We consider estimation of a linear functional of the treatment effect from adaptively collected data. This problem finds a variety of applications including off-policy evaluation in contextual bandits, and estimation of the average treatment effect in causal inference. While a certain class of augmented inverse propensity weighting (AIPW) estimators enjoys desirable asymptotic properties including the semi-parametric efficiency, much less is known about their non-asymptotic theory with adaptively collected data. To fill in the gap, we first present generic upper bounds on the mean-squared error of the class of AIPW estimators that crucially depends on a sequentially weighted error between the treatment effect and its estimates. Motivated by this, we propose a general reduction scheme that allows one to produce a sequence of estimates for the treatment effect via online learning to minimize the sequentially weighted estimation error.

First-order methods (FOMs) are arguably the most scalable algorithms for equilibrium computation in large extensive-form games. To operationalize these methods, a distance-generating function, acting as a regularizer for the strategy space, must be chosen. The ratio between the strong convexity modulus and the diameter of the regularizer is a key parameter in the analysis of FOMs.A natural question is then: what is the optimal distance-generating function for extensive-form decision spaces? In this paper, we make a number of contributions, ultimately establishing that the weight-one dilated entropy (DilEnt) distance-generating function is optimal up to logarithmic factors. The DilEnt regularizer is notable due to its iterate-equivalence with Kernelized OMWU (KOMWU)---the algorithm with state-of-the-art dependence on the game tree size in extensive-form games---when used in conjunction with the online mirror descent (OMD) algorithm.

Differential privacy (DP) is a formal notion that restricts the privacy leakage of an algorithm when running on sensitive data, in which privacy-utility trade-off is one of the central problems in private data analysis. In this work, we investigate the fundamental limits of differential privacy in online learning algorithms and present evidence that separates three types of constraints: no DP, pure DP, and approximate DP. We first describe a hypothesis class that is online learnable under approximate DP but not online learnable under pure DP under the adaptive adversarial setting. This indicates that approximate DP must be adopted when dealing with adaptive adversaries. We then prove that any private online learner must make an infinite number of mistakes for almost all hypothesis classes.

We consider the problem of multiclass transductive online learning when the number of labels can be unbounded. Previous works by Ben-David et al. [1997] and Hanneke et al. [2024] only consider the case of binary and finite label spaces respectively. The latter work determined that their techniques fail to extend to the case of unbounded label spaces, and they pose the question of characterizing the optimal mistake bound for unbounded label spaces. We answer this question, by showing that a new dimension, termed the Level-constrained Littlestone dimension, characterizes online learnability in this setting. Along the way, we show that the trichotomy of possible minimax rates established by Hanneke et al. [2024] for finite label spaces in the realizable setting continues to hold even when the label space is unbounded.

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}\}) .

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.