We study the stochastic linear bandits with heavy-tailed noise. Two principled strategies for handling heavy-tailed noise, truncation and median-of-means, have been introduced to heavy-tailed bandits. Nonetheless, these methods rely on specific noise assumptions or bandit structures, limiting their applicability to general settings. The recent work [Huang et al.2024] develop a soft truncation method via the adaptive Huber regression to address these limitations. However, their method suffers undesired computational cost: it requires storing all historical data and performing a full pass over these data at each round. In this paper, we propose a \emph{one-pass} algorithm based on the online mirror descent framework. Our method updates using only current data at each round, reducing the per-round computational cost from $\mathcal{O}(t \log T)$ to $\mathcal{O}(1)$ with respect to current round $t$ and the time horizon $T$, and achieves a near-optimal and variance-aware regret of order $\widetilde{\mathcal{O}}\big(d T^{\frac{1-\varepsilon}{2(1+\varepsilon)}} \sqrt{\sum_{t=1}^T \nu_t^2} + d T^{\frac{1-\varepsilon}{2(1+\varepsilon)}}\big)$ where $d$ is the dimension and $\nu_t^{1+\varepsilon}$ is the $(1+\varepsilon)$-th central moment of reward at round $t$.

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.

We study the generalized linear bandit (GLB) problem, a contextual multi-armed bandit framework that extends the classical linear model by incorporating a non-linear link function, thereby modeling a broad class of reward distributions such as Bernoulli and Poisson. While GLBs are widely applicable to real-world scenarios, their non-linear nature introduces significant challenges in achieving both computational and statistical efficiency. Existing methods typically trade off between two objectives, either incurring high per-round costs for optimal regret guarantees or compromising statistical efficiency to enable constant-time updates. In this paper, we propose a jointly efficient algorithm that attains a nearly optimal regret bound with $\mathcal{O}(1)$ time and space complexities per round. The core of our method is a tight confidence set for the online mirror descent (OMD) estimator, which is derived through a novel analysis that leverages the notion of mix loss from online prediction. The analysis shows that our OMD estimator, even with its one-pass updates, achieves statistical efficiency comparable to maximum likelihood estimation, thereby leading to a jointly efficient optimistic method.

Dynamic regret minimization offers a principled way for non-stationary online learning, where the algorithm's performance is evaluated against changing comparators. Prevailing methods often employ a two-layer online ensemble, consisting of a group of base learners with different configurations and a meta learner that combines their outputs. Given the evident computational overhead associated with two-layer algorithms, this paper investigates how to attain optimal dynamic regret *without* deploying a model ensemble. To this end, we introduce the notion of *underlying dynamic regret*, a specific form of the general dynamic regret that can encompass many applications of interest. We show that almost optimal dynamic regret can be obtained using a single-layer model alone. This is achieved by an adaptive restart equipped with wavelet detection, wherein a novel streaming wavelet operator is introduced to online update the wavelet coefficients via a carefully designed binary indexed tree. We apply our method to the *online label shift* adaptation problem, leading to new algorithms with optimal dynamic regret and significantly improved computation/storage efficiency compared to prior arts. Extensive experiments validate our proposal.

Complementary-label learning is a weakly supervised learning problem in which each training example is associated with one or multiple complementary labels indicating the classes to which it does not belong. Existing consistent approaches have relied on the uniform distribution assumption to model the generation of complementary labels, or on an ordinary-label training set to estimate the transition matrix in non-uniform cases. However, either condition may not be satisfied in real-world scenarios. In this paper, we propose a novel consistent approach that does not rely on these conditions. Inspired by the positive-unlabeled (PU) learning literature, we propose an unbiased risk estimator based on the Selected-Completely-at-Random assumption for complementary-label learning. We then introduce a risk-correction approach to address overfitting problems. Furthermore, we find that complementary-label learning can be expressed as a set of negative-unlabeled binary classification problems when using the one-versus-rest strategy. Extensive experimental results on both synthetic and real-world benchmark datasets validate the superiority of our proposed approach over state-of-the-art methods.

We study a new class of MDPs that employs multinomial logit (MNL) function approximation to ensure valid probability distributions over the state space. Despite its significant benefits, incorporating the non-linear function raises substantial challenges in both *statistical* and *computational* efficiency. The best-known result of Hwang and Oh [2023] has achieved an $\widetilde{\mathcal{O}}(\kappa^{-1}dH^2\sqrt{K})$ regret upper bound, where $\kappa$ is a problem-dependent quantity, $d$ is the feature dimension, $H$ is the episode length, and $K$ is the number of episodes. However, we observe that $\kappa^{-1}$ exhibits polynomial dependence on the number of reachable states, which can be as large as the state space size in the worst case and thus undermines the motivation for function approximation. Additionally, their method requires storing all historical data and the time complexity scales linearly with the episode count, which is computationally expensive. In this work, we propose a statistically efficient algorithm that achieves a regret of $\widetilde{\mathcal{O}}(dH^2\sqrt{K} + \kappa^{-1}d^2H^2)$, eliminating the dependence on $\kappa^{-1}$ in the dominant term for the first time. We then address the computational challenges by introducing an enhanced algorithm that achieves the same regret guarantee but with only constant cost. Finally, we establish the first lower bound for this problem, justifying the optimality of our results in $d$ and $K$.

We investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible comparator sequence. Let $T$ be the time horizon and $P_T$ be the path length that essentially reflects the non-stationarity of environments, the state-of-the-art dynamic regret is $\mathcal{O}(\sqrt{T(1+P_T)})$. Although this bound is proved to be minimax optimal for convex functions, in this paper, we demonstrate that it is possible to further enhance the guarantee for some easy problem instances, particularly when online functions are smooth. Specifically, we introduce novel online algorithms that can exploit smoothness and replace the dependence on $T$ in dynamic regret with problem-dependent quantities: the variation in gradients of loss functions, the cumulative loss of the comparator sequence, and the minimum of these two terms. These quantities are at most $\mathcal{O}(T)$ while could be much smaller in benign environments. Therefore, our results are adaptive to the intrinsic difficulty of the problem, since the bounds are tighter than existing results for easy problems and meanwhile safeguard the same rate in the worst case. Notably, our proposed algorithms can achieve favorable dynamic regret with only one gradient per iteration, sharing the same gradient query complexity as the static regret minimization methods. To accomplish this, we introduce the collaborative online ensemble framework. The proposed framework employs a two-layer online ensemble to handle non-stationarity, and uses optimistic online learning and further introduces crucial correction terms to enable effective collaboration within the meta-base two layers, thereby attaining adaptivity. We believe the framework can be useful for broader problems.

The stochastically extended adversarial (SEA) model, introduced by Sachs et al. (2022), serves as an interpolation between stochastic and adversarial online convex optimization. Under the smoothness condition on expected loss functions, it is shown that the expected static regret of optimistic follow-the-regularized-leader (FTRL) depends on the cumulative stochastic variance $\sigma_{1:T}^2$ and the cumulative adversarial variation $\Sigma_{1:T}^2$ for convex functions. Sachs et al. (2022) also provide a regret bound based on the maximal stochastic variance $\sigma_{\max}^2$ and the maximal adversarial variation $\Sigma_{\max}^2$ for strongly convex functions. Inspired by their work, we investigate the theoretical guarantees of optimistic online mirror descent (OMD) for the SEA model with smooth expected loss functions. For convex and smooth functions, we obtain the same $\mathcal{O}(\sqrt{\sigma_{1:T}^2}+\sqrt{\Sigma_{1:T}^2})$ regret bound, but with a relaxation of the convexity requirement from individual functions to expected functions. For strongly convex and smooth functions, we establish an $\mathcal{O}\left(\frac{1}{\lambda}\left(\sigma_{\max}^2+\Sigma_{\max}^2\right)\log \left(\left(\sigma_{1:T}^2 + \Sigma_{1:T}^2\right)/\left(\sigma_{\max}^2+\Sigma_{\max}^2\right)\right)\right)$ bound, better than their $\mathcal{O}((\sigma_{\max}^2$ $ + \Sigma_{\max}^2) \log T)$ result. For exp-concave and smooth functions, our approach yields a new $\mathcal{O}(d\log(\sigma_{1:T}^2+\Sigma_{1:T}^2))$ bound. Moreover, we introduce the first expected dynamic regret guarantee for the SEA model with convex and smooth expected functions, which is more favorable than static regret bounds in non-stationary environments. Furthermore, we expand our investigation to scenarios with non-smooth expected loss functions and propose novel algorithms built upon optimistic OMD with an implicit update, successfully attaining both static and dynamic regret guarantees.

Imitation learning from human feedback studies how to train well-performed imitation agents with an annotator's relative comparison of two demonstrations (one demonstration is better/worse than the other), which is usually easier to collect than the perfect expert data required by traditional imitation learning. However, in many real-world applications, it is still expensive or even impossible to provide a clear pairwise comparison between two demonstrations with similar quality. This motivates us to study the problem of imitation learning with vague feedback, where the data annotator can only distinguish the paired demonstrations correctly when their quality differs significantly, i.e., one from the expert and another from the non-expert. By modeling the underlying demonstration pool as a mixture of expert and non-expert data, we show that the expert policy distribution can be recovered when the proportion $\alpha$ of expert data is known. We also propose a mixture proportion estimation method for the unknown $\alpha$ case. Then, we integrate the recovered expert policy distribution with generative adversarial imitation learning to form an end-to-end algorithm. Experiments show that our methods outperform standard and preference-based imitation learning methods on various tasks.

This paper investigates the logistic bandit problem, a variant of the generalized linear bandit model that utilizes a logistic model to depict the feedback from an action. While most existing research focuses on the binary logistic bandit problem, the multinomial case, which considers more than two possible feedback values, offers increased practical relevance and adaptability for use in complex decision-making problems such as reinforcement learning. In this paper, we provide an algorithm that enjoys both statistical and computational efficiency for the logistic bandit problem. In the binary case, our method improves the state-of-the-art binary logistic bandit method by reducing the per-round computation cost from $\mathcal{O}(\log T)$ to $\mathcal{O}(1)$ with respect to the time horizon $T$, while still preserving the minimax optimal guarantee up to logarithmic factors. In the multinomial case, with $K+1$ potential feedback values, our algorithm achieves an $\tilde{\mathcal{O}}(K\sqrt{T})$ regret bound with $\mathcal{O}(1)$ computational cost per round. The result not only improves the $\tilde{\mathcal{O}}(K\sqrt{\kappa T})$ bound for the best-known tractable algorithm—where the large constant $\kappa$ increases exponentially with the diameter of the parameter domain—but also reduces the $\mathcal{O}(T)$ computational complexity demanded by the previous method.

Dealing with distribution shifts is one of the central challenges for modern machine learning. One fundamental situation is the covariate shift, where the input distributions of data change from the training to testing stages while the input-conditional output distribution remains unchanged. In this paper, we initiate the study of a more challenging scenario --- continuous covariate shift --- in which the test data appear sequentially, and their distributions can shift continuously. Our goal is to adaptively train the predictor such that its prediction risk accumulated over time can be minimized. Starting with the importance-weighted learning, we theoretically show the method works effectively if the time-varying density ratios of test and train inputs can be accurately estimated. However, existing density ratio estimation methods would fail due to data scarcity at each time step. To this end, we propose an online density ratio estimation method that can appropriately reuse historical information. Our method is proven to perform well by enjoying a dynamic regret bound, which finally leads to an excess risk guarantee for the predictor. Empirical results also validate the effectiveness.

In plenty of real-world applications, data are collected in a streaming fashion, and their accurate labels are hard to obtain. For instance, in the environmental monitoring task, sensors are collecting the data all the time. Still, their labels are scarce because the labeling process requires human effort and can conceal annotation errors. This paper investigates the problem of learning with weakly labeled data streams, in which data are continuously collected, and only a limited subset of streaming data is labeled but potentially with noise. This setting is challenging and of great importance but rarely studied in the literature. When the data are constantly gathered with unknown noise on labels, it is quite challenging to design algorithms to obtain a well-generalized classifier. To address this difficulty, we propose a novel noise transition matrix estimation approach for data streams with scarce noisy labels by online anchor points identification. Based on that, we propose an adaptive learning algorithm for weakly labeled data streams via model reuse and effectively alleviate the negative influence of label noise with unlabeled data. Both theoretical analysis and extensive experiments justify and validate the effectiveness of the proposed approach.

The standard supervised learning paradigm works effectively when training data shares the same distribution as the upcoming testing samples. However, this stationary assumption is often violated in real-world applications, especially when testing data appear in an online fashion. In this paper, we formulate and investigate the problem of \emph{online label shift} (OLaS): the learner trains an initial model from the labeled offline data and then deploys it to an unlabeled online environment where the underlying label distribution changes over time but the label-conditional density does not. The non-stationarity nature and the lack of supervision make the problem challenging to be tackled. To address the difficulty, we construct a new unbiased risk estimator that utilizes the unlabeled data, which exhibits many benign properties albeit with potential non-convexity. Building upon that, we propose novel online ensemble algorithms to deal with the non-stationarity of the environments. Our approach enjoys optimal \emph{dynamic regret}, indicating that the performance is competitive with a clairvoyant who knows the online environments in hindsight and then chooses the best decision for each round. The obtained dynamic regret bound scales with the intensity and pattern of label distribution shift, hence exhibiting the adaptivity in the OLaS problem. Extensive experiments are conducted to validate the effectiveness and support our theoretical findings.

In conventional supervised learning, a training dataset is given with ground-truth labels from a known label set, and the learned model will classify unseen instances to known labels. In real situations, when the learned models do not work well, users generally attribute the failure to the inadequate selection of learning algorithms or the lack of enough labeled training samples. In this paper, we point out that there is an important category of failure, which owes to the fact that there are unknown classes in the training data misperceived as other labels, and thus their existence was unknown from the given supervision. Such problems of unknown unknown classes can hardly be addressed by common re-selection of algorithms or accumulation of training samples. For this purpose, we propose the exploratory machine learning, where in this paradigm once user encounters unsatisfactory learning performance, she can examine the possibility and, if unknown unknowns really exist, deploy the optimal strategy of feature space augmentation to make the unknown classes observable and be enabled for learning. Theoretical analysis and empirical study on both synthetic and real datasets validate the efficacy of our proposal.

The learnware paradigm attempts to change the current style of machine learning deployment, i.e., user builds her own machine learning application almost from scratch, to a style where the previous efforts of other users can be reused, given a publicly available pool of machine learning models constructed by previous users for various tasks. Each learnware is a high-quality pre-trained model associated with its specification. Although there are many models in the learnware market, only a few, even none, may be potentially helpful for the current job. Therefore, how to identify and deploy useful models becomes one of the main concerns, which particularly matters when the user’s job involves certain unseen parts not covered by the current learnware market. It becomes more challenging because, due to the privacy consideration, the raw data used for training models in the learnware market are inaccessible. In this paper, we develop a novel scheme that works can effectively reuse the learnwares even when the user’s job involves unseen parts. Despite the raw training data are inaccessible, our approach can provably identify samples from the unseen parts while assigning the rest to proper models in the market for predicting under a certain condition. Empirical studies also validate the efficacy of our approach.

Bioinformatics (2020) doi: 10.1093/bioinformatics/btaa567 In the originally published version of this manuscript, author affiliation 1 was incorrect. The incorrect affiliation was as follows: “Key Laboratory of Biomedical Information Engineering of Ministry of Education, Biomedical Informatics & Genomics Center, School of Life Science and Technology, Zhongnan Hospital of Wuhan University, Wuhan 430071, China.” The correct affiliation should read: “Key Laboratory of Biomedical Information Engineering of Ministry of Education, Biomedical Informatics & Genomics Center, School of Life Science and Technology, Xi'an Jiaotong University, Xi'an 710049, P. R. China.” This error has been corrected online.

We investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible comparator sequence. Let $T$ be the time horizon and $P_T$ be the path-length that essentially reflects the non-stationarity of environments, the state-of-the-art dynamic regret is $\mathcal{O}(\sqrt{T(1+P_T)})$. Although this bound is proved to be minimax optimal for convex functions, in this paper, we demonstrate that it is possible to further enhance the dynamic regret by exploiting the smoothness condition. Specifically, we propose novel online algorithms that are capable of leveraging smoothness and replace the dependence on $T$ in the dynamic regret by problem-dependent quantities: the variation in gradients of loss functions, the cumulative loss of the comparator sequence, and the minimum of the previous two terms. These quantities are at most $\mathcal{O}(T)$ while could be much smaller in benign environments. Therefore, our results are adaptive to the intrinsic difficulty of the problem, since the bounds are tighter than existing results for easy problems and meanwhile guarantee the same rate in the worst case.

This paper studies the problem of learning with augmented classes (LAC), where augmented classes unobserved in the training data might emerge in the testing phase. Previous studies generally attempt to discover augmented classes by exploiting geometric properties, achieving inspiring empirical performance yet lacking theoretical understandings particularly on the generalization ability. In this paper we show that, by using unlabeled training data to approximate the potential distribution of augmented classes, an unbiased risk estimator of the testing distribution can be established for the LAC problem under mild assumptions, which paves a way to develop a sound approach with theoretical guarantees. Moreover, the proposed approach can adapt to complex changing environments where augmented classes may appear and the prior of known classes may change simultaneously. Extensive experiments confirm the effectiveness of our proposed approach.

Online learning in dynamic environments has recently drawn considerable attention, where dynamic regret is usually employed to compare decisions of online algorithms to dynamic comparators. In previous works, dynamic regret bounds are typically established in terms of regularity of comparators $C_T$ or that of online functions $V_T$. Recently, Jadbabaie et al. [2015] propose an algorithm that can take advantage of both regularities and enjoy an $\tilde{O}(\sqrt{1+D_T} + \min\{\sqrt{(1+D_T)C_T}, (1+D_T)^{1/3}V_T^{1/3}T^{1/3}\})$ dynamic regret, where $D_T$ is an additional quantity to measure the niceness of environments. The regret bound adapts to the smaller regularity of problem environments and is tighter than all existing dynamic regret guarantees. Nevertheless, their algorithm involves non-convex programming at each iteration, and thus requires burdensome computations. In this paper, we design a simple algorithm based on the online ensemble, which provably enjoys the same (even slightly stronger) guarantee as the state-of-the-art rate, yet is much more efficient because our algorithm does not involve any non-convex problem solving. Empirical studies also verify the efficacy and efficiency.

MOTIVATION: CircRNAs are an abundant class of non-coding RNAs with widespread, cell-/tissue-specific patterns. Previous work suggested that epigenetic features might be related to circRNA expression. However, the contribution of epigenetic changes to circRNA expression has not been investigated systematically. Here, we built a machine learning framework named CIRCScan, to predict circRNA expression in various cell lines based on the sequence and epigenetic features. RESULTS: The predicted accuracy of the expression status models was high with area under the curve of receiver operating characteristic (ROC) values of 0.89-0.92 and the false-positive rates of 0.17-0.25. Predicted expressed circRNAs were further validated by RNA-seq data. The performance of expression-level prediction models was also good with normalized root-mean-square errors of 0.28-0.30 and Pearson's correlation coefficient r over 0.4 in all cell lines, along with Spearman's correlation coefficient ρ of 0.33-0.46. Noteworthy, H3K79me2 was highly ranked in modeling both circRNA expression status and levels across different cells. Further analysis in additional nine cell lines demonstrated a significant enrichment of H3K79me2 in circRNA flanking intron regions, supporting the potential involvement of H3K79me2 in circRNA expression regulation. AVAILABILITY AND IMPLEMENTATION: The CIRCScan assembler is freely available online for academic use at https://github.com/johnlcd/CIRCScan. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Genome-wide association studies (GWASs) are an effective strategy to identify susceptibility loci for human complex diseases. However, missing heritability is still a big problem. Most GWASs single-nucleotide polymorphisms (SNPs) are located in noncoding regions, which has been considered to be the unexplored territory of the genome. Recently, data from the Encyclopedia of DNA Elements (ENCODE) and Roadmap Epigenomics projects have shown that many GWASs SNPs in the noncoding regions fall within regulatory elements. In this study, we developed a pipeline named functional disease-associated SNPs prediction (FDSP), to identify novel susceptibility loci for complex diseases based on the interpretation of the functional features for known disease-associated variants with machine learning. We applied our pipeline to predict novel susceptibility SNPs for type 2 diabetes (T2D) and hypertension. The predicted SNPs could explain heritability beyond that explained by GWAS-associated SNPs. Functional annotation by expression quantitative trait loci analyses showed that the target genes of the predicted SNPs were significantly enriched in T2D or hypertension-related pathways in multiple tissues. Our results suggest that combining GWASs and regulatory features data could identify additional functional susceptibility SNPs for complex diseases. We hope FDSP could help to identify novel susceptibility loci for complex diseases and solve the missing heritability problem.