Gradient-variation online learning aims to achieve regret guarantees that scale with variations in the gradients of online functions, which is crucial for attaining fast convergence in games and robustness in stochastic optimization, hence receiving increased attention. Existing results often require the smoothness condition by imposing a fixed bound on gradient Lipschitzness, which may be unrealistic in practice. Recent efforts in neural network optimization suggest a generalized smoothness condition, allowing smoothness to correlate with gradient norms. In this paper, we systematically study gradient-variation online learning under generalized smoothness. We extend the classic optimistic mirror descent algorithm to derive gradient-variation regret by analyzing stability over the optimization trajectory and exploiting smoothness locally.

Online learning methods, like the seminal Passive-Aggressive (PA) classifier, are still highly effective for high-dimensional streaming data, out-of-core processing, and other throughput-sensitive applications. Many such algorithms rely on fast adaptation to individual errors as a key to their convergence. While such algorithms enjoy low theoretical regret, in real-world deployment they can be sensitive to individual outliers that cause the algorithm to over-correct. When such outliers occur at the end of the data stream, this can cause the final solution to have unexpectedly low accuracy. We design a weighted reservoir sampling (WRS) approach to obtain a stable ensemble model from the sequence of solutions without requiring additional passes over the data, hold-out sets, or a growing amount of memory.

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}) .

This paper reports on findings from a comparative study on the effectiveness and efficiency of federated unlearning strategies within Federated Online Learning to Rank (FOLTR), with specific attention to systematically analysing the unlearning capabilities of methods in a verifiable manner. Federated approaches to ranking of search results have recently garnered attention to address users privacy concerns. In FOLTR, privacy is safeguarded by collaboratively training ranking models across decentralized data sources, preserving individual user data while optimizing search results based on implicit feedback, such as clicks. Recent legislation introduced across numerous countries is establishing the so called "the right to be forgotten", according to which services based on machine learning models like those in FOLTR should provide capabilities that allow users to remove their own data from those used to train models. This has sparked the development of unlearning methods, along with evaluation practices to measure whether unlearning of a user data successfully occurred. Current evaluation practices are however often controversial, necessitating the use of multiple metrics for a more comprehensive assessment -- but previous proposals of unlearning methods only used single evaluation metrics. This paper addresses this limitation: our study rigorously assesses the effectiveness of unlearning strategies in managing both under-unlearning and over-unlearning scenarios using adapted, and newly proposed evaluation metrics. Thanks to our detailed analysis, we uncover the strengths and limitations of five unlearning strategies, offering valuable insights into optimizing federated unlearning to balance data privacy and system performance within FOLTR. We publicly release our code and complete results at https://github.com/Iris1026/Unlearning-for-FOLTR.git.

Massive Open Online Courses (MOOCs) lack direct interaction between learners and instructors, making it challenging for learners to understand new knowledge concepts. Recently, learners have increasingly used Large Language Models (LLMs) to support them in acquiring new knowledge. However, LLMs are prone to hallucinations which limits their reliability. Retrieval-Augmented Generation (RAG) addresses this issue by retrieving relevant documents before generating a response. However, the application of RAG across different MOOCs is limited by unstructured learning material. Furthermore, current RAG systems do not actively guide learners toward their learning needs. To address these challenges, we propose a Graph RAG pipeline that leverages Educational Knowledge Graphs (EduKGs) and Personal Knowledge Graphs (PKGs) to guide learners to understand knowledge concepts in the MOOC platform CourseMapper. Specifically, we implement (1) a PKG-based Question Generation method to recommend personalized questions for learners in context, and (2) an EduKG-based Question Answering method that leverages the relationships between knowledge concepts in the EduKG to answer learner selected questions. To evaluate both methods, we conducted a study with 3 expert instructors on 3 different MOOCs in the MOOC platform CourseMapper. The results of the evaluation show the potential of Graph RAG to empower learners to understand new knowledge concepts in a personalized learning experience.

We formalize the problem of online learning-unlearning, where a model is updated sequentially in an online setting while accommodating unlearning requests between updates. After a data point is unlearned, all subsequent outputs must be statistically indistinguishable from those of a model trained without that point. We present two online learner-unlearner (OLU) algorithms, both built upon online gradient descent (OGD). The first, passive OLU, leverages OGD's contractive property and injects noise when unlearning occurs, incurring no additional computation. The second, active OLU, uses an offline unlearning algorithm that shifts the model toward a solution excluding the deleted data. Under standard convexity and smoothness assumptions, both methods achieve regret bounds comparable to those of standard OGD, demonstrating that one can maintain competitive regret bounds while providing unlearning guarantees.

Online Resource Allocation problem is a central problem in many areas of Computer Science, Operations Research, and Economics. In this problem, we sequentially receive $n$ stochastic requests for $m$ kinds of shared resources, where each request can be satisfied in multiple ways, consuming different amounts of resources and generating different values. The goal is to achieve a $(1-ε)$-approximation to the hindsight optimum, where $ε>0$ is a small constant, assuming each resource has a large budget. In this paper, we investigate the learnability and robustness of online resource allocation. Our primary contribution is a novel Exponential Pricing algorithm with the following properties: 1. It requires only a \emph{single sample} from each of the $n$ request distributions to achieve a $(1-ε)$-approximation for online resource allocation with large budgets. Such an algorithm was previously unknown, even with access to polynomially many samples, as prior work either assumed full distributional knowledge or was limited to i.i.d.\,or random-order arrivals. 2. It is robust to corruptions in the outliers model and the value augmentation model. Specifically, it maintains its $(1 - ε)$-approximation guarantee under both these robustness models, resolving the open question posed in Argue, Gupta, Molinaro, and Singla (SODA'22). 3. It operates as a simple item-pricing algorithm that ensures incentive compatibility. The intuition behind our Exponential Pricing algorithm is that the price of a resource should adjust exponentially as it is overused or underused. It differs from conventional approaches that use an online learning algorithm for item pricing. This departure guarantees that the algorithm will never run out of any resource, but loses the usual no-regret properties of online learning algorithms, necessitating a new analytical approach.

DV ANCEMENTS in AI-driven technologies have significantly enhanced modern education through personalized tutoring and adaptive learning strategies on online platforms [1], [2]. Intelligent T utoring Systems (ITSs) exemplify this progress by leveraging advanced machine learning and natural language processing models to create interactive learning environments that improve outcomes across domains like literacy [3], mathematics [4], language learning [5], biology [6] and other STEM fields [7]. As human learners interact with ITSs, often through question-and-answer scenarios with immediate responses, their performance data becomes crucial for learner modeling, enabling systems to track progress, predict future performance, and adapt instruction accordingly [8]. Learner models like Bayesian Knowledge Tracing (BKT) and other knowledge tracing variants utilize the learner performance data to uncover learning characteristics, estimate knowledge states and acquisition [9]. However, in real-world scenarios, missing learner performance data is prevalent due to factors, such as learner dropout or disengagement [10], technical issues or incomplete data logging [11], biased sampling within experimental groups [12], and more. These challenges often lead to sparse data, where items (i.e., questions or problems) remain unattempted (e.g., learners may bypass the question, leave it unanswered due to a lack of response initiation, or make no attempt to engage with it), alongside limited learner interactions [13], [14]. As shown in Figure 1, missing performance records can occur along both the attempt and question dimensions during learner-ITS interactions. In the right portion of the figure's two matrices, entries marked with "?

We revisit online binary classification by shifting the focus from competing with the best-in-class binary loss to competing against relaxed benchmarks that capture smoothed notions of optimality. Instead of measuring regret relative to the exact minimal binary error -- a standard approach that leads to worst-case bounds tied to the Littlestone dimension -- we consider comparing with predictors that are robust to small input perturbations, perform well under Gaussian smoothing, or maintain a prescribed output margin. Previous examples of this were primarily limited to the hinge loss. Our algorithms achieve regret guarantees that depend only on the VC dimension and the complexity of the instance space (e.g., metric entropy), and notably, they incur only an $O(\log(1/\gamma))$ dependence on the generalized margin $\gamma$. This stands in contrast to most existing regret bounds, which typically exhibit a polynomial dependence on $1/\gamma$. We complement this with matching lower bounds. Our analysis connects recent ideas from adversarial robustness and smoothed online learning.

We consider the relationship between learnability of a ``base class'' of functions on a set X and learnability of a class of statistical functions derived from the base class. For example, we refine results showing that learnability of a family of functions implies learnability of the family of functions mapping a function in the class to its expectation under a distribution. We will look at both Probably Approximately Correct (PAC) learning, where example inputs and outputs are chosen at random, and online learning, where the examples are chosen adversarially. We establish improved bounds on the sample complexity of learning for statistical classes, stated in terms of combinatorial dimensions of the base class. We do this by adapting techniques introduced in model theory for ``randomizing a structure''. We give particular attention to classes derived from logical formulas, and relate learnability of the statistical classes to properties of the formula. Finally, we provide bounds on the complexity of learning the statistical classes built on top of a logic-based hypothesis class.