My research lies at the intersection of causality, reinforcement learning, world models, and multi-agent systems. I aim to develop causal foundation world models that enable agents to interpret the past, reason about the future, and act reliably in dynamic, non-stationary, and open-ended environments. My work spans causal representation learning (e.g., CausalVAE), causal reasoning in large language models, and causality-driven exploration in open-ended worlds. These contributions have appeared in leading venues such as NeurIPS, ICML, ICLR, CVPR, and KDD, and have been recognized through over 770 citations and the Rising Star in AI award (2024). Looking forward, my agenda focuses on scalable, trustworthy causal world models for healthcare, robotics, scientific discovery, and digital systems.

Congmin Zheng, Jiachen Zhu, Zhuoying Ou, Yuxiang Chen, Kangning Zhang, Rong Shan, Zeyu Zheng, Mengyue Yang, Jianghao Lin, Yong Yu, Weinan Zhang. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Macroeconomic outcomes emerge from individuals’ decisions, making it essential to model how agents interact with macro policy via consumption, investment, and labor choices. We formulate this as a dynamic Stackelberg game: the government (leader) sets policies, and agents (followers) respond by optimizing their behavior over time. Unlike static models, this dynamic formulation captures temporal dependencies and strategic feedback critical to policy design. However, as the number of agents increases, explicitly simulating all agent–agent and agent–government interactions becomes computationally infeasible. To address this, we propose the Dynamic Stackelberg Mean Field Game (DSMFG) framework, which approximates these complex interactions via agent–population and government–population couplings. This approximation preserves individual-level feedback while ensuring scalability, enabling DSMFG to jointly model three core features of real-world policy-making: dynamic feedback, asymmetry, and large-scale. We further introduce Stackelberg Mean Field Reinforcement Learning (SMFRL), a data-driven algorithm that learns the leader’s optimal policies while maintaining personalized responses for individual agents. Empirically, we validate our approach in a large-scale simulated economy, where it scales to 1,000 agents (vs. 100 in prior work) and achieves a 4× GDP gain over classical economic methods and a 19× improvement over the static 2022 U.S. federal income tax policy.

Prevalent in biomedical applications (e.g., human phenotype research), multimodal datasets can provide valuable insights into the underlying physiological mechanisms. However, current machine learning (ML) models designed to analyze these datasets often lack interpretability and identifiability guarantees, which are essential for biomedical research. Recent advances in causal representation learning have shown promise in identifying interpretable latent causal variables with formal theoretical guarantees. Unfortunately, most current work on multimodal distributions either relies on restrictive parametric assumptions or yields only coarse identification results, limiting their applicability to biomedical research that favors a detailed understanding of the mechanisms. In this work, we aim to develop flexible identification conditions for multimodal data and principled methods to facilitate the understanding of biomedical datasets. Theoretically, we consider a nonparametric latent distribution (c.f., parametric assumptions in previous work) that allows for causal relationships across potentially different modalities. We establish identifiability guarantees for each latent component, extending the subspace identification results from previous work. Our key theoretical contribution is the structural sparsity of causal connections between modalities, which, as we will discuss, is natural for a large collection of biomedical systems. Empirically, we present a practical framework to instantiate our theoretical insights. We demonstrate the effectiveness of our approach through extensive experiments on both numerical and synthetic datasets. Results on a real-world human phenotype dataset are consistent with established biomedical research, validating our theoretical and methodological framework.

In sequential decision-making (SDM) tasks, methods like reinforcement learning (RL) and heuristic search have made notable advances in specific cases. However, they often require extensive exploration and face challenges in generalizing across diverse environments due to their limited grasp of the underlying decision dynamics. In contrast, large language models (LLMs) have recently emerged as powerful general-purpose tools, due to their capacity to maintain vast amounts of domain-specific knowledge. To harness this rich prior knowledge for efficiently solving complex SDM tasks, we propose treating LLMs as prior action distributions and integrating them into RL frameworks through Bayesian inference methods, making use of variational inference and direct posterior sampling. The proposed approaches facilitate the seamless incorporation of fixed LLM priors into both policy-based and value-based RL frameworks. Our experiments show that incorporating LLM-based action priors significantly reduces exploration and optimization complexity, substantially improving sample efficiency compared to traditional RL techniques, e.g., using LLM priors decreases the number of required samples by over 90\% in offline learning scenarios.

In-context learning with large language models (LLMs) delivers strong few-shot performance by choosing few-shot demonstrations from the entire training dataset. However, previous few-shot in-context learning methods, which calculate similarity scores for choosing demonstrations, incur high computational costs by repeatedly retrieving large-scale datasets for each query. This is due to their failure to recognize that not all demonstrations are equally informative, and many less informative demonstrations can be inferred from a core set of highly informative ones. To this end, we propose FEEDER (FEw yet Essential Demonstration prE-selectoR), a novel \emph{pre-selection} framework that identifies a core subset of demonstrations containing the most informative examples. This subset, referred to as the FEEDER set, consists of demonstrations that capture both the ''sufficiency'' and ''necessity'' information to infer the entire dataset. Notice that FEEDER is selected before the few-shot in-context learning, enabling more efficient few-shot demonstrations choosing in a smaller set. To identify FEEDER, we propose a novel effective tree based algorithm. Once selected, it can replace the original dataset, leading to improved efficiency and prediction accuracy in few-shot in-context learning. Additionally, FEEDER also benefit fine-tuning LLMs, we propose a bi-level optimization method enabling more efficient training without sacrificing performance when datasets become smaller. Our experiments are on 6 text classification datasets, 1 reasoning dataset, and 1 semantic-parsing dataset, across 6 LLMs (ranging from 335M to 7B parameters), demonstrate that: (i) In few-shot inference, FEEDER achieves superior (or comparable) performance while utilizing only half the input training data. (ii) In fine-tuning, FEEDER significantly boosts the performance of LLMs.

We address the problem of reward hacking, where maximising a proxy reward does not necessarily increase the true reward. This is a key concern for Large Language Models (LLMs), as they are often fine-tuned on human preferences that may not accurately reflect a true objective. Existing work uses various tricks such as regularisation, tweaks to the reward model, and reward hacking detectors, to limit the influence that such proxy preferences have on a model. Luckily, in many contexts such as medicine, education, and law, a sparse amount of expert data is often available. In these cases, it is often unclear whether the addition of proxy data can improve policy learning. We outline a set of sufficient conditions on proxy feedback that, if satisfied, indicate that proxy data can provably improve the sample complexity of learning the ground truth policy. These conditions can inform the data collection process for specific tasks. The result implies a parameterisation for LLMs that achieves this improved sample complexity. We detail how one can adapt existing architectures to yield this improved sample complexity.

Steering cooperative multi-agent reinforcement learning (MARL) towards desired outcomes is challenging, particularly when the global guidance from a human on the whole multi-agent system is impractical in a large-scale MARL. On the other hand, designing external mechanisms (e.g., intrinsic rewards and human feedback) to coordinate agents mostly relies on empirical studies, lacking a easy-to-use research tool. In this work, we employ multi-agent influence diagrams (MAIDs) as a graphical framework to address the above issues. First, we introduce the concept of MARL interaction paradigms (orthogonal to MARL learning paradigms), using MAIDs to analyze and visualize both unguided self-organization and global guidance mechanisms in MARL. Then, we design a new MARL interaction paradigm, referred to as the targeted intervention paradigm that is applied to only a single targeted agent, so the problem of global guidance can be mitigated. In implementation, we introduce a causal inference technique—referred to as Pre-Strategy Intervention (PSI)—to realize the targeted intervention paradigm. Since MAIDs can be regarded as a special class of causal diagrams, a composite desired outcome that integrates the primary task goal and an additional desired outcome can be achieved by maximizing the corresponding causal effect through the PSI. Moreover, the bundled relevance graph analysis of MAIDs provides a tool to identify whether an MARL learning paradigm is workable under the design of an MARL interaction paradigm. In experiments, we demonstrate the effectiveness of our proposed targeted intervention, and verify the result of relevance graph analysis.

Simulating collective decision-making involves more than aggregating individual behaviors; it emerges from dynamic interactions among individuals. While large language models (LLMs) offer strong potential for social simulation, achieving quantitative alignment with real-world data remains a key challenge. To bridge this gap, we propose the \textbf{M}ean-\textbf{F}ield \textbf{LLM} (\textbf{MF-LLM}) framework, the first to incorporate mean field theory into LLM-based social simulation. MF-LLM models bidirectional interactions between individuals and the population through an iterative process, generating population signals to guide individual decisions, which in turn update the signals. This interplay produces coherent trajectories of collective behavior. To improve alignment with real-world data, we introduce \textbf{IB-Tune}, a novel fine-tuning method inspired by the \textbf{I}nformation \textbf{B}ottleneck principle, which retains population signals most predictive of future actions while filtering redundant history. Evaluated on a real-world social dataset, MF-LLM reduces KL divergence to human population distributions by \textbf{47\%} compared to non-mean-field baselines, enabling accurate trend forecasting and effective intervention planning. Generalizing across 7 domains and 4 LLM backbones, MF-LLM provides a scalable, high-fidelity foundation for social simulation.

Federated continual learning (FCL) has garnered increasing attention for its ability to support distributed computation in environments with evolving data distributions. However, the emergence of new tasks introduces both temporal and cross-client shifts, making catastrophic forgetting a critical challenge. Most existing works aggregate knowledge from clients into a global model, which may not enhance client performance since irrelevant knowledge could introduce interference, especially in heterogeneous scenarios. Additionally, directly applying decentralized approaches to FCL suffers from ineffective group formation caused by task changes. To address these challenges, we propose a decentralized dynamic cooperation framework for FCL, where clients establish dynamic cooperative learning coalitions to balance the acquisition of new knowledge and the retention of prior learning, thereby obtaining personalized models. To maximize model performance, each client engages in selective cooperation, dynamically allying with others who offer meaningful performance gains. This results in non-overlapping, variable coalitions at each stage of the task. Moreover, we use coalitional affinity game to simulate coalition relationships between clients. By assessing both client gradient coherence and model similarity, we quantify the client benefits derived from cooperation. We also propose a merge-blocking algorithm and a dynamic cooperative evolution algorithm to achieve cooperative and dynamic equilibrium. Comprehensive experiments demonstrate the superiority of our method compared to various baselines. Code is available at: https://github.com/ydn3229/DCFCL.

Chain-of-Thought (CoT) prompting plays an indispensable role in endowing large language models (LLMs) with complex reasoning capabilities. However, CoT currently faces two fundamental challenges: (1) Sufficiency, which ensures that the generated intermediate inference steps comprehensively cover and substantiate the final conclusion; and (2) Necessity, which identifies the inference steps that are truly indispensable for the soundness of the resulting answer. We propose a causal framework that characterizes CoT reasoning through the dual lenses of sufficiency and necessity. Incorporating causal Probability of Sufficiency and Necessity allows us not only to determine which steps are logically sufficient or necessary to the prediction outcome, but also to quantify their actual influence on the final reasoning outcome under different intervention scenarios, thereby enabling the automated addition of missing steps and the pruning of redundant ones. Extensive experimental results on various mathematical and commonsense reasoning benchmarks confirm substantial improvements in reasoning efficiency and reduced token usage without sacrificing accuracy. Our work provides a promising direction for improving LLM reasoning performance and cost-effectiveness. The code will be publicly available upon acceptance at: https://anonymous.4open.science/r/causalmath-1CEF.

When building a world model, a common assumption is that the environment has a single, unchanging underlying causal rule, like applying Newton's laws to every situation. However, in truly open-ended environments, the apparent causal mechanism may drift over time because the agent continually encounters novel contexts and operates within a limited observational window. This brings about a problem that, when building a world model, even subtle shifts in policy or environment states can alter the very observed causal mechanisms. In this work, we introduce the Meta-Causal Graph as world models for open-ended environments, a minimal unified representation that efficiently encodes the transformation rules governing how causal structures shift across different latent world states. A single Meta-Causal Graph is composed of multiple causal subgraphs, each triggered by meta state, which is in the latent state space. Building on this representation, we introduce a Causality-Seeking Agent whose objectives are to (1) identify the meta states that trigger each subgraph, (2) discover the corresponding causal relationships by agent curiosity-driven intervention policy, and (3) iteratively refine the Meta-Causal Graph through ongoing curiosity-driven exploration and agent experiences. Experiments on both synthetic tasks and a challenging robot arm manipulation task demonstrate that our method robustly captures shifts in causal dynamics and generalizes effectively to previously unseen contexts.

Selection bias poses a widely recognized challenge for unbiased evaluation and learning in many industrial scenarios. For example, in recommender systems, it arises from the users' selective interactions with items. Recently, doubly robust and its variants have been widely studied to achieve debiased learning of prediction models, however, all of them consider a simple exact matching scenario, i.e., the units (such as user-item pairs in a recommender system) are the same between the training and test sets. In practice, there may be limited or even no overlap in units between the training and test. In this paper, we consider a more practical scenario: the joint distribution of the feature and rating is the same in the training and test sets. Theoretical analysis shows that the previous DR estimator is biased even if the imputed errors and learned propensities are correct in this scenario. In addition, we propose a novel super-population doubly robust estimator (SuperDR), which can achieve a more accurate estimation and desirable generalization error bound compared to the existing DR estimators, and extend the joint learning algorithm for training the prediction and imputation models. We conduct extensive experiments on three real-world datasets, including a large-scale industrial dataset, to show the effectiveness of our method. The code is available at https://github.com/ChunyuanZheng/neurips-25-SuperDR.

Ranking items regarding individual user interests is a core technique of multiple downstream tasks such as recommender systems. Learning such a personalized ranker typically relies on the implicit feedback from users' past click-through behaviors. However, collected feedback is biased toward previously highly-ranked items and directly learning from it would result in "rich-get-richer" phenomena. In this paper, we propose a simple yet sufficient unbiased learning-to-rank paradigm named InfoRank that aims to simultaneously address both position and popularity biases. We begin by consolidating the impacts of those biases into a single observation factor, thereby providing a unified approach to addressing bias-related issues. Subsequently, we minimize the mutual information between the observation estimation and the relevance estimation conditioned on the input features. By doing so, our relevance estimation can be proved to be free of bias. To implement InfoRank, we first incorporate an attention mechanism to capture latent correlations within user-item features, thereby generating estimations of observation and relevance. We then introduce a regularization term, grounded in conditional mutual information, to promote conditional independence between relevance estimation and observation estimation. Experimental evaluations conducted across three extensive recommendation and search datasets reveal that InfoRank learns more precise and unbiased ranking strategies.

Learning-to-rank is a core technique in the top-N recommendation task, where an ideal ranker would be a mapping from an item set to an arrangement (a.k.a. permutation). Most existing solutions fall in the paradigm of probabilistic ranking principle (PRP), i.e., first score each item in the candidate set and then perform a sort operation to generate the top ranking list. However, these approaches neglect the contextual dependence among candidate items during individual scoring, and the sort operation is non-differentiable. To bypass the above issues, we propose Set-To-Arrangement Ranking (STARank), a new framework directly generates the permutations of the candidate items without the need for individually scoring and sort operations; and is end-to-end differentiable. As a result, STARank can operate when only the ground-truth permutations are accessible without requiring access to the ground-truth relevance scores for items. For this purpose, STARank first reads the candidate items in the context of the user browsing history, whose representations are fed into a Plackett-Luce module to arrange the given items into a list. To effectively utilize the given ground-truth permutations for supervising STARank, we leverage the internal consistency property of Plackett-Luce models to derive a computationally efficient list-wise loss. Experimental comparisons against 9 the state-of-the-art methods on 2 learning-to-rank benchmark datasets and 3 top-N real-world recommendation datasets demonstrate the superiority of STARank in terms of conventional ranking metrics. Notice that these ranking metrics do not consider the effects of the contextual dependence among the items in the list, we design a new family of simulation-based ranking metrics, where existing metrics can be regarded as special cases. STARank can consistently achieve better performance in terms of PBM and UBM simulation-based metrics.

Learning representations purely from observations concerns the problem of learning a low-dimensional, compact representation which is beneficial to prediction models. Under the hypothesis that the intrinsic latent factors follow some casual generative models, we argue that by learning a causal representation, which is the minimal sufficient causes of the whole system, we can improve the robustness and generalization performance of machine learning models. In this paper, we develop a learning method to learn such representation from observational data by regularizing the learning procedure with mutual information measures, according to the hypothetical factored causal graph. We theoretically and empirically show that the models trained with the learned causal representations are more robust under adversarial attacks and distribution shifts compared with baselines.

When solving decision-making tasks, humans typically depend on information from two key sources: (1) Historical policy data, which provides interaction replay from the environment, and (2) Analytical insights in natural language form, exposing the invaluable thought process or strategic considerations. Despite this, the majority of preceding research focuses on only one source: they either use historical replay exclusively to directly learn policy or value functions, or engaged in language model training utilizing mere language corpus. In this paper, we argue that a powerful autonomous agent should cover both sources. Thus, we propose ChessGPT, a GPT model bridging policy learning and language modeling by integrating data from these two sources in Chess games. Specifically, we build a large-scale game and language dataset related to chess. Leveraging the dataset, we showcase two model examples ChessCLIP and ChessGPT, integrating policy learning and language modeling. Finally, we propose a full evaluation framework for evaluating language model's chess ability. Experimental results validate our model and dataset's effectiveness. We open source our code, model, and dataset at https://github.com/waterhorse1/ChessGPT.

An intelligent conversational agent (a.k.a., chat-bot) could embrace conversational technologies to obtain user preferences online, to overcome inherent limitations of recommender systems trained over the offline historical user behaviors. In this paper, we propose CORE, a new offline-training and online-checking framework to plug a COnversational agent into REcommender systems. Unlike most prior conversational recommendation approaches that systemically combine conversational and recommender parts through a reinforcement learning framework, CORE bridges the conversational agent and recommender system through a unified uncertainty minimization framework, which can be easily applied to any existing recommendation approach. Concretely, CORE treats a recommender system as an offline estimator to produce an estimated relevance score for each item, while CORE regards a conversational agent as an online checker that checks these estimated scores in each online session. We define uncertainty as the sum of unchecked relevance scores. In this regard, the conversational agent acts to minimize uncertainty via querying either attributes or items. Towards uncertainty minimization, we derive the certainty gain of querying each attribute and item, and develop a novel online decision tree algorithm to decide what to query at each turn. Our theoretical analysis reveals the bound of the expected number of turns of CORE in a cold-start setting. Experimental results demonstrate that CORE can be seamlessly employed on a variety of recommendation approaches, and can consistently bring significant improvements in both hot-start and cold-start settings.

Out-of-distribution (OOD) generalization is indispensable for learning models in the wild, where testing distribution typically unknown and different from the training. Recent methods derived from causality have shown great potential in achieving OOD generalization. However, existing methods mainly focus on the invariance property of causes, while largely overlooking the property of sufficiency and necessity conditions. Namely, a necessary but insufficient cause (feature) is invariant to distribution shift, yet it may not have required accuracy. By contrast, a sufficient yet unnecessary cause (feature) tends to fit specific data well but may have a risk of adapting to a new domain. To capture the information of sufficient and necessary causes, we employ a classical concept, the probability of sufficiency and necessary causes (PNS), which indicates the probability of whether one is the necessary and sufficient cause. To associate PNS with OOD generalization, we propose PNS risk and formulate an algorithm to learn representation with a high PNS value. We theoretically analyze and prove the generalizability of the PNS risk. Experiments on both synthetic and real-world benchmarks demonstrate the effectiveness of the proposed method. The detailed implementation can be found at the GitHub repository: https://github.com/ymy4323460/CaSN.

The issue of fairness in recommendation systems has recently become a matter of growing concern for both the academic and industrial sectors due to the potential for bias in machine learning models. One such bias is that of feedback loops, where the collection of data from an unfair online system hinders the accurate evaluation of the relevance scores between users and items. Given that recommendation systems often recommend popular content and vendors, the underlying relevance scores between users and items may not be accurately represented in the training data. Hence, this creates a feedback loop in which the user is not longer recommended based on their true relevance score but instead based on biased training data. To address this problem of feedback loops, we propose a two-stage representation learning framework, B-FAIR, aimed at rectifying the unfairness caused by biased historical data in recommendation systems. The framework disentangles the context data into sensitive and non-sensitive components using a variational autoencoder and then applies a novel Balanced Fairness Objective (BFO) to remove bias in the observational data when training a recommendation model. The efficacy of B-FAIR is demonstrated through experiments on both synthetic and real-world benchmarks, showing improved performance over state-of-the-art algorithms.

Debiased recommendation has recently attracted increasing attention from both industry and academic communities. Traditional models mostly rely on the inverse propensity score (IPS), which can be hard to estimate and may suffer from the high variance issue. To alleviate these problems, in this article, we propose a novel debiased recommendation framework based on user feature balancing. The general idea is to introduce a projection function to adjust user feature distributions, such that the ideal unbiased learning objective can be upper bounded by a solvable objective purely based on the offline dataset. In the upper bound, the projected user distributions are expected to be equal given different items. From the causal inference perspective, this requirement aims to remove the causal relation from the user to the item, which enables us to achieve unbiased recommendation, bypassing the computation of IPS. To efficiently balance the user distributions upon each item pair, we propose three strategies, including clipping, sampling, and adversarial learning to improve the training process. For more robust optimization, we deploy an explicit model to capture the potential latent confounders in recommendation systems. To the best of our knowledge, this article is the first work on debiased recommendation based on confounder balancing. In the experiments, we compare our framework with many state-of-the-art methods based on synthetic, semi-synthetic, and real-world datasets. Extensive experiments demonstrate that our model is effective in promoting the recommendation performance.

Top-N recommendation, which aims to learn user ranking-based preference, has long been a fundamental problem in a wide range of applications. Traditional models usually motivate themselves by designing complex or tailored architectures based on different assumptions. However, the training data of recommender system can be extremely sparse and imbalanced, which poses great challenges for boosting the recommendation performance. To alleviate this problem, in this paper, we propose to reformulate the recommendation task within the causal inference framework, which enables us to counterfactually simulate user ranking-based preferences to handle the data scarce problem. The core of our model lies in the counterfactual question: "what would be the user's decision if the recommended items had been different?''. To answer this question, we firstly formulate the recommendation process with a series of structural equation models (SEMs), whose parameters are optimized based on the observed data. Then, we actively indicate many recommendation lists (called intervention in the causal inference terminology) which are not recorded in the dataset, and simulate user feedback according to the learned SEMs for generating new training samples. Instead of randomly intervening on the recommendation list, we design a learning-based method to discover more informative training samples. Considering that the learned SEMs can be not perfect, we, at last, theoretically analyze the relation between the number of generated samples and the model prediction error, based on which a heuristic method is designed to control the negative effect brought by the prediction error. Extensive experiments are conducted based on both synthetic and real-world datasets to demonstrate the effectiveness of our framework.

Learning disentanglement aims at finding a low dimensional representation which consists of multiple explanatory and generative factors of the observational data. The framework of variational autoencoder (VAE) is commonly used to disentangle independent factors from observations. However, in real scenarios, factors with semantics are not necessarily independent. Instead, there might be an underlying causal structure which renders these factors dependent. We thus propose a new VAE based framework named CausalVAE, which includes a Causal Layer to transform independent exogenous factors into causal endogenous ones that correspond to causally related concepts in data. We further analyze the model identifiabitily, showing that the proposed model learned from observations recovers the true one up to a certain degree. Experiments are conducted on various datasets, including synthetic and real word benchmark CelebA. Results show that the causal representations learned by CausalVAE are semantically interpretable, and their causal relationship as a Directed Acyclic Graph (DAG) is identified with good accuracy. Furthermore, we demonstrate that the proposed CausalVAE model is able to generate counterfactual data through "do-operation" to the causal factors.

Contextual multi-armed bandit (MAB) achieves cutting-edge performance on a variety of problems. When it comes to real-world scenarios such as recommendation system and online advertising, however, it is essential to consider the resource consumption of exploration. In practice, there is typically non-zero cost associated with executing a recommendation (arm) in the environment, and hence, the policy should be learned with a fixed exploration cost constraint. It is challenging to learn a global optimal policy directly, since it is a NP-hard problem and significantly complicates the exploration and exploitation trade-off of bandit algorithms. Existing approaches focus on solving the problems by adopting the greedy policy which estimates the expected rewards and costs and uses a greedy selection based on each arm’s expected reward/cost ratio using historical observation until the exploration resource is exhausted. However, existing methods are hard to extend to infinite time horizon, since the learning process will be terminated when there is no more resource. In this paper, we propose a hierarchical adaptive contextual bandit method (HATCH) to conduct the policy learning of contextual bandits with a budget constraint. HATCH adopts an adaptive method to allocate the exploration resource based on the remaining resource/time and the estimation of reward distribution among different user contexts. In addition, we utilize full of contextual feature information to find the best personalized recommendation. Finally, in order to prove the theoretical guarantee, we present a regret bound analysis and prove that HATCH achieves a regret bound as low as . The experimental results demonstrate the effectiveness and efficiency of the proposed method on both synthetic data sets and the real-world applications.