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General Machine Learning · Online Learning, Active Learning and Bandits

Soumya Basu

We study bandit learning in matching markets with two-sided reward uncertainty, extending prior research primarily focused on single-sided uncertainty. Leveraging the concept of `super-stability' from Irving (1994), we demonstrate the advantage of the Extended Gale-Shapley (GS) algorithm over the standard GS algorithm in achieving true stable matchings under incomplete information. By employing the Extended GS algorithm, our centralized algorithm attains a logarithmic pessimal stable regret dependent on an instance-dependent admissible gap parameter. This algorithm is further adapted to a decentralized setting with a constant regret increase. Finally, we establish a novel centralized instance-dependent lower bound for binary stable regret, elucidating the roles of the admissible gap and super-stable matching in characterizing the complexity of stable matching with bandit feedback.

General Machine Learning · Online Learning, Active Learning and Bandits

Yegon Kim, Hyunsu Kim, Gyeonghoon Ko, Juho Lee

Accurately solving partial differential equations (PDEs) is critical to understanding complex scientific and engineering phenomena, yet traditional numerical solvers are computationally expensive. Surrogate models offer a more efficient alternative, but their development is hindered by the cost of generating sufficient training data from numerical solvers. In this paper, we present a novel framework for active learning (AL) in PDE surrogate modeling that reduces this cost. Unlike the existing AL methods for PDEs that always acquire entire PDE trajectories, our approach strategically generates only the most important time steps with the numerical solver, while employing the surrogate model to approximate the remaining steps. This dramatically reduces the cost incurred by each trajectory and thus allows the active learning algorithm to try out a more diverse set of trajectories given the same budget. To accommodate this novel framework, we develop an acquisition function that estimates the utility of a set of time steps by approximating its resulting variance reduction. We demonstrate the effectiveness of our method on several benchmark PDEs, including the Burgers' equation, Korteweg–De Vries equation, Kuramoto–Sivashinsky equation, the incompressible Navier-Stokes equation, and the compressible Navier-Stokes equation.Experiments show that our approach improves performance by large margins over the best existing method. Our method not only reduces average error but also the 99\%, 95\%, and 50\% quantiles of error, which is rare for an AL algorithm. All in all, our approach offers a data-efficient solution to surrogate modeling for PDEs.

Theory · Online Learning and Bandits

Tao Jin, Yue Wu, Quanquan Gu, Farzad Farnoud

We study the problem of efficiently aggregating the preferences of items from multiple information sources (oracles) and infer the ranking under both the weak stochastic transitivity (WST) and the strong stochastic transitivity (SST) conditions. When the underlying preference model satisfies the WST condition, we propose an algorithm named RMO-WST, which has a bi-level design: at the higher level, it actively allocates comparison budgets to all undetermined pairs until the full ranking is recovered; at the lower level, it attempts to compare the pair of items and selects the more accurate oracles simultaneously. We prove that the sample complexity of RMO-WST is $ \tilde O( N\sum_{i=2}^{N}H_{\sigma^{-1}(i),{\sigma^{-1}(i-1)}} )$, where $N$ is the number of items to rank, $H$ is a problem-dependent hardness factor, and $\sigma^{-1}(i)$ represents the $i$-th best item. We also provide a tight lower bound that matches the upper bound of approximate ranking under the WST condition, answering a previously open problem. In addition, when the SST condition is satisfied, we propose an algorithm named RMO-SST, which can achieve an $\tilde{O}(\sum_{i=1}^{N} H_i \log(N))$ sample complexity. This outperforms the best-known sample complexity by a factor of $\log(N)$. The theoretical advantages of our algorithms are verified by empirical experiments in a simulated environment.

General Machine Learning · Online Learning, Active Learning and Bandits

Kiran Thekumparampil, Gaurush Hiranandani, Kousha Kalantari, Shoham Sabach, Branislav Kveton

We study learning human preferences from limited comparison feedback, a core machine learning problem that is at the center of reinforcement learning from human feedback (RLHF). We formulate the problem as learning a Plackett-Luce (PL) model from a limited number of $K$-subset comparisons over a universe of $N$ items, where typically $K \ll N$. Our objective is to select the $K$-subsets such that all items can be ranked with minimal mistakes within the budget. We solve the problem using the D-optimal design, which minimizes the worst-case ranking loss under the estimated PL model. All known algorithms for this problem are computationally infeasible in our setting because we consider exponentially many subsets in $K$. To address this challenge, we propose a randomized Frank-Wolfe algorithm with memoization and sparse updates that has a low $O(N^2 + K^2)$ per-iteration complexity. We analyze it and demonstrate its empirical superiority on synthetic and open-source NLP datasets.

General Machine Learning · Online Learning, Active Learning and Bandits

Haosen Ge, Hamsa Bastani, Osbert Bastani

Conformal prediction has emerged as an effective strategy for uncertainty quantification by modifying a model to output sets of labels instead of a single label. These prediction sets come with the guarantee that they contain the true label with high probability. However, conformal prediction typically requires a large calibration dataset of i.i.d. examples. We consider the online learning setting, where examples arrive over time, and the goal is to construct prediction sets dynamically. Departing from existing work, we assume semi-bandit feedback, where we *only observe the true label if it is contained in the prediction set*. For instance, consider calibrating a document retrieval model to a new domain; in this setting, a user would only be able to provide the true label if the target document is in the prediction set of retrieved documents. We propose a novel conformal prediction algorithm targeted at this setting, and prove that it obtains sublinear regret compared to the optimal conformal predictor. We evaluate our algorithm on a retrieval task, an image classification task, and an auction price-setting task, and demonstrate that it empirically achieves good performance compared to several baselines.

General Machine Learning · Online Learning, Active Learning and Bandits

Maximilian Graf, Victor Thuot, Nicolas Verzelen

We study the problem of clustering a set of items based on bandit feedback. Each of the $n$ items is characterized by a feature vector, with a possibly large dimension $d$. The items are partitioned into two unknown groups, such that items within the same group share the same feature vector. We consider a sequential and adaptive setting in which, at each round, the learner selects one item and one feature, then observes a noisy evaluation of the item's feature. The learner's objective is to recover the correct partition of the items, while keeping the number of observations as small as possible. We provide an algorithm which relies on finding a relevant feature for the clustering task, leveraging the Sequential Halving algorithm. With probability at least $1-\delta$, we obtain an accurate recovery of the partition and derive an upper bound on the required budget . Furthermore, we derive an instance-dependent lower bound, which is tight in some relevant cases.

General Machine Learning · Online Learning, Active Learning and Bandits

Yash Kheshwani, Avishek Ghosh, Nikhil Karamchandani

This work investigates the problem of best arm identification for multi-agent multi-armed bandits. We consider $N$ agents grouped into $M$ clusters, where each cluster solves a stochastic bandit problem. The mapping between agents and bandits is \textit{a priori} unknown. Each bandit is associated with $K$ arms, and the goal is to identify the best arm for each agent under a $\delta$-probably correct ($\delta$-PC) framework, while minimizing sample complexity and communication overhead. We propose two novel algorithms: \emph{Clustering then Best Arm Identification} (\texttt{Cl-BAI}) and \emph{Best Arm Identification then Clustering} (\texttt{BAI-Cl}). \texttt{Cl-BAI} employs a two-phase approach that first clusters agents based on the bandit problems they are learning, followed by identifying the best arm for each cluster. \texttt{BAI-Cl} reverses the sequence by identifying the best arms first and then clustering agents accordingly. Both algorithms exploit the successive elimination framework to ensure computational efficiency and high accuracy. Theoretical analysis establishes $\delta$-PC guarantees for both methods, derives bounds on their sample complexity, and provides a lower bound for the problem class. Moreover, when $M$ is small (a constant), we show that the sample complexity of (a variant of) \texttt{BAI-Cl} is (order-wise) minimax optimal. Experiments on synthetic and real-world (Movie Lens, Yelp) data demonstrates the superior performance of the proposed algorithms in terms of sample and communication efficiency, particularly in settings where $M \ll N$.

General Machine Learning · Online Learning, Active Learning and Bandits

Yuxiao Wen

In combinatorial semi-bandits, a learner repeatedly selects from a combinatorial decision set of arms, receives the realized sum of rewards, and observes the rewards of the individual selected arms as feedback. In this paper, we extend this framework to include \emph{graph feedback}, where the learner observes the rewards of all neighboring arms of the selected arms in a feedback graph $G$. We establish that the optimal regret over a time horizon $T$ scales as $\widetilde{\Theta}(S\sqrt{T}+\sqrt{\alpha ST})$, where $S$ is the size of the combinatorial decisions and $\alpha$ is the independence number of $G$. This result interpolates between the known regrets $\widetilde\Theta(S\sqrt{T})$ under full information (i.e., $G$ is complete) and $\widetilde\Theta(\sqrt{KST})$ under the semi-bandit feedback (i.e., $G$ has only self-loops), where $K$ is the total number of arms. A key technical ingredient is to realize a convexified action using a random decision vector with negative correlations. We also show that online stochastic mirror descent (OSMD) that only realizes convexified actions in expectation is suboptimal.

Theory · Online Learning and Bandits

Kapilan Balagopalan, Tuan Nguyen, Yao Zhao, Kwang-Sung Jun

The best arm identification problem requires identifying the best alternative (i.e., arm) in active experimentation using the smallest number of experiments (i.e., arm pulls), which is crucial for cost-efficient and timely decision-making processes. In the fixed confidence setting, an algorithm must stop data-dependently and return the estimated best arm with a correctness guarantee. Since this stopping time is random, we desire its distribution to have light tails. Unfortunately, many existing studies focus on high probability or in expectation bounds on the stopping time, which allow heavy tails and, for high probability bounds, even not stopping at all. We first prove that this never-stopping event can indeed happen for some popular algorithms. Motivated by this, we propose algorithms that provably enjoy an exponential-tailed stopping time, which improves upon the polynomial tail bound reported by Kalyanakrishnan et al. (2012). The first algorithm is based on a fixed budget algorithm called Sequential Halving along with a doubling trick. The second algorithm is a meta algorithm that takes in any fixed confidence algorithm with a high probability stopping guarantee and turns it into one that enjoys an exponential-tailed stopping time. Our results imply that there is much more to be desired for contemporary fixed confidence algorithms.

General Machine Learning · Online Learning, Active Learning and Bandits

Jingruo Sun, Wenzhi Gao, Ellen Vitercik, Yinyu Ye

Online linear programming (OLP) has found broad applications in revenue management and resource allocation. State-of-the-art OLP algorithms achieve low regret by repeatedly solving linear programming (LP) subproblems that incorporate updated resource information. However, LP-based methods are computationally expensive and often inefficient for large-scale applications. By contrast, recent first-order OLP algorithms are more computationally efficient but typically suffer from weaker regret guarantees. To address these shortcomings, we propose a new algorithm that combines the strengths of LP-based and first-order OLP algorithms. Our algorithm re-solves the LP subproblems periodically at a predefined frequency $f$ and uses the latest dual prices to guide online decision-making. In parallel, a first-order method runs during each interval between LP re-solves and smooths resource consumption. Our algorithm achieves $\mathcal{O}(\log (T/f) + \sqrt{f})$ regret and delivers a "wait-less" online decision-making process that balances computational efficiency and regret guarantees. Extensive experiments demonstrate at least $10$-fold improvements in regret over first-order methods and $100$-fold improvements in runtime over LP-based methods.

General Machine Learning · Online Learning, Active Learning and Bandits

Osman Berke Guney, Ketan Saichandran, Karim Elzokm, Ziming Zhang, Vijaya Kolachalama

In many practical applications, including medicine, acquiring all relevant data for machine learning models is often infeasible due to constraints on time, cost, and resources. This makes it important to selectively acquire only the most informative features, yet traditional static feature selection methods fall short in scenarios where feature importance varies across instances. Here, we propose an active feature acquisition (AFA) framework, which dynamically selects features based on their importance to each individual case. Our method leverages local explanation techniques to generate instance-specific feature importance rankings. We then reframe the AFA problem as a feature prediction task, introducing a policy network grounded in a decision transformer architecture. This policy network is trained to select the next most informative feature by learning from the feature importance rankings. As a result, features are acquired sequentially, ordered by their predictive significance, leading to more efficient feature selection and acquisition. Extensive experiments on multiple datasets demonstrate that our approach outperforms current state-of-the-art AFA methods in both predictive accuracy and feature acquisition efficiency. These findings highlight the promise of an explainability-driven AFA strategy in scenarios where the cost of feature acquisition is a key concern.

General Machine Learning · Online Learning, Active Learning and Bandits

Zhiyong Wang, Jiahang Sun, Mingze Kong, Jize Xie, Qinghua Hu, John C. S. Lui, Zhongxiang Dai

The contextual multi-armed bandit (MAB) is a widely used framework for problems requiring sequential decision-making under uncertainty, such as recommendation systems. In applications involving a large number of users, the performance of contextual MAB can be significantly improved by facilitating collaboration among multiple users. This has been achieved by the clustering of bandits (CB) methods, which adaptively group the users into different clusters and achieve collaboration by allowing the users in the same cluster to share data. However, classical CB algorithms typically rely on numerical reward feedback, which may not be practical in certain real-world applications. For instance, in recommendation systems, it is more realistic and reliable to solicit preference feedback between pairs of recommended items rather than absolute rewards. To address this limitation, we introduce the first "clustering of dueling bandit algorithms" to enable collaborative decision-making based on preference feedback. We propose two novel algorithms: (1) Clustering of Linear Dueling Bandits (COLDB) which models the user reward functions as linear functions of the context vectors, and (2) Clustering of Neural Dueling Bandits (CONDB) which uses a neural network to model complex, non-linear user reward functions. Both algorithms are supported by rigorous theoretical analyses, demonstrating that user collaboration leads to improved regret bounds. Extensive empirical evaluations on synthetic and real-world datasets further validate the effectiveness of our methods, establishing their potential in real-world applications involving multiple users with preference-based feedback.

General Machine Learning · Online Learning, Active Learning and Bandits

Ramya Ramalingam, Shayan Kiyani, Aaron Roth

Existing algorithms for online conformal prediction---guaranteeing marginal coverage in adversarial settings---are variants of online gradient descent (OGD), but their analyses of worst-case coverage do not follow from the regret guarantee of OGD. What is the relationship between no-regret learning and online conformal prediction? We observe that although standard regret guarantees imply marginal coverage in i.i.d. settings, this connection fails as soon as we either move to adversarial environments or ask for group conditional coverage. On the other hand, we show a tight connection between *threshold calibrated* coverage and swap-regret in adversarial settings, which extends to group-conditional (multi-valid) coverage. We also show that algorithms in the *follow the regularized leader* family of no regret learning algorithms (which includes online gradient descent) can be used to give group-conditional coverage guarantees in adversarial settings for arbitrary grouping functions. Via this connection we analyze and conduct experiments using a multi-group generalization of the ACI algorithm of Gibbs & Candes (2021).

General Machine Learning · Online Learning, Active Learning and Bandits

Côme Fiegel, Pierre Menard, Tadashi Kozuno, Michal Valko, Vianney Perchet

We study the problem of learning in zero-sum matrix games with repeated play and bandit feedback. Specifically, we focus on developing uncoupled algorithms that guarantee, without communication between players, convergence of the last-iterate to a Nash equilibrium. Although the non-bandit case has been studied extensively, this setting has only been explored recently, with a bound of $\mathcal{O}(T^{-1/8})$ on the exploitability gap. We show that, for uncoupled algorithms, guaranteeing convergence of the policy profiles to a Nash equilibrium is detrimental to the performances, with the best attainable rate being $\mathcal{O}(T^{-1/4})$ in contrast to the usual $\mathcal{O}(T^{-1/2})$ rate for convergence of the average iterates. We then propose two algorithms that achieve this optimal rate. The first algorithm leverages a straightforward tradeoff between exploration and exploitation, while the second employs a regularization technique based on a two-step mirror descent approach.

General Machine Learning · Online Learning, Active Learning and Bandits

Yuhang Li, Guoxu Zhou, Zhenhao Huang, Xinqi Chen, Yuning Qiu, Qibin Zhao

Class-Incremental Learning (CIL) has gained considerable attention due to its capacity to accommodate new classes during learning. Replay-based methods demonstrate state-of-the-art performance in CIL but suffer from high memory consumption to save a set of old exemplars for revisiting. To address this challenge, many memory-efficient replay methods have been developed by exploiting image compression techniques. However, the gains are often bittersweet when pixel-level compression methods are used. Here, we present a simple yet efficient approach that employs tensor decomposition to address these limitations. This method fully exploits the low intrinsic dimensionality and pixel correlation of images to achieve high compression efficiency while preserving sufficient discriminative information, significantly enhancing performance. We also introduce a hybrid exemplar selection strategy to improve the representativeness and diversity of stored exemplars. Extensive experiments across datasets with varying resolutions consistently demonstrate that our approach substantially boosts the performance of baseline methods, showcasing strong generalization and robustness.

General Machine Learning · Online Learning, Active Learning and Bandits

Yu-Jie Zhang, Peng Zhao, Masashi Sugiyama

Non-stationary online learning has drawn much attention in recent years. Despite considerable progress, dynamic regret minimization has primarily focused on convex functions, leaving the functions with stronger curvature (e.g., squared or logistic loss) underexplored. In this work, we address this gap by showing that the regret can be substantially improved by leveraging the concept of mixability, a property that generalizes exp-concavity to effectively capture loss curvature. Let $d$ denote the dimensionality and $P_T$ the path length of comparators that reflects the environmental non-stationarity. We demonstrate that an exponential-weight method with fixed-share updates achieves an $\mathcal{O}(d T^{1/3} P_T^{2/3} \log T)$ dynamic regret for mixable losses, improving upon the best-known $\mathcal{O}(d^{10/3} T^{1/3} P_T^{2/3} \log T)$ result (Baby & Wang, 2021) in $d$. More importantly, this improvement arises from a simple yet powerful analytical framework that exploits the mixability, which avoids the Karush–Kuhn–Tucker-based analysis required by existing work.

General Machine Learning · Online Learning, Active Learning and Bandits

Jianting Chen

Core-set selection (CS) for deep learning has become crucial for enhancing training efficiency and understanding datasets by identifying the most informative subsets. However, most existing methods rely on heuristics or complex optimization, struggling to balance efficiency and effectiveness. To address this, we propose a novel CS objective that adaptively balances losses between core-set and non-core-set samples by minimizing the sum of squared losses across all samples. Building on this objective, we introduce theMaximum Reduction as Maximum Contribution criterion (MRMC), which identifies samples with the maximal reduction in loss as those making the maximal contribution to overall convergence. Additionally, a balance constraint is incorporated to ensure an even distribution of contributions from the core-set. Experimental results demonstrate that MRMC improves training efficiency significantly while preserving model performance with minimal cost.

General Machine Learning · Online Learning, Active Learning and Bandits

Taeckyung Lee, Sorn Chottananurak, Junsu Kim, Jinwoo Shin, Taesik Gong, Sung-Ju Lee

Deep learning models perform poorly when domain shifts exist between training and test data. Test-time adaptation (TTA) is a paradigm to mitigate this issue by adapting pre-trained models using only unlabeled test samples. However, existing TTA methods can fail under severe domain shifts, while recent active TTA approaches requiring full-class labels are impractical due to high labeling costs. To address this issue, we introduce a new setting of TTA with binary feedback, which uses a few binary feedbacks from annotators to indicate whether model predictions are correct, thereby significantly reducing the labeling burden of annotators. Under the setting, we propose BiTTA, a novel dual-path optimization framework that leverages reinforcement learning to balance binary feedback-guided adaptation on uncertain samples with agreement-based self-adaptation on confident predictions. Experiments show BiTTA achieves substantial accuracy improvements over state-of-the-art baselines, demonstrating its effectiveness in handling severe distribution shifts with minimal labeling effort.

General Machine Learning · Online Learning, Active Learning and Bandits

Naram Mhaisen, George Iosifidis

We revisit the Follow the Regularized Leader (FTRL) framework for Online Convex Optimization (OCO) over compact sets, focusing on achieving dynamic regret guarantees. Prior work has highlighted the framework’s limitations in dynamic environments due to its tendency to produce "lazy" iterates. However, building on insights showing FTRL's ability to produce "agile" iterates, we show that it can indeed recover known dynamic regret bounds through optimistic composition of future costs and careful linearization of past costs, which can lead to pruning some of them. This new analysis of FTRL against dynamic comparators yields a principled way to interpolate between greedy and agile updates and offers several benefits, including refined control over regret terms, optimism without cyclic dependence, and the application of minimal recursive regularization akin to AdaFTRL. More broadly, we show that it is not the "lazy" projection style of FTRL that hinders (optimistic) dynamic regret, but the decoupling of the algorithm’s state (linearized history) from its iterates, allowing the state to grow arbitrarily. Instead, pruning synchronizes these two when necessary.

General Machine Learning · Online Learning, Active Learning and Bandits

Rohan Deb, Kiran Thekumparampil, Kousha Kalantari, Gaurush Hiranandani, Shoham Sabach, Branislav Kveton

Supervised fine-tuning (SFT) is the most common way of adapting large language models (LLMs) to a new domain. In this paper, we improve the efficiency of SFT by selecting an informative subset of training examples. Specifically, for a fixed budget of training examples, which determines the computational cost of fine-tuning, we select those that maximize information gain, as measured by the Fisher information matrix of the SFT objective. We approximate it efficiently by linearization at the last layer of the LLM. Our approach is computationally efficient, analyzable, and performs well empirically. We demonstrate this on several problems, with both quantitative results and LLM-as-a-judge evaluations.