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General Machine Learning · Online Learning, Active Learning and Bandits

Jiancheng Zhang, Meiqing Li, Qi Zhang, Yinglun Zhu

Real-world datasets across image and text domains are often characterized by skewed class distributions and noisy annotations, which jointly degrade model performance, particularly on minority classes. Among existing solutions, active learning offers an effective and efficient paradigm by selectively querying the most informative and balanced samples for annotation. We propose an innovative active learning framework that mitigates class imbalance and selects the most informative samples to annotate. Leveraging foundation model priors, our algorithm enables imbalance-aware co-decisions between foundation model and small model to tackle noisy and imbalanced labels across various domains. We introduce the first study to systematically explore active learning under the dual challenges of label noise and class imbalance across image and text domains. Extensive experiments on imbalanced datasets demonstrate that our method achieves substantial annotation savings—over 50\% compared to the best active learning baseline—while preserving performance and robustness to label noise.

General Machine Learning · Online Learning, Active Learning and Bandits

Jiajun Chen, Jin Tian, Chris Quinn

Counterfactual reasoning is one of the fundamental facets of human cognition, involved in various tasks such as explanation, credit assignment, blame, and responsibility. It describes the queries what would have happened had some intervention been performed given that something else, corresponding to Layer 3 of the Pearl Causal Hierarchy. In this project, we examine a specific type of counterfactual quantities, called counterfactual direct (Str-DE), indirect (Str-IE), and spurious (Str-SE) effects for quantifying fairness in a sequential decision-making framework. Building on these measures, we formulate an online causally-fair learning problem with multiple long-term constraints and study it in both non-parametric contextual bandits and parametric logistic bandits settings. We achieve sublinear regret and violations bounds for both bandits settings with round-wise counterfactual fairness constraints (that are a priori unknown) without Slater’s condition. In particular, for logistic bandits, we obtain nearly optimal regret bound with leading term similar to that for unconstrained case (Zhang et al., 2025).

General Machine Learning · Online Learning, Active Learning and Bandits

Hang Yu, Yu-Hu Yan, Peng Zhao

Gradient-variation online learning has drawn increasing attention due to its deep connections to game theory, optimization, etc. It has been studied extensively in the full-information setting, but is underexplored with bandit feedback. In this work, we focus on gradient variation in Bandit Convex Optimization (BCO) with two-point feedback. By proposing a refined analysis on the *non-consecutive* gradient variation, a fundamental quantity in gradient variation with bandits, we improve the dimension dependence for both convex and strongly convex functions compared with the best known results (Chiang et al., 2013). Our improved analysis for the non-consecutive gradient variation also implies other favorable problem-dependent guarantees, such as gradient-variance and small-loss regrets. Beyond the two-point setup, we demonstrate the versatility of our technique by achieving the *first* gradient-variation bound for one-point bandit linear optimization over hyper-rectangular domains. Finally, we validate the effectiveness of our results in more challenging tasks such as dynamic/universal regret minimization and bandit games, establishing the *first* gradient-variation dynamic and universal regret bounds for two-point BCO and fast convergence rates in bandit games.

General Machine Learning · Online Learning, Active Learning and Bandits

Daniel Weitekamp, Glen Smith, Ken Koedinger, Christopher MacLellan

In interactive task learning (ITL), AI agents learn new capabilities from limited human instruction provided during task execution. STAND is a new method of data-efficient rule precondition induction specifically designed for these human-in-the-loop training scenarios. A key feature of STAND is its self-awareness of its own learning—it can provide accurate metrics of training progress back to users. STAND beats popular methods like XGBoost, decision trees, random forests, and version spaces at small-data precondition induction tasks, and is highly accurate at estimating when its performance improves on holdout examples. In our evaluations, we find that STAND shows more monotonic improvement than other models with low rates of error recurrence. These features of STAND support a more consistent training experience, enabling human instructors to estimate when they are finished training and providing active-learning support by identifying trouble spots where more training is required.

General Machine Learning · Online Learning, Active Learning and Bandits

Yifan Zhu, John Duchi, Benjamin Van Roy

We prove that Thompson sampling exhibits $\tilde{O}(\sigma d \sqrt{T} + d r \sqrt{\mathrm{Tr}(\Sigma_0)})$ Bayesian regret in the linear-Gaussian bandit with a $\mathcal{N}(\mu_0, \Sigma_0)$ prior distribution on the coefficients, where $d$ is the dimension, $T$ is the time horizon, $r$ is the maximum $\ell_2$ norm of the actions, and $\sigma^2$ is the noise variance. In contrast to existing regret bounds, this shows that to within logarithmic factors, the prior-dependent ''burn-in'' term $d r \sqrt{\mathrm{Tr}(\Sigma_0)}$ decouples additively from the minimax (long run) regret \sigma d \sqrt{T}. Previous regret bounds exhibit a multiplicative dependence on these terms. We establish these results via a new ''elliptical potential'' lemma, and also provide a lower bound indicating that the burn-in term is unavoidable.

General Machine Learning · Online Learning, Active Learning and Bandits

Chloé Rouyer, Ronald Ortner, Peter Auer

We study a variant of the stochastic multi-armed bandit problem in which the learner aims to identify and play an arbitrary arm whose mean reward exceeds a known satisficing threshold $S$, rather than optimizing against the best arm. Prior work has shown that when such a satisficing arm exists, time-independent bounds on the satisficing regret are achievable, but these guarantees deteriorate when an arm lies close to the threshold. We focus on instances in which the excess gap $\Delta_*$ (gap between the best arm and the threshold) is small relative to the suboptimality gaps $\Delta_i$, a regime that exposes this limitation. To capture this challenge, we introduce a refined notion of regret and propose a new algorithm, uncertain-UCB, which achieves *satisficing* pseudo-regret of $ O \left(\sum_{i: \Delta_i > \Delta_*} \frac{\log(K/\Delta_*)}{\Delta_i}\right), $ while recovering standard pseudo-regret bounds when no arm exceeds the threshold. Further, we establish a near-matching lower bound in the small excess-gap regime, showing that any algorithm incurs at least $ \Omega \left(\sum_{i: \Delta_i > \Delta_*} \frac{\log \left(\left(\sum_{i:\Delta_i > \Delta_*} \Delta_*/\Delta_i\right)^{-1}\right)}{\Delta_i}\right) $ satisficing pseudo-regret.

General Machine Learning · Online Learning, Active Learning and Bandits

Youngmin Oh

We study linear dueling bandits in volatile environments characterized by the simultaneous presence of post-serving contexts, delayed feedback, and adversarial corruption. Feedback is subject to unknown stochastic or adversarial delays and a cumulative corruption budget $\mathcal{C}$. To address these challenges, we propose \term, which integrates a learned approximator that predicts post-serving contexts from pre-serving information. It further employs an adaptive weighting strategy that clips feature vectors to mitigate the impact of corrupted and delayed observations simultaneously. Under standard regularity conditions and a parametric post-serving mapping, we rigorously establish that our algorithm is delay-regime-agnostic, achieving a regret upper bound of $\widetilde{\mathcal{O}}(d(\sqrt{T} + \mathcal{C} + \mathcal{D}))$, where $d$ is the total feature dimension and $\mathcal{D}$ encapsulates the delay complexity. Crucially, our analysis reveals an additive cost structure between corruption and delay, avoiding the multiplicative degradation typical of prior works. We further establish lower bounds that nearly match our upper bounds up to a $\sqrt{d}$ factor for adversarial delays in the absence of post-serving contexts.

General Machine Learning · Online Learning, Active Learning and Bandits

Mengtong Hu, Ziyang Gong, Xu Shi, Ling Zhou, Peter Song

Online learning for the Cox model is challenging because its partial likelihood is non-decomposable, with each risk set requiring a summation over all samples. We propose Collaborative Operation of Linked Survival Analysis (COLSA), an online learning framework that replaces the partial likelihood with the full likelihood using sieve approximation of the baseline hazard. The proposed likelihood function is decomposable and eliminates the need to store historical data in memory, enabling efficient online updates. Moreover, COLSA maintains sufficient statistics for a higher-order basis and employs data-driven basis projection to adaptively scale model complexity to the effective sample size. Unlike existing online Cox methods, COLSA achieves asymptotic normality and attains the same statistical efficiency as the pooled-data partial likelihood estimator, without accessing full data and only requiring constant memory. Simulation studies and application to kidney transplant data demonstrate that COLSA outperforms existing online methods and matches the performance of full-data estimation.

General Machine Learning · Online Learning, Active Learning and Bandits

seohwa Hwang, Junyong Park

We introduce Box Thirding (B3), a flexible and efficient algorithm for Best Arm Identification (BAI) under fixed budget constraints. It is designed for both anytime BAI and scenarios with large $N$, where the number of arms is too large for exhaustive evaluation within a limited budget $T$. The algorithm employs a Remedian Estimation strategy: in each iteration, three arms are compared—the best-performing arm is explored further, the median is retained for future comparisons, and the weakest is discarded. Even without prior knowledge of $T$, B3 achieves an $\epsilon$ -best arm misidentification probability comparable to Sequential Halving, which requires $T$ as a prior, applied to a randomly selected subset of $c_0$ arms that fit within the budget. Empirical results show that B3 outperforms existing methods for the limited budget constraint in terms of simple regret, as demonstrated on the New Yorker Cartoon Caption Contest dataset.

Theory · Online Learning and Bandits

Ibne Farabi Shihab, SANJEDA AKTER, Anuj Sharma

We study black-box optimization of Lipschitz functions under noisy evaluations. Existing adaptive discretization methods implicitly avoid suboptimal regions but do not provide explicit certificates of optimality or measurable progress guarantees. We introduce **Certificate-Guided Pruning (CGP)**, which maintains an explicit *active set* $A_t$ of potentially optimal points via confidence-adjusted Lipschitz envelopes. Any point outside $A_t$ is certifiably suboptimal with high probability, and under a margin condition with near-optimality dimension $\alpha$, we prove Vol $(A_t)$ shrinks at a controlled rate yielding sample complexity $Õ(\varepsilon^{-(2+\alpha)})$. We develop three extensions: CGP-Adaptive learns $L$ online with $O(\log T)$ overhead; CGP-TR scales to $d > 50$ via trust regions with local certificates; and CGP-Hybrid switches to GP refinement when local smoothness is detected. Experiments on 12 benchmarks ($d \in [2, 100]$) show CGP variants match or exceed strong baselines while providing principled stopping criteria via certificate volume.

General Machine Learning · Online Learning, Active Learning and Bandits

Ricardo N. Ferreira, Joao Xavier, Claudia Soares

Addressing Constrained Online Convex Optimization (COCO), we introduce CLASP (Convex Losses And Squared Penalties), a framework that minimizes cumulative loss together with squared constraint violations. We propose two variants of CLASP, CLASP-I and CLASP-F, allowing for a joint or separate handling of the static decision set and the time-varying constraints, a decoupling flexibility that affords simpler implementations when projections onto the static decision set are easy. Our theoretical analysis departs from prior work by fully leveraging the variety of \emph{cutter operators}, and contraction properties such as the strongly quasi-nonexpansiveness, a proof strategy not previously applied in this setting. For convex losses, both CLASP algorithms achieve regret $O\left(T^{\max\\{\beta,1-\beta\\}}\right)$ and cumulative squared penalty $O\left(T^{\\{1-\beta\\}}\right)$ for any $\beta \in (0,1)$. Most importantly, for strongly convex problems, we provide the first logarithmic guarantees on both regret and cumulative squared penalty: In the strongly convex case, both CLASP algorithms guarantee that the regret is upper bounded by $O( \log T )$ and the cumulative squared penalty is also upper bounded by $O( \log T )$.

General Machine Learning · Online Learning, Active Learning and Bandits

Liangxiao Jiang, Liangxiao Jiang, Chaoqun Li, Shanshan Si

In crowdsourcing scenarios, to mitigate the impact of noisy labels assigned by non-expert workers, each instance is typically annotated multiple times by different workers. However, repeated annotation can introduce instance- or label-level redundancy, thereby inflating annotation costs. Despite its practical importance, research on repeated annotation strategies remains limited, and no existing strategy simultaneously avoids being offline, instance-unaware, and model-centric. In this paper, we propose a model-agnostic active annotation strategy, MA$^3$S, that addresses these limitations: (1) To reduce label redundancy caused by offline procedure, MA$^3$S estimates instance uncertainties with a general Beta distribution and updates them online as new labels arrive. (2) To prevent instance redundancy induced by instance-unaware designs, MA$^3$S constructs a nearest-neighbor graph to propagate instance uncertainties, reducing repeated annotations of similar instances. (3) To avoid being model-centric, MA$^3$S actively selects instances for annotation based solely on the estimated uncertainties, without relying on model feedback. Extensive experiments on synthetic and real-world datasets demonstrate that MA$^3$S consistently outperforms existing annotation strategies.

General Machine Learning · Online Learning, Active Learning and Bandits

MohammadHossein Bateni, Zahra Hadizadeh, MohammadTaghi Hajiaghayi, Mahdi JafariRaviz, Shayan Taherijam

We study networked binary classification on a directed acyclic graph (DAG) where each agent observes only a subset of the feature columns of a shared finite dataset. Agents act sequentially along the DAG: each receives prediction columns from its parents (if any), augments its local features with these columns, fits a logistic predictor by minimizing binary cross-entropy (BCE), and forwards its prediction column to its outgoing neighbors. We ask whether this sequential distributed training procedure achieves *information aggregation*, meaning that some agent attains small excess loss compared to the best logistic predictor trained with access to all feature columns. This question was studied for linear regression under squared loss by Kearns, Roth, and Ryu (2026). Extending their guarantees to classification is nontrivial because their analysis relies on quadratic structure that does not directly transfer to BCE with a logistic link. We analyze the resulting sequential logit-passing protocol and prove: (i) an excess loss upper bound of $O(M/\sqrt{D})$ on depth-$D$ paths under the condition that every $M$ contiguous subsequence of $M$ agents collectively observe all features, and (ii) a close lower bound showing instances with excess loss of at least $\Omega(k/D)$ where $k$ is the dimension of the feature space. Together, these results identify network depth as a fundamental bottleneck for information aggregation in networked logistic regression.

General Machine Learning · Online Learning, Active Learning and Bandits

Abdelhamid Ezzerg, Ilija Bogunovic, Jeremias Knoblauch

Bayesian Optimization is critically vulnerable to extreme outliers. Existing provably robust methods typically assume a bounded cumulative corruption budget, which makes them defenseless against even a single corruption of sufficient magnitude. To address this, we introduce a new adversary whose budget is only bounded in the frequency of corruptions, not in their magnitude. We then derive RCGP-UCB, an algorithm coupling the upper confidence bound (UCB) approach with a Robust Conjugate Gaussian Process (RCGP). We present stable and adaptive versions of RCGP-UCB, and prove that they achieve sublinear regret in the presence of up to $O(T^{1/4})$ and $O(T^{1/7})$ corruptions with possibly infinite magnitude. This robustness comes at near zero cost: without outliers, RCGP-UCB's regret bounds match those of the standard GP-UCB algorithm.

General Machine Learning · Online Learning, Active Learning and Bandits

Amith Bhat Hosadurga Anand, Aadirupa Saha, Haipeng Luo

In this paper, we address the standard $K$-armed multi-armed bandit (MAB) with $M$ heterogeneous data sources, each exhibiting unknown and distinct noise variances, $\sigma_j^2$. We propose SOAR (Source-Optimistic Adaptive Regret Minimization), a novel algorithm that adaptively balances exploration and exploitation by jointly constructing upper confidence bounds for arm rewards and lower confidence bounds for data source variances. Our theoretical analysis establishes that SOAR achieves a regret bound of $\tilde{O}\left({\sigma^*}^2 \sum_{i=2}^K \tfrac{1}{\Delta_i}\right),$ along with a preprocessing cost that depends only on the problem parameters $\\{\sigma_j\\}_{j = 1}^M$, $K$, and grows at most logarithmically with the horizon $T$; where ${\sigma^\*}^2$ is the minimum source variance, and $\Delta_i$ denotes the suboptimality-gap of the $i$-th arm reward. The $\tilde O(.)$ notation hides the polylogarithmic factors in these problem parameters. This near-optimal instance dependence regret analysis of SOAR underscores its effectiveness in dynamically managing heteroscedastic noise without incurring significant overhead. Experiments on synthetic problem instances and a real dataset (MovieLens 25M) demonstrate that our method significantly outperforms baseline bandit algorithms in terms of regret performance. Our work opens a new direction for adaptively leveraging multiple heterogeneous data sources, extending beyond traditional bandit frameworks.

General Machine Learning · Online Learning, Active Learning and Bandits

Runzhe Gu, Wenguang Sun, Bowen Gang, Xintao Xia

Online evaluation of large language models increasingly relies on sequentially collected pairwise preferences, enabling human-aligned assessment and continuous data collection until closely performing models can be reliably distinguished. However, adaptive sampling and continuous monitoring invalidate classical fixed-sample inference, rendering existing ranking procedures largely heuristic. We propose SERPANT (Sequential E-value Ranking and Pruning via Adaptive Null Testing), a principled framework for online LLM ranking with anytime-valid guarantees. SERPANT formulates model comparison as a collection of pairwise hypothesis tests and constructs e-processes to ensure family-wise error rate control at any monitoring time. Anytime validity provides a theoretical justification for early stopping, enabling substantial cost savings from expensive human annotation. To improve efficiency, we introduce a novel tournament-based sampling strategy that adaptively selects comparisons based on past outcomes. The proposed framework further provides anytime-valid confidence sets for top-k model identification. Theoretical and empirical results on benchmark datasets validate the efficiency and statistical guarantees.

General Machine Learning · Online Learning, Active Learning and Bandits

Haodong Lu, Chongyang Zhao, Minhui Xue, Lina Yao, Kristen Moore, Dong Gong

Continual learning (CL) with large pre-trained models is challenged by task interference and catastrophic forgetting. Existing LoRA-based Mixture-of-Experts (MoE) methods mitigate forgetting by adding new task-specific adapters and freezing old ones, but often suffer from redundancy, interference, and ambiguous routing due to coarse-grained experts and routing. Coarse-grained experts (i.e., full LoRA adapters with large rank) encode low-specialty information. Newly added experts often duplicate or conflict with existing ones, causing redundancy and interference. Their low specialization further confuses the router, accelerating routing degradation and forgetting as experts accumulate. In this work, we propose MoRAM (Mixture of Rank-1 Associative Memory). Grounded in the view that weight matrices function as linear associative memories, MoRAM achieves CL as gradual incrementing of atomic rank-1 memory experts. Each rank-1 adapter acts as a fine-grained MoE expert or an associative memory unit. By viewing rank-1 adapters as key–value pairs, we eliminate explicit routers in MoE-LoRA, using a self-activation mechanism where each memory atom evaluates its own relevance via its intrinsic key. This transforms the adaptation process into robust, content-addressable retrieval. Extensive experiments on CLIP and LLMs demonstrate that \ours significantly outperforms state-of-the-art baselines, achieving superior plasticity-stability trade-offs, improving generalization while mitigating forgetting.

General Machine Learning · Online Learning, Active Learning and Bandits

Gianmarco Genalti, Achraf Azize, Vianney Perchet

Network routers that enforce Quality-of-Service (QoS) guarantees must decide, at every clock cycle, which expiring packet of information to transmit, even when the value of the packet is unknown until it is processed. We frame this problem as the Online Packet Scheduling with Deadlines (OPSD) problem under Partial Feedback: packets arrive at every clock cycle, with different deadlines, but the weights are only observed after execution. Under a stochastic assumption on the unknown weights, we explore different variants of the OPSD problem with bandit feedback. We establish a connection between our setting and the sleeping bandits problem, and set our learning goal to $\alpha$-regret minimization. We provide algorithms with provable $\alpha$-regret guarantees under different spans of slackness, distinguishing systems allowing for randomization and systems that do not. In every scenario, our algorithms achieve an $\alpha$-regret upper bound of $\widetilde{\mathcal{O}}\left(\sqrt{KT}\right)$, matching the lower bound for the standard bandit setting. In the practically relevant case of $2$-bounded deadline instances, where the deadline is set at most one clock cycle away from the arrival, our deterministic algorithm achieves the provably tightest possible competitive ratio. Remarkably, when the number of distinct packet types $K\ge 2$ is finite, it is possible to break the well-established $\Phi = \frac{1+\sqrt{5}}{2}$ competitive ratio barrier and attain a tighter competitive ratio $\theta_K$ ranging in $[\sqrt{2}, \Phi)$.

General Machine Learning · Online Learning, Active Learning and Bandits

Humaira Kousar, Hasnain Irshad Bhatti, Jaekyun Moon

Efficient data selection is crucial for enhancing the training efficiency of deep neural networks and minimizing annotation requirements. Traditional methods often face high computational costs, limiting their scalability and practical use. We introduce PruneFuse, a novel strategy that leverages pruned networks for data selection and later fuses them with the original network to optimize training. PruneFuse operates in two stages: First, it applies structured pruning to create a smaller pruned network that, due to its structural coherence with the original network, is well-suited for the data selection task. This small network is then trained and selects the most informative samples from the dataset. Second, the trained pruned network is seamlessly fused with the original network. This integration leverages the insights gained during the training of the pruned network to facilitate the learning process of the fused network while leaving room for the network to discover more robust solutions. Extensive experimentation on various datasets demonstrates that PruneFuse significantly reduces computational costs for data selection, achieves better performance than baselines, and accelerates the overall training process.

Reinforcement Learning · Everything Else

Long-Fei Li, Yu-Yang Qian, Peng Zhao, Zhi-Hua Zhou

Reinforcement Learning from Human Feedback (RLHF) has shown remarkable success in aligning Large Language Models (LLMs) with human preferences. Traditional RLHF methods rely on a fixed dataset, which often suffers from limited coverage. To this end, online RLHF has emerged as a promising direction, enabling iterative data collection and refinement. Despite its potential, this paradigm faces a key bottleneck: the requirement to continuously integrate new data into the dataset and re-optimize the model from scratch at each iteration, resulting in computational and storage costs that grow linearly with the number of iterations. In this work, we address this challenge by proposing a *one-pass* reward modeling method that eliminates the need to store historical data and achieves constant-time updates per iteration. Specifically, we first formalize RLHF as a contextual preference bandit and develop a new algorithm based on online mirror descent with a tailored local norm, replacing the standard maximum likelihood estimation for reward modeling. We then apply it to various online RLHF settings, including passive data collection, active data collection, and deployment-time adaptation. We provide theoretical guarantees showing that our method enhances both statistical and computational efficiency. Finally, we design practical algorithms for LLMs and conduct experiments with the Llama-3-8B-Instruct and Qwen2.5-7B-Instruct models on Ultrafeedback and Mixture2 datasets, validating the effectiveness of our approach.