Continuous K-Max Bandits

We study the $K$-Max combinatorial multi-armed bandits problem with continuous outcome distributions and weak value-index feedback: each base arm has an unknown continuous outcome distribution, and in each round the learning agent selects $K$ arms, obtains the maximum value sampled from these $K$ arms as reward and observes this reward together with the corresponding arm index as feedback. This setting captures critical applications in recommendation systems, distributed computing, server scheduling, etc. The continuous $K$-Max bandits introduce unique challenges, including discretization error from continuous-to-discrete conversion, non-deterministic tie-breaking under limited feedback, and biased estimation due to partial observability. Our key contribution is the computationally efficient algorithm DCK-UCB, which combines adaptive discretization with bias-corrected confidence bounds to tackle these challenges. For general continuous distributions, we prove that DCK-UCB achieves a $\widetilde{\mathcal{O}}(T^{3/4})$ regret upper bound, establishing the first sublinear regret guarantee for this setting. Furthermore, we identify an important special case with exponential distributions under full-bandit feedback. In this case, our proposed algorithm MLE-Exp enables $\widetilde{\mathcal{O}}(\sqrt{T})$ regret upper bound through maximal log-likelihood estimation, achieving near-minimax optimality.

Offline Learning for Combinatorial Multi-armed Bandits

The combinatorial multi-armed bandit (CMAB) is a fundamental sequential decision-making framework, extensively studied over the past decade. However, existing work primarily focuses on the online setting, overlooking the substantial costs of online interactions and the readily available offline datasets. To overcome these limitations, we introduce Off-CMAB, the first offline learning framework for CMAB. Central to our framework is the combinatorial lower confidence bound (CLCB) algorithm, which combines pessimistic reward estimations with combinatorial solvers. To characterize the quality of offline datasets, we propose two novel data coverage conditions and prove that, under these conditions, CLCB achieves a near-optimal suboptimality gap, matching the theoretical lower bound up to a logarithmic factor. We validate Off-CMAB through practical applications, including learning to rank, large language model (LLM) caching, and social influence maximization, showing its ability to handle nonlinear reward functions, general feedback models, and out-of-distribution action samples that excludes optimal or even feasible actions. Extensive experiments on synthetic and real-world datasets further highlight the superior performance of CLCB.

"Stones from Other Hills can Polish Jade": Zero-shot Anomaly Image Synthesis via Cross-domain Anomaly Injection

Industrial image anomaly detection (IAD) is a pivotal topic with huge value. Due to anomaly's nature, real anomalies in a specific modern industrial domain (i.e. domain-specific anomalies) are usually too rare to collect, which severely hinders IAD. Thus, zero-shot anomaly synthesis (ZSAS), which synthesizes pseudo anomaly images without any domain-specific anomaly, emerges as a vital technique for IAD. However, existing solutions are either unable to synthesize authentic pseudo anomalies, or require cumbersome training. Thus, we focus on ZSAS and propose a brand-new paradigm that can realize both authentic and training-free ZSAS. It is based on a chronically-ignored fact: Although domain-specific anomalies are rare, real anomalies from other domains (i.e. cross-domain anomalies) are actually abundant and directly applicable to ZSAS. Specifically, our new ZSAS paradigm makes three-fold contributions: First, we propose a novel method named Cross-domain Anomaly Injection (CAI), which directly exploits cross-domain anomalies to enable highly authentic ZSAS in a training-free manner. Second, to supply CAI with sufficient cross-domain anomalies, we build the first domain-agnostic anomaly dataset within our best knowledge, which provides ZSAS with abundant real anomaly patterns. Third, we propose a CAI-guided Diffusion Mechanism, which further breaks the quantity limit of real anomalies and enable unlimited anomaly synthesis. Our head-to-head comparison with existing ZSAS solutions justifies our paradigm's superior performance for IAD and demonstrates it as an effective and pragmatic ZSAS solution.

Combinatorial Rising Bandit

Combinatorial online learning is a fundamental task to decide the optimal combination of base arms in sequential interactions with systems providing uncertain rewards, which is applicable to diverse domains such as robotics, social advertising, network routing and recommendation systems. In real-world scenarios, we often observe rising rewards, where the selection of a base arm not only provides an instantaneous reward but also contributes to the enhancement of future rewards, {\it e.g.}, robots enhancing proficiency through practice and social influence strengthening in the history of successful recommendations. To address this, we introduce the problem of combinatorial rising bandit to minimize policy regret and propose a provably efficient algorithm, called Combinatorial Rising Upper Confidence Bound (CRUCB), of which regret upper bound is close to a regret lower bound. To the best of our knowledge, previous studies do not provide a sub-linear regret lower bound, making it impossible to assess the efficiency of their algorithms. However, we provide the sub-linear regret lower bound for combinatorial rising bandit and show that CRUCB is provably efficient by showing that the regret upper bound is close to the regret lower bound. In addition, we empirically demonstrate the effectiveness and superiority of CRUCB not only in synthetic environments but also in realistic applications of deep reinforcement learning.

Combinatorial Multivariant Multi-Armed Bandits with Applications to Episodic Reinforcement Learning and Beyond

We introduce a novel framework of combinatorial multi-armed bandits (CMAB) with multivariant and probabilistically triggering arms (CMAB-MT), where the outcome of each arm is a $d$-dimensional multivariant random variable and the feedback follows a general arm triggering process. Compared with existing CMAB works, CMAB-MT not only enhances the modeling power but also allows improved results by leveraging distinct statistical properties for multivariant random variables. For CMAB-MT, we propose a general 1-norm multivariant and triggering probability-modulated smoothness condition, and an optimistic CUCB-MT algorithm built upon this condition. Our framework can include many important problems as applications, such as episodic reinforcement learning (RL) and probabilistic maximum coverage for goods distribution, all of which meet the above smoothness condition and achieve matching or improved regret bounds compared to existing works. Through our new framework, we build the first connection between the episodic RL and CMAB literature, by offering a new angle to solve the episodic RL through the lens of CMAB, which may encourage more interactions between these two important directions.

Can Graph Learning Improve Task Planning?

Task planning is emerging as an important research topic alongside the development of large language models (LLMs). It aims to break down complex user requests into solvable sub-tasks, thereby fulfilling the original requests. In this context, the sub-tasks can be naturally viewed as a graph, where the nodes represent the sub-tasks, and the edges denote the dependencies among them. Consequently, task planning is a decision-making problem that involves selecting a connected path or subgraph within the corresponding graph and invoking it. In this paper, we explore graph learning-based methods for task planning, a direction that is orthogonal to the prevalent focus on prompt design. Our interest in graph learning stems from a theoretical discovery: the biases of attention and auto-regressive loss impede LLMs' ability to effectively navigate decision-making on graphs, which is adeptly addressed by graph neural networks (GNNs). This theoretical insight led us to integrate GNNs with LLMs to enhance overall performance. Extensive experiments demonstrate that GNN-based methods surpass existing solutions even without training, and minimal training can further enhance their performance. Additionally, our approach complements prompt engineering and fine-tuning techniques, with performance further enhanced by improved prompts or a fine-tuned model.

ALPINE: Unveiling the Planning Capability of Autoregressive Learning in Language Models

In this paper, we present the findings of our Project ALPINE which stands for ``Autoregressive Learning for Planning In NEtworks." Project ALPINE initiates a theoretical investigation into the development of planning capabilities in Transformer-based language models through their autoregressive learning mechanisms, aiming to identify any potential limitations in their planning abilities. We abstract planning as a network path-finding task where the objective is to generate a valid path from a specified source node to a designated target node. In terms of expressiveness, we show that the Transformer is capable of executing path-finding by embedding the adjacency and reachability matrices within its weights. Our theoretical analysis of the gradient-based learning dynamic of the Transformer reveals that the Transformer is capable of learning both the adjacency matrix and a limited form of the reachability matrix. These theoretical insights are then validated through experiments, which demonstrate that the Transformer indeed learns the adjacency matrix and an incomplete reachability matrix, which aligns with the predictions made in our theoretical analysis. Additionally, when applying our methodology to a real-world planning benchmark, called Blocksworld, our observations remain consistent. Our theoretical and empirical analyses further unveil a potential limitation of Transformer in path-finding: it cannot identify reachability relationships through transitivity, and thus would fail when path concatenation is needed to generate a path. In summary, our findings shed new light on how the internal mechanisms of autoregressive learning enable planning in networks. This study may contribute to our understanding of the general planning capabilities in other related domains.

Test-Time Training on Graphs with Large Language Models

Graph Neural Networks have demonstrated great success in various fields of multimedia. However, the distribution shift between the training and test data challenges the effectiveness of GNNs. To mitigate this challenge, Test-Time Training (TTT) has been proposed as a promising approach. Traditional TTT methods require a demanding unsupervised training strategy to capture the information from test to benefit the main task. Inspired by the great annotation ability of Large Language Models (LLMs) on Text-Attributed Graphs (TAGs), we propose to enhance the test-time training on graphs with LLMs as annotators. In this paper, we design a novel Test-Time Training pipeline, LLMTTT, which conducts the test-time adaptation under the annotations by LLMs on a carefully-selected node set. Specifically, LLMTTT introduces a hybrid active node selection strategy that considers not only node diversity and representativeness, but also prediction signals from the pre-trained model. Given annotations from LLMs, a two-stage training strategy is designed to tailor the test-time model with the limited and noisy labels. A theoretical analysis ensures the validity of our method and extensive experiments demonstrate that the proposed LLMTTT can achieve a significant performance improvement compared to existing Out-of-Distribution (OOD) generalization methods.

Provable Risk-Sensitive Distributional Reinforcement Learning with General Function Approximation

In the realm of reinforcement learning (RL), accounting for risk is crucial for making decisions under uncertainty, particularly in applications where safety and reliability are paramount. In this paper, we introduce a general framework on Risk-Sensitive Distributional Reinforcement Learning (RS-DisRL), with static Lipschitz Risk Measures (LRM) and general function approximation. Our framework covers a broad class of risk-sensitive RL, and facilitates analysis of the impact of estimation functions on the effectiveness of RSRL strategies and evaluation of their sample complexity. We design two innovative meta-algorithms: \texttt{RS-DisRL-M}, a model-based strategy for model-based function approximation, and \texttt{RS-DisRL-V}, a model-free approach for general value function approximation. With our novel estimation techniques via Least Squares Regression (LSR) and Maximum Likelihood Estimation (MLE) in distributional RL with augmented Markov Decision Process (MDP), we derive the first $\widetilde{\mathcal{O}}(\sqrt{K})$ dependency of the regret upper bound for RSRL with static LRM, marking a pioneering contribution towards statistically efficient algorithms in this domain.

Single-cell Multi-view Clustering via Community Detection with Unknown Number of Clusters

Single-cell multi-view clustering enables the exploration of cellular heterogeneity within the same cell from different views. Despite the development of several multi-view clustering methods, two primary challenges persist. Firstly, most existing methods treat the information from both single-cell RNA (scRNA) and single-cell Assay of Transposase Accessible Chromatin (scATAC) views as equally significant, overlooking the substantial disparity in data richness between the two views. This oversight frequently leads to a degradation in overall performance. Additionally, the majority of clustering methods necessitate manual specification of the number of clusters by users. However, for biologists dealing with cell data, precisely determining the number of distinct cell types poses a formidable challenge. To this end, we introduce scUNC, an innovative multi-view clustering approach tailored for single-cell data, which seamlessly integrates information from different views without the need for a predefined number of clusters. The scUNC method comprises several steps: initially, it employs a cross-view fusion network to create an effective embedding, which is then utilized to generate initial clusters via community detection. Subsequently, the clusters are automatically merged and optimized until no further clusters can be merged. We conducted a comprehensive evaluation of scUNC using three distinct single-cell datasets. The results underscored that scUNC outperforms the other baseline methods.