses all active topics in this research area, including recent trends. Our survey highlights the paradigm shifts towards more sophisticated user profiling methods, emphasizing implicit data collection, multi-behavior modeling, and the integration of graph data structures. We also address the critical need for privacy-preserving techniques and the push towards explainability and fairness in user modeling approaches. By examining the definitions of core terminology, we aim to clarify ambiguities and foster a clearer understanding of the field by proposing two novel encyclopedic definitions of the main terms. Furthermore, we explore the application of user modeling in various domains, such as fake news detection, cybersecurity, and personalized education. This survey serves as a comprehensive resource for researchers and practitioners, offering insights into the evolution of user modeling and profiling and guiding the development of more personalized, ethical, and effective AI systems.

We continue the study of the computational complexity of differentially private PAC learning and how it is situated within the foundations of machine learning. A recent line of work uncovered a qualitative equivalence between the private PAC model and Littlestone's mistake-bounded model of online learning, in particular, showing that any concept class of Littlestone dimension $d$ can be privately PAC learned using $\mathrm{poly}(d)$ samples. This raises the natural question of whether there might be a generic conversion from online learners to private PAC learners that also preserves computational efficiency. We give a negative answer to this question under reasonable cryptographic assumptions (roughly, those from which it is possible to build indistinguishability obfuscation for all circuits). We exhibit a concept class that admits an online learner running in polynomial time with a polynomial mistake bound, but for which there is no computationally-efficient differentially private PAC learner. Our construction and analysis strengthens and generalizes that of Bun and Zhandry (TCC 2016-A), who established such a separation between private and non-private PAC learner.

We study the problem of online learning Markov Decision Processes (MDPs) when both the transition distributions and loss functions are chosen by an adversary. We present an algorithm that, under a mixing assumption, achieves O(\sqrt{T\log \Pi } \log \Pi) regret with respect to a comparison set of policies \Pi . The regret is independent of the size of the state and action spaces. When expectations over sample paths can be computed efficiently and the comparison set \Pi has polynomial size, this algorithm is efficient. We also consider the episodic adversarial online shortest path problem.