Generalized Category Discovery (GCD) aims to identify unlabeled samples by leveraging the base knowledge from labeled ones, where the unlabeled set consists of both base and novel classes. Since clustering methods are time-consuming at inference, parametric-based approaches have become more popular. However, recent parametric-based methods suffer from inferior base discrimination due to unreliable self-supervision. To address this issue, we propose a Reciprocal Learning Framework (RLF) that introduces an auxiliary branch devoted to base classification. During training, the main branch filters the pseudo-base samples to the auxiliary branch. In response, the auxiliary branch provides more reliable soft labels for the main branch, leading to a virtuous cycle. Furthermore, we introduce Class-wise Distribution Regularization (CDR) to mitigate the learning bias towards base classes. CDR essentially increases the prediction confidence of the unlabeled data and boosts the novel class performance. Combined with both components, our proposed method, RLCD, achieves superior performance in all classes with negligible extra computation. Comprehensive experiments across seven GCD datasets validate its superiority. Our codes are available at https://github.com/APORduo/RLCD.

Large language models (LLMs) have shown that generative pretraining can distill vast world knowledge into compact token representations. While LLMs encapsulate extensive world knowledge, they remain limited in modeling the behavioral knowledge contained within user interaction histories. User behavior forms a distinct modality, where each action—defined by multi-dimensional attributes such as time, context, and transaction type—constitutes a behavioral token. Modeling these high-cardinality, sparse, and irregular sequences is challenging, and discriminative models often falter under limited supervision. To bridge this gap, we extend generative pretraining to user behavior, learning transferable representations from unlabeled behavioral data analogous to how LLMs learn from text. We present PANTHER, a hybrid generative–discriminative framework that unifies user behavior pretraining and downstream adaptation, enabling large-scale sequential user representation learning and real-time inference. PANTHER introduces: (1) Structured Tokenization to compress multi-dimensional transaction attributes into an interpretable vocabulary; (2) Sequence Pattern Recognition Module (SPRM) for modeling periodic transaction motifs; (3) a Unified User-Profile Embedding that fuses static demographics with dynamic transaction histories, enabling both personalized predictions and population-level knowledge transfer; and (4) Real-time scalability enabled by offline caching of pre-trained embeddings for millisecond-level inference.Fully deployed and operational online at WeChat Pay, PANTHER delivers a 25.6\% boost in next-transaction prediction HitRate@1 and a 38.6\% relative improvement in fraud detection recall over baselines. Cross-domain evaluations on public benchmarks (CCT, MBD, MovieLens-1M, Yelp) show strong generalization, achieving up to 21\% HitRate@1 gains over transformer baselines, establishing PANTHER as a scalable, high-performance framework for industrial user sequential behavior modeling.

Improving Multi-modal Large Language Models (MLLMs) in the post-training stage typically relies on supervised fine-tuning (SFT) or reinforcement learning (RL), which require expensive and manually annotated multi-modal data--an ultimately unsustainable resource. This limitation has motivated a growing interest in unsupervised paradigms as a third stage of post-training after SFT and RL. While recent efforts have explored this direction, their methods are complex and difficult to iterate. To address this, we propose MM-UPT, a simple yet effective framework for unsupervised post-training of MLLMs, enabling continual self-improvement without any external supervision. The training method of MM-UPT builds upon GRPO, replacing traditional reward signals with a self-rewarding mechanism based on majority voting over multiple sampled responses. Our experiments demonstrate that such training method effectively improves the reasoning ability of Qwen2.5-VL-7B (e.g., 66.3\%$\rightarrow$72.9\% on MathVista, 62.9\%$\rightarrow$68.7\% on We-Math), using standard dataset without ground truth labels. To further explore scalability, we extend our framework to a data self-generation setting, designing two strategies that prompt the MLLM to synthesize new training samples on its own. Additional experiments show that combining these synthetic data with the unsupervised training method can also boost performance, highlighting a promising approach for scalable self-improvement. Overall, MM-UPT offers a new paradigm for autonomous enhancement of MLLMs, serving as a critical third step after initial SFT and RL in the absence of external supervision. Our code is available at \url{https://github.com/waltonfuture/MM-UPT}.

T-cell receptors (TCRs) recognize peptide-MHC (pMHC) complexes through intricate structural interactions, which is a core component of adaptive immunity. However, the diverse and cross-reactive nature of TCRs poses great challenges for accurate prediction of TCR-epitope interactions, hampering the advancement and broad application of TCR-related therapies. Here, we present SageTCR, a bi-level graph neural network (GNN) framework that leverages structural data to predict TCR-pMHC binding possibilities. Harnessing the pretrained language models, SageTCR encodes detailed structural arrangement at both residue-level and atomic-level and effectively integrates the bimodal representations via attention mechanisms. To tackle the deficiency of experimental structures, we explore comprehensive data augmentation strategies to enrich the training and increase the generalizability while concurrently preserving the characteristic TCR-pMHC diagonal binding mode. SageTCR demonstrates superior performance compared to six methods with different deep learning architectures. Furthermore, SageTCR offers the interpretability by identifying and focusing on the conformational features of pivotal contact residues on the interface, which can provide valuable insights for TCR engineering and immunotherapy design.

In this paper, we use matrix information theory as an analytical tool to analyze the dynamics of the information interplay between data representations and classification head vectors in the supervised learning process. Specifically, inspired by the theory of Neural Collapse, we introduce matrix mutual information ratio (MIR) and matrix entropy difference ratio (HDR) to assess the interactions of data representation and class classification heads in supervised learning, and we determine the theoretical optimal values for MIR and HDR when Neural Collapse happens. Our experiments show that MIR and HDR can effectively explain many phenomena occurring in neural networks, for example, the standard supervised training dynamics, linear mode connectivity, and the performance of label smoothing and pruning. Additionally, we use MIR and HDR to gain insights into the dynamics of grokking, which is an intriguing phenomenon observed in supervised training, where the model demonstrates generalization capabilities long after it has learned to fit the training data. Furthermore, we introduce MIR and HDR as loss terms in supervised and semi-supervised learning to optimize the information interactions among samples and classification heads. The empirical results provide evidence of the method’s effectiveness, demonstrating that the utilization of MIR and HDR not only aids in comprehending the dynamics throughout the training process but can also enhances the training procedure itself.

In this paper, we conduct a comprehensive analysis of two dual-branch (Siamese architecture) self-supervised learning approaches, namely Barlow Twins and spectral contrastive learning, through the lens of matrix mutual information. We prove that the loss functions of these methods implicitly optimize both matrix mutual information and matrix joint entropy. This insight prompts us to further explore the category of single-branch algorithms, specifically MAE and U-MAE, for which mutual information and joint entropy become the entropy. Building on this intuition, we introduce the Matrix Variational Masked Auto-Encoder (M-MAE), a novel method that leverages the matrix-based estimation of entropy as a regularizer and subsumes U-MAE as a special case. The empirical evaluations underscore the effectiveness of M-MAE compared with the state-of-the-art methods, including a 3.9% improvement in linear probing ViT-Base, and a 1% improvement in fine-tuning ViT-Large, both on ImageNet.

Semi-supervised learning has made remarkable strides by effectively utilizing a limited amount of labeled data while capitalizing on the abundant information present in unlabeled data. However, current algorithms often prioritize aligning image predictions with specific classes generated through self-training techniques, thereby neglecting the inherent relationships that exist within these classes. In this paper, we present a new approach called OTMatch, which leverages semantic relationships among classes by employing an optimal transport loss function to match distributions. We conduct experiments on many standard vision and language datasets. The empirical results show improvements in our method above baseline, this demonstrates the effectiveness and superiority of our approach in harnessing semantic relationships to enhance learning performance in a semi-supervised setting.

Continual learning requires learning incremental tasks with dynamic data distributions. So far, it has been observed that employing a combination of contrastive loss and distillation loss for training in continual learning yields strong performance. To the best of our knowledge, however, this contrastive continual learning framework lacks convincing theoretical explanations. In this work, we fill this gap by establishing theoretical performance guarantees, which reveal how the performance of the model is bounded by training losses of previous tasks in the contrastive continual learning framework. Our theoretical explanations further support the idea that pre-training can benefit continual learning. Inspired by our theoretical analysis of these guarantees, we propose a novel contrastive continual learning algorithm called CILA, which uses adaptive distillation coefficients for different tasks. These distillation coefficients are easily computed by the ratio between average distillation losses and average contrastive losses from previous tasks. Our method shows great improvement on standard benchmarks and achieves new state-of-the-art performance.

The maximum entropy encoding framework provides a unified perspective for many non-contrastive learning methods like SimSiam, Barlow Twins, and MEC. Inspired by this framework, we introduce Matrix-SSL, a novel approach that leverages matrix information theory to interpret the maximum entropy encoding loss as matrix uniformity loss. Furthermore, Matrix-SSL enhances the maximum entropy encoding method by seamlessly incorporating matrix alignment loss, directly aligning covariance matrices in different branches. Experimental results reveal that Matrix-SSL outperforms state-of-the-art methods on the ImageNet dataset under linear evaluation settings and on MS-COCO for transfer learning tasks. Specifically, when performing transfer learning tasks on MS-COCO, our method outperforms previous SOTA methods such as MoCo v2 and BYOL up to 3.3% with only 400 epochs compared to 800 epochs pre-training. We also try to introduce representation learning into the language modeling regime by fine-tuning a 7B model using matrix cross-entropy loss, with a margin of 3.1% on the GSM8K dataset over the standard cross-entropy loss.

We provide a statistical analysis of regularization-based continual learning on a sequence of linear regression tasks, with emphasis on how different regularization terms affect the model performance. We first derive the convergence rate for the oracle estimator obtained as if all data were available simultaneously. Next, we consider a family of generalized $\ell_2$-regularization algorithms indexed by matrix-valued hyperparameters, which includes the minimum norm estimator and continual ridge regression as special cases. As more tasks are introduced, we derive an iterative update formula for the estimation error of generalized $\ell_2$-regularized estimators, from which we determine the hyperparameters resulting in the optimal algorithm. Interestingly, the choice of hyperparameters can effectively balance the trade-off between forward and backward knowledge transfer and adjust for data heterogeneity. Moreover, the estimation error of the optimal algorithm is derived explicitly, which is of the same order as that of the oracle estimator. In contrast, our lower bounds for the minimum norm estimator and continual ridge regression show their suboptimality. A byproduct of our theoretical analysis is the equivalence between early stopping and generalized $\ell_2$-regularization in continual learning, which may be of independent interest. Finally, we conduct experiments to complement our theory.

Large Language Models (LLMs) have transformed natural language processing and extended their powerful capabilities to multi-modal domains. As LLMs continue to advance, it is crucial to develop diverse and appropriate metrics for their evaluation. In this paper, we introduce a novel rank-based metric, Diff-eRank, grounded in information theory and geometry principles. Diff-eRank assesses LLMs by analyzing their hidden representations, providing a quantitative measure of how efficiently they eliminate redundant information during training. We demonstrate the applicability of Diff-eRank in both single-modal (e.g., language) and multi-modal settings. For language models, our results show that Diff-eRank increases with model size and correlates well with conventional metrics such as loss and accuracy. In the multi-modal context, we propose an alignment evaluation method based on the eRank, and verify that contemporary multi-modal LLMs exhibit strong alignment performance based on our method. Our code is publicly available at https://github.com/waltonfuture/Diff-eRank.

Continual learning aims to incrementally acquire new concepts in data streams while resisting forgetting previous knowledge. With the rise of powerful pre-trained models (PTMs), there is a growing interest in training incremental learning systems using these foundation models, rather than learning from scratch. Existing works often view PTMs as a strong initial point and directly apply parameter-efficient tuning (PET) in the first session for adapting to downstream tasks. In the following sessions, most methods freeze model parameters for tackling forgetting issues. However, applying PET directly to downstream data cannot fully explore the inherent knowledge in PTMs. Additionally, freezing the parameters in incremental sessions hinders models' plasticity to novel concepts not covered in the first session. To solve the above issues, we propose a Slow And Fast parameter-Efficient tuning (SAFE) framework. In particular, to inherit general knowledge from foundation models, we include a transfer loss function by measuring the correlation between the PTM and the PET-applied model. After calibrating in the first session, the slow efficient tuning parameters can capture more informative features, improving generalization to incoming classes. Moreover, to further incorporate novel concepts, we strike a balance between stability and plasticity by fixing slow efficient tuning parameters and continuously updating the fast ones. Specifically, a cross-classification loss with feature alignment is proposed to circumvent catastrophic forgetting. During inference, we introduce an entropy-based aggregation strategy to dynamically utilize the complementarity in the slow and fast learners. Extensive experiments on seven benchmark datasets verify the effectiveness of our method by significantly surpassing the state-of-the-art.

Real-world large-scale datasets are both noisily labeled and class-imbalanced. The issues seriously hurt the generalization of trained models. It is hence significant to address the simultaneous incorrect labeling and class-imbalance, i.e., the problem of learning with noisy labels on long-tailed data. Previous works develop several methods for the problem. However, they always rely on strong assumptions that are invalid or hard to be checked in practice. In this paper, to handle the problem and address the limitations of prior works, we propose a representation calibration method RCAL. Specifically, RCAL works with the representations extracted by unsupervised contrastive learning. We assume that without incorrect labeling and class imbalance, the representations of instances in each class conform to a multivariate Gaussian distribution, which is much milder and easier to be checked. Based on the assumption, we recover underlying representation distributions from polluted ones resulting from mislabeled and class-imbalanced data. Additional data points are then sampled from the recovered distributions to help generalization. Moreover, during classifier training, representation learning takes advantage of representation robustness brought by contrastive learning, which further improves the classifier performance. We derive theoretical results to discuss the effectiveness of our representation calibration. Experiments on multiple benchmarks justify our claims and confirm the superiority of the proposed method.

Contrastive learning has shown outstanding performances in both supervised and unsupervised learning, and has recently been introduced to solve weakly supervised learning problems such as semi-supervised learning and noisy label learning. Despite the empirical evidence showing that semi-supervised labels improve the representations of contrastive learning, it remains unknown if noisy supervised information can be directly used in training instead of after manual denoising. Therefore, to explore the mechanical differences between semi-supervised and noisy-labeled information in helping contrastive learning, we establish a unified theoretical framework of contrastive learning under weak supervision. Specifically, we investigate the most intuitive paradigm of jointly training supervised and unsupervised contrastive losses. By translating the weakly supervised information into a similarity graph under the framework of spectral clustering based on the posterior probability of weak labels, we establish the downstream classification error bound. We prove that semi-supervised labels improve the downstream error bound whereas noisy labels have limited effects under such a paradigm. Our theoretical findings here provide new insights for the community to rethink the role of weak supervision in helping contrastive learning.

Due to the limited availability of data, existing few-shot learning methods trained from scratch fail to achieve satisfactory performance. In contrast, large-scale pre-trained models such as CLIP demonstrate remarkable few-shot and zero-shot capabilities. To enhance the performance of pre-trained models for downstream tasks, fine-tuning the model on downstream data is frequently necessary. However, fine-tuning the pre-trained model leads to a decrease in its generalizability in the presence of distribution shift, while the limited number of samples in few-shot learning makes the model highly susceptible to overfitting. Consequently, existing methods for fine-tuning few-shot learning primarily focus on fine-tuning the model's classification head or introducing additional structure. In this paper, we introduce a fine-tuning approach termed Feature Discrimination Alignment (FD-Align). Our method aims to bolster the model's generalizability by preserving the consistency of spurious features across the fine-tuning process. Extensive experimental results validate the efficacy of our approach for both ID and OOD tasks. Once fine-tuned, the model can seamlessly integrate with existing methods, leading to performance improvements. Our code can be found in https://github.com/skingorz/FD-Align.

Few-shot learning aims to adapt models trained on the base dataset to novel tasks where the categories were not seen by the model before. This often leads to a relatively concentrated distribution of feature values across channels on novel classes, posing challenges in determining channel importance for novel tasks. Standard few-shot learning methods employ geometric similarity metrics such as cosine similarity and negative Euclidean distance to gauge the semantic relatedness between two features. However, features with high geometric similarities may carry distinct semantics, especially in the context of few-shot learning. In this paper, we demonstrate that the importance ranking of feature channels is a more reliable indicator for few-shot learning than geometric similarity metrics. We observe that replacing the geometric similarity metric with Kendall’s rank correlation only during inference is able to improve the performance of few-shot learning across a wide range of methods and datasets with different domains. Furthermore, we propose a carefully designed differentiable loss for meta-training to address the non-differentiability issue of Kendall’s rank correlation. By replacing geometric similarity with differentiable Kendall’s rank correlation, our method can integrate with numerous existing few-shot approaches and is ready for integrating with future state-of-the-art methods that rely on geometric similarity metrics. Extensive experiments validate the efficacy of the rank-correlation-based approach, showcasing a significant improvement in few-shot learning.

Pretext-based self-supervised learning learns the semantic representation via a handcrafted pretext task over unlabeled data and then uses the learned representation for downstream tasks, which effectively reduces the sample complexity of downstream tasks under Conditional Independence (CI) condition. However, the downstream sample complexity gets much worse if the CI condition does not hold. One interesting question is whether we can make the CI condition hold by using downstream data to refine the unlabeled data to boost self-supervised learning. At first glance, one might think that seeing downstream data in advance would always boost the downstream performance. However, we show that it is not intuitively true and point out that in some cases, it hurts the final performance instead. In particular, we prove both model-free and model-dependent lower bounds of the number of downstream samples used for data refinement. Moreover, we conduct various experiments on both synthetic and real-world datasets to verify our theoretical results.

Nowadays model uncertainty has become one of the most important problems in both academia and industry. In this paper, we mainly consider the scenario in which we have a common model set used for model averaging instead of selecting a single final model via a model selection procedure to account for this model's uncertainty in order to improve reliability and accuracy of inferences. Here one main challenge is to learn the prior over the model set. To tackle this problem, we propose two data-based algorithms to get proper priors for model averaging. One is for meta-learner, the analysts should use historical similar tasks to extract the information about the prior. The other one is for base-learner, a subsampling method is used to deal with the data step by step. Theoretically, an upper bound of risk for our algorithm is presented to guarantee the performance of the worst situation. In practice, both methods perform well in simulations and real data studies, especially with poor quality data.

In recent years, a variety of normalization methods have been proposed to help training neural networks, such as batch normalization (BN), layer normalization (LN), weight normalization (WN), group normalization (GN), etc. However, some necessary tools to analyze all these normalization methods are lacking. In this paper, we first propose a lemma to define some necessary tools. Then, we use these tools to make a deep analysis on popular normalization methods and obtain the following conclusions: 1) Most of the normalization methods can be interpreted in a unified framework, namely normalizing pre-activations or weights onto a sphere; 2) Since most of the existing normalization methods are scaling invariant, we can conduct optimization on a sphere with scaling symmetry removed, which can help to stabilize the training of network; 3) We prove that training with these normalization methods can make the norm of weights increase, which could cause adversarial vulnerability as it amplifies the attack. Finally, a series of experiments are conducted to verify these claims.

Few-shot learning (FSL) has attracted increasing attention in recent years but remains challenging, due to the intrinsic difficulty in learning to generalize from a few examples. This paper proposes an adaptive margin principle to improve the generalization ability of metric-based meta-learning approaches for few-shot learning problems. Specifically, we first develop a class-relevant additive margin loss, where semantic similarity between each pair of classes is considered to separate samples in the feature embedding space from similar classes. Further, we incorporate the semantic context among all classes in a sampled training task and develop a task-relevant additive margin loss to better distinguish samples from different classes. Our adaptive margin method can be easily extended to a more realistic generalized FSL setting. Extensive experiments demonstrate that the proposed method can boost the performance of current metric-based meta-learning approaches, under both the standard FSL and generalized FSL settings.

We study locally differentially private (LDP) bandits learning in this paper. First, we propose simple black-box reduction frameworks that can solve a large family of context-free bandits learning problems with LDP guarantee. Based on our frameworks, we can improve previous best results for private bandits learning with one-point feedback, such as private Bandits Convex Optimization etc, and obtain the first results for Bandits Convex Optimization (BCO) with multi-point feedback under LDP. LDP guarantee and black-box nature make our frameworks more attractive in real applications compared with previous specifically designed and relatively weaker differentially private (DP) algorithms. Further, we also extend our algorithm to Generalized Linear Bandits with regret bound $\tilde{\mc{O}}(T^{3/4}/\varepsilon)$ under $(\varepsilon, \delta)$-LDP and it is conjectured to be optimal. Note given existing $\Omega(T)$ lower bound for DP contextual linear bandits (Shariff & Sheffet, NeurIPS 2018), our result shows a fundamental difference between LDP and DP for contextual bandits.

Recurrent Neural Networks (RNNs) have been widely used in processing natural language tasks and achieve huge success. Traditional RNNs usually treat each token in a sentence uniformly and equally. However, this may miss the rich semantic structure information of a sentence, which is useful for understanding natural languages. Since semantic structures such as word dependence patterns are not parameterized, it is a challenge to capture and leverage structure information. In this paper, we propose an improved variant of RNN, Multi-Channel RNN (MC-RNN), to dynamically capture and leverage local semantic structure information. Concretely, MC-RNN contains multiple channels, each of which represents a local dependence pattern at a time. An attention mechanism is introduced to combine these patterns at each step, according to the semantic information. Then we parameterize structure information by adaptively selecting the most appropriate connection structures among channels. In this way, diverse local structures and dependence patterns in sentences can be well captured by MC-RNN. To verify the effectiveness of MC-RNN, we conduct extensive experiments on typical natural language processing tasks, including neural machine translation, abstractive summarization, and language modeling. Experimental results on these tasks all show significant improvements of MC-RNN over current top systems.

In this paper, we propose to tackle the challenging few-shot learning (FSL) problem by learning global class representations using both base and novel class training samples. In each training episode, an episodic class mean computed from a support set is registered with the global representation via a registration module. This produces a registered global class representation for computing the classification loss using a query set. Though following a similar episodic training pipeline as existing meta learning based approaches, our method differs significantly in that novel class training samples are involved in the training from the beginning. To compensate for the lack of novel class training samples, an effective sample synthesis strategy is developed to avoid overfitting. Importantly, by joint base-novel class training, our approach can be easily extended to a more practical yet challenging FSL setting, i.e., generalized FSL, where the label space of test data is extended to both base and novel classes. Extensive experiments show that our approach is effective for both of the two FSL settings.

We study the Combinatorial Pure Exploration problem with Continuous and Separable reward functions (CPE-CS) in the stochastic multi-armed bandit setting. In a CPE-CS instance, we are given several stochastic arms with unknown distributions, as well as a collection of possible decisions. Each decision has a reward according to the distributions of arms. The goal is to identify the decision with the maximum reward, using as few arm samples as possible. The problem generalizes the combinatorial pure exploration problem with linear rewards, which has attracted significant attention in recent years. In this paper, we propose an adaptive learning algorithm for the CPE-CS problem, and analyze its sample complexity. In particular, we introduce a new hardness measure called the consistent optimality hardness, and give both the upper and lower bounds of sample complexity. Moreover, we give examples to demonstrate that our solution has the capacity to deal with non-linear reward functions.

In this paper, we study the Multi-Round Influence Maximization (MRIM) problem, where influence propagates in multiple rounds independently from possibly different seed sets, and the goal is to select seeds for each round to maximize the expected number of nodes that are activated in at least one round. MRIM problem models the viral marketing scenarios in which advertisers conduct multiple rounds of viral marketing to promote one product. We consider two different settings: 1) the non-adaptive MRIM, where the advertiser needs to determine the seed sets for all rounds at the very beginning, and 2) the adaptive MRIM, where the advertiser can select seed sets adaptively based on the propagation results in the previous rounds. For the non-adaptive setting, we design two algorithms that exhibit an interesting tradeoff between efficiency and effectiveness: a cross-round greedy algorithm that selects seeds at a global level and achieves $1/2 - \varepsilon$ approximation ratio, and a within-round greedy algorithm that selects seeds round by round and achieves $1-e^-(1-1/e) -\varepsilon \approx 0.46 - \varepsilon$ approximation ratio but saves running time by a factor related to the number of rounds. For the adaptive setting, we design an adaptive algorithm that guarantees $1-e^-(1-1/e) -\varepsilon$ approximation to the adaptive optimal solution. In all cases, we further design scalable algorithms based on the reverse influence sampling approach and achieve near-linear running time. We conduct experiments on several real-world networks and demonstrate that our algorithms are effective for the MRIM task.

We introduce the community exploration problem that has various real-world applications such as online advertising. In the problem, an explorer allocates limited budget to explore communities so as to maximize the number of members he could meet. We provide a systematic study of the community exploration problem, from offline optimization to online learning. For the offline setting where the sizes of communities are known, we prove that the greedy methods for both of non-adaptive exploration and adaptive exploration are optimal. For the online setting where the sizes of communities are not known and need to be learned from the multi-round explorations, we propose an ``upper confidence'' like algorithm that achieves the logarithmic regret bounds. By combining the feedback from different rounds, we can achieve a constant regret bound.

Public opinion polling is usually done by random sampling from the entire population, treating individual opinions as independent. In the real world, individuals' opinions are often correlated, e.g., among friends in a social network. In this paper, we explore the idea of partitioned sampling, which partitions individuals with high opinion similarities into groups and then samples every group separately to obtain an accurate estimate of the population opinion. We rigorously formulate the above idea as an optimization problem. We then show that the simple partitions which contain only one sample in each group are always better, and reduce finding the optimal simple partition to a well-studied Min-r-Partition problem. We adapt an approximation algorithm and a heuristic algorithm to solve the optimization problem. Moreover, to obtain opinion similarity efficiently, we adapt a well-known opinion evolution model to characterize social interactions, and provide an exact computation of opinion similarities based on the model. We use both synthetic and real-world datasets to demonstrate that the partitioned sampling method results in significant improvement in sampling quality and it is robust when some opinion similarities are inaccurate or even missing.