In many multi-agent applications, tasks yield rewards only when executed by a coalition meeting an unknown size threshold; otherwise, feedback is fully censored. This censorship creates an identifiability problem: agents cannot distinguish stochastic failure from insufficient coordination. We formalize this setting as the Threshold-Activated Cooperative Multi-Armed Bandit (TAC-MAB) and analyze it under both centralized and decentralized coordination. We show that a centralized algorithm (C-TAC) achieves cumulative regret O(log T), decomposed into a structural-search term that captures the cost of resolving feasibility under censored feedback and a statistical-monitoring term for value estimation. We then introduce D-TAC, a decentralized event-triggered protocol in which agents synchronize only when their structural beliefs change. Empirically, D-TAC achieves a 23x reduction in communication relative to the centralized baseline while preserving feasibility alignment under conservative belief fusion. These results characterize the coordination cost of learning under censored feedback and show that near-centralized communication efficiency is achievable without continuous synchronization.
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General Machine Learning · Online Learning, Active Learning and Bandits
We study a widely used Bayesian optimization method, Gaussian process Thompson sampling (GP-TS), under the assumption that the objective function is a sample path from a GP. Compared with the GP upper confidence bound (GP-UCB) with established high-probability and expected regret bounds, most analyses of GP-TS have been limited to expected regret. Moreover, whether the recent analyses of GP-UCB for the lenient regret and the improved cumulative regret upper bound can be applied to GP-TS remains unclear. To fill these gaps, this paper shows several regret bounds: (i) a regret lower bound for GP-TS, which implies that GP-TS suffers from a polynomial dependence on $1/\delta$ with probability $\delta$, (ii) an upper bound of the second moment of cumulative regret, which directly suggests an improved regret upper bound on $\delta$, (iii) expected lenient regret upper bounds, and (iv) an improved cumulative regret upper bound on the time horizon $T$. Along the way, we provide several useful lemmas, including a relaxation of the necessary condition from recent analysis to obtain improved regret upper bounds on $T$.
General Machine Learning · Online Learning, Active Learning and Bandits
Bagging-based ensembles, most notably Adaptive Random Forests, are among the strongest performers for learning from data streams. A common denominator across these methods is their reliance on Hoeffding Trees as base learners, which grow incrementally by testing whether a candidate split is significantly better than its alternatives using concentration inequalities. Despite their empirical success, existing Hoeffding Trees variants lack valid statistical guarantees. Current analyses rely on fixed-sample concentration bounds, while split decisions are made using data-dependent stopping rules, which invalidates their guarantees and can drive the probabilty of incorrect splits to one. We introduce a principled alternative based on \emph{anytime-valid inference}. Our method provides: (i) anytime-valid control of false splits under arbitrary data streams, including non-stationary settings; (ii) finite commitment time under a predictive advantage; and (iii) under stationary i.i.d.\ data, risk is monotone decreasing and strictly improves at every split. Empirically, we evaluate both standalone trees and their use within Adaptive Random Forests on non-stationary streams. Our method improves performance while producing substantially smaller trees.
General Machine Learning · Online Learning, Active Learning and Bandits
We revisit the standard perturbation-based approach of Abernethy et al. (2008) in the context of unconstrained Bandit Linear Optimization (uBLO). We show the surprising result that in the unconstrained setting, this approach effectively reduces Bandit Linear Optimization (BLO) to a standard Online Linear Optimization (OLO) problem. Our framework improves on prior work in several ways. First, we derive expected-regret guarantees when our perturbation scheme is combined with comparator-adaptive OLO algorithms, leading to new insights about the impact of different adversarial models on the resulting comparator-adaptive rates. We extend our analysis to dynamic regret, obtaining the optimal $\sqrt{P_T}$ path-length dependencies without prior knowledge of $P_T$. We then develop the first high-probability guarantees for both static and dynamic regret in uBLO. Finally, we discuss lower bounds on the static regret, and prove the folklore $\Omega(\sqrt{dT})$ rate for adversarial linear bandits on the unit Euclidean ball, which is of independent interest.
Efficient Online Influence Maximization under the Independent Cascade Model with Node-Level Feedback
Theory · Online Learning and Bandits
Influence maximization is an important research area in social network analysis, where the goal is to select a small set of seed nodes so as to maximize the expected spread of influence under a stochastic diffusion process. Classical approximation algorithms for this problem rely on full knowledge of the underlying influence probabilities and operate in an offline manner. In many real-world settings, however, these probabilities are unknown and must be learned from data, raising the question: \emph{can one still obtain strong performance guarantees while simultaneously learning the diffusion model parameters through repeated interactions?} In this paper, we study the problem of \emph{online influence maximization} under the independent cascade model, where influence probabilities are unknown and feedback is limited to \emph{node-level} activation outcomes. Prior work relies on a \emph{pair oracle} which needs to perform a joint optimization over seed sets and feasible parameters. This oracle is difficult to implement in practice and it was open whether one can achieve sublinear regret using only a \emph{standard} offline oracle. We resolve this question by designing an online learning algorithm that achieves $\widetilde{O}(\sqrt{T})$ regret using only a \emph{standard} offline oracle. Finally, we validate our theoretical results via experiments on real and synthetic data.
General Machine Learning · Online Learning, Active Learning and Bandits
In reinforcement learning, human preference feedback is emerging as a viable alternative to expert-designed reward functions, which can be difficult to engineer in real-world problems. However, despite the growing importance of preference feedback, how to effectively *elicit* preferences remains a fundamental open problem. This work focuses on the *compatible reward identification* task. The aim is to derive, starting from preference feedback, a reward function compatible with the observed preferences and accurate across the *entire* state-action space, ensuring higher transferability, safety, and interpretability. Indeed, the most common *reinforcement learning from human feedback* objective is to learn the *optimal policy*, requiring accuracy only in the portion of the state-action space that the agent visits. However, this goal cannot provide the same guarantees as compatible reward identification. First, we discuss commonalities and differences between the two goals. Then, we consider deterministic preferences, deriving the minimum number of interactions needed to identify the set of compatible rewards, and showing that using fewer queries may lead to arbitrarily large suboptimality. Finally, we focus on stochastic preferences generated via the Bradley-Terry (BT) model. We introduce the concepts of *query basis* and its *index*, relating them to the problem complexity. Upon this, we discuss the connection between the index of a basis and the BT model, as well as the limitations that the model induces in this setting. Additionally, we devise an algorithm to identify a nearly-optimal query basis with polynomial human query complexity.
Deep Learning · Large Language Models
Users increasingly face the challenge of selecting an appropriate LLM for a given task from a rapidly growing pool of LLMs, each with distinct but often opaque latent properties. Compounding this challenge, users may lack the vocabulary or awareness to explicitly articulate the characteristics they value in an LLM's responses or deployment. We propose an interaction-efficient active learning framework in which a dueling bandit algorithm iteratively selects pairs of LLMs, collects user feedback about their responses, and updates its belief about the user's latent preferences. We introduce a novel belief-aware upper confidence bound strategy that balances exploration of the model pool with exploitation of inferred preferences, enabling efficient alignment between user needs and LLM capabilities under user-specified cost and time budgets. Through diverse experiments on LLMs and human studies, we experimentally verify that our model can efficiently match users to LLMs at a lower cost.
General Machine Learning · Online Learning, Active Learning and Bandits
We propose Bayesian Forest Thompson Sampling (BFTS), which performs Thompson sampling using arm-wise Bayesian Additive Regression Trees (BART) to model each action's mean reward and generate MCMC-based posterior draws for decision-making. We derive an information-theoretic Bayesian regret bound of order $\widetilde{\mathcal O}(K\sigma\sqrt{T})$ for ideal posterior sampling under a correctly specified Bayesian design. Empirically, BFTS achieves competitive regret on nonlinear synthetic benchmarks with near-nominal uncertainty calibration, attains the best average rank across nine OpenML contextual bandit benchmarks, and yields higher estimated policy values than linear, neural, and tree-ensemble baselines in a Drink Less micro-randomized trial case study. Across OpenML benchmarks, BFTS is robust to hyperparameter choices.
General Machine Learning · Online Learning, Active Learning and Bandits
We address the problem of multi-group mean estimation, which seeks to allocate a finite sampling budget across multiple groups to obtain uniformly accurate estimates of their means. Unlike classical multi-armed bandits, whose objective is to minimize regret by identifying and exploiting the best arm, the optimal allocation in this setting requires sampling every group on the order of $\Theta(T)$ times. This fundamental distinction makes exploration-free algorithms both natural and effective. Our work makes three contributions. First, we strengthen the existing results on subgaussian variance concentration using the Hanson-Wright inequality and identify a class of strictly subgaussian distributions that yield sharper guarantees. Second, we design exploration-free non-adaptive and adaptive algorithms, and we establish tighter regret bounds than the existing results. Third, we extend the framework to contextual bandit settings, an underexplored direction, and propose algorithms that leverage side information with provable guarantees. Overall, these results position exploration-free allocation as a principled and efficient approach to multi-group mean estimation, with potential applications in experimental design, personalization, and other domains requiring accurate multi-group inference.
General Machine Learning · Online Learning, Active Learning and Bandits
Always-on edge systems must keep learning as conditions change under tight compute budgets and must detect unreliable predictions. Bayesian binary neural networks are attractive in this setting, but mean-field Bernoulli posteriors can saturate on long non-stationary streams, wiping out epistemic uncertainty and freezing plasticity. We propose BiMU, derived from a bounded-memory variational objective that balances stability, plasticity, and forgetting. BiMU combines a data term with controlled relaxation toward the prior and an uncertainty-dependent step size that prevents saturation and sustains informative uncertainty. This non-degenerate posterior enables fully online, buffer-free active querying via Monte Carlo disagreement, reducing label queries and backpropagation updates under imbalance. BiMU sustains learning and strong OOD detection on 1000-task Permuted-MNIST, and on OpenLORIS-Object achieves up to 32× label/update savings at matched accuracy under class imbalance and feature compression.
Reinforcement Learning · Online
Aligning large language models (LLM) with human preference plays a key role in building modern generative models and can be achieved by reinforcement learning from human feedback (RLHF). Despite their superior performance, current RLHF approaches often require a large amount of human-labelled preference data, which is expensive to collect. In this paper, inspired by the success of active learning, we address this problem by proposing query-efficient RLHF methods. We first formalize the alignment problem as a contextual dueling bandit problem and design an active-query-based proximal policy optimization (APPO) algorithm with an $\tilde{O}(d^2/\Delta)$ instance-dependent regret bound and an $\tilde{O}(d^2/\Delta^2)$ query complexity, where $d$ is the dimension of feature space and $\Delta$ is the sub-optimality gap over all the contexts. We then propose ADPO, a practical version of our algorithm based on direct preference optimization (DPO) and apply it to fine-tuning LLMs. Our experiments show that ADPO, while only making about half of queries for human preference, matches the performance of DPO, establishing it as a data-efficient alternative to DPO. The codes are available at https://github.com/jkx19/ActiveQuery.
General Machine Learning · Online Learning, Active Learning and Bandits
Online conformal prediction (OCP) seeks prediction intervals that achieve long-run $1-\alpha$ coverage for arbitrary (possibly adversarial) data streams, while remaining as informative as possible. Existing OCP methods often require manual learning-rate tuning to work well, and may also require algorithm-specific analyses. Here, we develop a general regret-to-coverage theory for interval-valued OCP based on the $(1-\alpha)$-pinball loss. Our first contribution is to identify *linearized regret* as a key notion, showing that controlling it implies coverage bounds for any online algorithm. This relies on a black-box reduction that depends only on the Fenchel conjugate of an upper bound on the linearized regret. Building on this theory, we propose UP-OCP, a parameter-free method for OCP, via a reduction to a two-asset portfolio selection problem, leveraging universal portfolio algorithms. We show strong finite-time bounds on the miscoverage of UP-OCP, even for polynomially growing predictions. Extensive experiments support that UP-OCP delivers consistently better size/coverage trade-offs than prior online conformal baselines.
General Machine Learning · Online Learning, Active Learning and Bandits
The probabilistic bisection algorithm (PBA) extends the classical binary search to settings with noisy responses, and is a foundational algorithm commonly used in basic problems such as root-finding. Despite its strong empirical success, its theoretical property, particularly the convergence rate, remains unclear. This paper establishes that PBA converges at a geometric rate, providing a rigorous justification for its empirical efficiency. Notably, this rate is optimal in the sense that it matches the performance of classical binary search under noiseless responses. The core of our analysis lies in directly characterizing the dynamics of PBA queries, which had not been examined in the prior literature. We show that the queries oscillate around the truth but steadily draw closer, thus leading to an estimator that rapidly concentrates on the truth. Beyond resolving the long-standing question of PBA’s convergence, our developed techniques offer new tools for analyzing PBA's dynamics, which may be of independent interest.
General Machine Learning · Online Learning, Active Learning and Bandits
Eliciting information to reduce uncertainty about latent group-level properties is a central problem in collective assessment, preference modeling, and opinion aggregation, and is especially important in survey-based studies. While natural language interactions provide a flexible interface, existing methods typically rely on fixed questionnaires and static respondent sets, and do not adapt to partial or missing responses across rounds. To address this gap, we study adaptive information elicitation through multi-turn interactions between a large language model and a group of individuals, where both queries and respondents are adaptively selected to infer latent group properties. We propose a theoretically grounded framework that, at each round, jointly selects a query and a subset of respondents based on previously observed responses to efficiently reduce uncertainty about a target latent quantity (e.g., group-level political inclination). Motivated by practical survey constraints, such as limited questions and costly participation, our strategy maximizes information gain under a fixed budget. To handle missing and incomplete responses, we combine graph neural networks for aggregating/imputing partial group information with an information-theoretic criterion that guides per-round selection. Across three real-world opinion datasets, we achieve consistent improvements in population-level response prediction under constrained budgets, including over a 12% relative gain on CES at a 10% respondent budget.
General Machine Learning · Online Learning, Active Learning and Bandits
Recommender systems (RS) may suffer from feedback-driven exposure concentration, where repeated engagement optimization collapses exposure onto a narrow set of categories, reducing catalog coverage and degrading long-horizon learning. Existing methods are often post hoc and typically lack principled uncertainty-aware risk estimates for regulating exposure under endogenous feedback. We therefore propose **CORAL**, a model-agnostic, uncertainty-aware framework that formulates exposure regulation as a constrained sequential decision problem. Specifically, we model self-reinforcing interactions to construct an exposure-saturation state, then derive an upper confidence bound on category-conditioned violation risk from observed history and incorporate it through a state-dependent penalty for adaptive intervention near saturation. Moreover, we provide theoretical guarantees for risk bounds, finite-time recovery, and efficient long-term performance. Extensive experiments on real-world datasets and controlled simulations validate the effectiveness of the proposed framework, which aligns with our theoretical analysis. Our code is available at: https://anonymous.4open.science/r/Coral_Rec-8400.
General Machine Learning · Online Learning, Active Learning and Bandits
Continual learning (CL) aims to train models sequentially over multiple domains without forgetting previously learned knowledge. However, existing CL methods optimize for in-domain performance and are therefore prone to learning spurious, domain-specific cues (``shortcut learning''), which limits generalization to unseen domains after deployment. In this paper, we address this limitation through *continual learning of domain-invariant representation*. We introduce a broad class of CL methods that sequentially learn representations capturing invariant structures across domains. Our methods are motivated by the observation that such invariant structures often preserve the underlying causal mechanisms, which can reduce the risk of overfitting to domain-specific cues and thus offer better out-of-domain generalization. Our proposed CL methods combine replay-based training with a tailored sequential invariance alignment to learn---and preserve---invariant structures over time. We evaluate our methods under a deployment-oriented protocol that measures performance on unseen target domains. Across six benchmark and real-world datasets spanning vision, medicine, manufacturing, and ecology, our methods consistently outperform existing CL baselines in terms of generalization to unseen target domains. As an ablation, we further show that na\"ive extensions of sequential training with existing domain-invariant representation learning (DIRL) methods provide only limited benefits. To the best of our knowledge, this is the first work to develop domain-invariant representation methods for CL.
General Machine Learning · Online Learning, Active Learning and Bandits
Existing auto-bidding algorithms in digital advertising often treat the value of an ad opportunity as the revenue obtained when an ad is shown and/or clicked, and bid accordingly. This can lead to wasteful spending because the true value is the marginal gain from paid exposure: even without winning a sponsored slot, an advertiser may still earn revenue via an organic search result (e.g., on Google or Amazon). Motivated by recent work, we model ad value as a treatment effect—the outcome difference between winning and losing the auction—and study online learning for bidding in second-price (Vickrey) auctions under this causal perspective. We develop algorithms that attain rate-optimal regret under several feedback models. A key ingredient exploits the information revealed by the second-price payment rule, which strictly improves regret relative to analogous learning problems in first-price auctions.
General Machine Learning · Online Learning, Active Learning and Bandits
We study the active learning problem of fixed-confidence top-$k$ identification from noisy pairwise comparisons under latent-utility models. The objective is to identify the top-$k$ items with probability at least $1-\delta$ while using as few comparisons as possible by adaptively selecting which pairs to compare. While pure exploration with dueling bandits has been studied, an algorithm achieving asymptotic optimality has not yet been established. We characterize the structure of the information-theoretic lower bound on sample complexity, revealing a structured saddle-point problem. This structure enables a primal--dual algorithm that learns the optimal comparison allocation online while being computationally efficient. We then construct an adaptive comparison-allocation strategy that tracks the optimal solution and prove that the resulting procedure is asymptotically optimal.
General Machine Learning · Online Learning, Active Learning and Bandits
Personalizing AI decision support for heterogeneous human decision-makers remains a key challenge. We study a collaboration workflow where AI provides a reduced prediction set via conformal prediction as an input for human, and human makes final decision. We use contextual bandits to learn the complex and intangible human decision function, where the optimal set size, governed by a significance parameter $\alpha$ (arms), varies across individuals and tasks (context). To address large arms spaces and high-dimensional contexts, we introduce the Adaptively Grouped Contextual Bandit (AGCB) framework, bypassing unreliable complex function online approximation in favor of directly exploiting Human-AI problem structure through two pillars: continuity-aware counterfactual reasoning that efficiently shares information across decisions, and a data-driven zooming mechanism that adaptively partitions the context space. The zooming mechanism performs a principled, native trade-off between intra-group estimation error and inter-group approximation bias, ensuring optimal granularity for both cumulative and simple regret objectives. Crucially, a single continuity assumption uniquely enables both the bias control for adaptive grouping and the robustness of our counterfactual updates. This leads to minimax-optimal regret rates. Empirical results confirm that AGCB significantly outperforms existing methods in heterogeneous, data-scarce environments.
Theory · Online Learning and Bandits
Contextual bandits serve as a foundational framework for sequential decision-making in domains like recommendation systems, IoT device management, and conversational AI, yet classical models overlook a critical practical constraint: acquiring extra observations incurs non-trivial costs, creating an unaddressed trade-off between information gain and expenditure. To fill this gap, we study contextual bandits with paid observations, where the learner actively chooses which actions to observe (at a specified cost) in each round, with the goal of minimizing total regret that combines learning losses and cumulative observation costs. We first design a near-optimal algorithm for adversarial environments, proving it achieves a regret rate significantly higher than that of cost-free contextual bandits—even for small observation costs—thus quantifying how paid observations reshape learning complexity. We then uncover a critical phase-transition phenomenon when incorporating free observation budgets: below a threshold budget, free observations only reduce total costs without changing the underlying regret rate, while above this threshold, they drastically improve learning efficiency, lowering the regret rate to match that of cost-free settings. To leverage this phenomenon, we develop a meta-controller that adaptively switches strategies based on the available budget, ensuring near-optimal performance across both low- and high-budget regimes. Furthermore, to address practical challenges like infinite policy spaces and computational inefficiency, we propose an oracle-efficient algorithm under a function approximation framework, which leverages an online regression oracle to maintain strong performance for stochastic losses. Our results also shed light on the scenarios about switching costs, budgeted constraints, model misspecification and the trade-offs involved in knapsack problems. Finally, we conduct numerical experiments to validate our theoretical findings and demonstrate practical efficiency. Key words: Contextual bandit, paid observation, function approximation, phase transition.