Nearly Tight Bounds for Cross-Learning Contextual Bandits with Graphical Feedback

The cross-learning contextual bandit problem with graphical feedback has recently attracted significant attention. In this setting, there is a contextual bandit with a feedback graph over the arms, and pulling an arm reveals the loss for all neighboring arms in the feedback graph across all contexts. Initially proposed by Han et al. (2024), this problem has broad applications in areas such as bidding in first price auctions, and explores a novel frontier in the feedback structure of bandit problems. A key theoretical question is whether an algorithm with $\widetilde{O}(\sqrt{\alpha T})$ regret exists, where $\alpha$ represents the independence number of the feedback graph. This question is particularly interesting because it concerns whether an algorithm can achieve a regret bound entirely independent of the number of contexts and matching the minimax regret of vanilla graphical bandits. Previous work has demonstrated that such an algorithm is impossible for adversarial contexts, but the question remains open for stochastic contexts. In this work, we affirmatively answer this open question by presenting an algorithm that achieves the minimax $\widetilde{O}(\sqrt{\alpha T})$ regret for cross-learning contextual bandits with graphical feedback and stochastic contexts. Notably, although that question is open even for stochastic bandits, we directly solve the strictly stronger adversarial bandit version of the problem.

TGB-Seq Benchmark: Challenging Temporal GNNs with Complex Sequential Dynamics

Future link prediction is a fundamental challenge in various real-world dynamic systems. To address this, numerous temporal graph neural networks (temporal GNNs) and benchmark datasets have been developed. However, these datasets often feature excessive repeated edges and lack complex sequential dynamics, a key characteristic inherent in many real-world applications such as recommender systems and ``Who-To-Follow'' on social networks. This oversight has led existing methods to inadvertently downplay the importance of learning sequential dynamics, focusing primarily on predicting repeated edges. In this study, we demonstrate that existing methods, such as GraphMixer and DyGFormer, are inherently incapable of learning simple sequential dynamics, such as ``a user who has followed OpenAI and Anthropic is more likely to follow AI at Meta next.'' Motivated by this issue, we introduce the Temporal Graph Benchmark with Sequential Dynamics (TGB-Seq), a new benchmark carefully curated to minimize repeated edges, challenging models to learn sequential dynamics and generalize to unseen edges. TGB-Seq comprises large real-world datasets spanning diverse domains, including e-commerce interactions, movie ratings, business reviews, social networks, citation networks and web link networks. Benchmarking experiments reveal that current methods usually suffer significant performance degradation and incur substantial training costs on TGB-Seq, posing new challenges and opportunities for future research. TGB-Seq datasets, leaderboards, and example codes are available at https://tgb-seq.github.io/.

High Probability Bound for Cross-Learning Contextual Bandits with Unknown Context Distributions

Motivated by applications in online bidding and sleeping bandits, we examine the problem of contextual bandits with cross learning, where the learner observes the loss associated with the action across all possible contexts, not just the current round's context. Our focus is on a setting where losses are chosen adversarially, and contexts are sampled i.i.d. from a specific distribution. This problem was first studied by Balseiro et al. (2019), who proposed an algorithm that achieves near-optimal regret under the assumption that the context distribution is known in advance. However, this assumption is often unrealistic. To address this issue, Schneider and Zimmert (2023) recently proposed a new algorithm that achieves nearly optimal expected regret. It is well-known that expected regret can be significantly weaker than high-probability bounds. In this paper, we present a novel, in-depth analysis of their algorithm and demonstrate that it actually achieves near-optimal regret with high probability. There are steps in the original analysis by Schneider and Zimmert (2023) that lead only to an expected bound by nature. In our analysis, we introduce several new insights. Specifically, we make extensive use of the weak dependency structure between different epochs, which was overlooked in previous analyses. Additionally, standard martingale inequalities are not directly applicable, so we refine martingale inequalities to complete our analysis.

Your Graph Recommender is Provably a Single-view Graph Contrastive Learning

Graph recommender (GR) is a type of graph neural network (GNNs) encoder that is customized for extracting information from the user-item interaction graph. Due to its strong performance on the recommendation task, GR has gained significant attention recently. Graph contrastive learning (GCL) is also a popular research direction that aims to learn, often unsupervised, GNNs with certain contrastive objectives. As a general graph representation learning method, GCLs have been widely adopted with the supervised recommendation loss for joint training of GRs. Despite the intersection of GR and GCL research, theoretical understanding of the relationship between the two fields is surprisingly sparse. This vacancy inevitably leads to inefficient scientific research. In this paper, we aim to bridge the gap between the field of GR and GCL from the perspective of encoders and loss functions. With mild assumptions, we theoretically show an astonishing fact that graph recommender is equivalent to a commonly-used single-view graph contrastive model. Specifically, we find that (1) the classic encoder in GR is essentially a linear graph convolutional network with one-hot inputs, and (2) the loss function in GR is well bounded by a single-view GCL loss with certain hyperparameters. The first observation enables us to explain crucial designs of GR models, e.g., the removal of self-loop and nonlinearity. And the second finding can easily prompt many cross-field research directions. We empirically show a remarkable result that the recommendation loss and the GCL loss can be used interchangeably. The fact that we can train GR models solely with the GCL loss is particularly insightful, since before this work, GCLs were typically viewed as unsupervised methods that need fine-tuning. We also discuss some potential future works inspired by our theory.

HAF-RM: A Hybrid Alignment Framework for Reward Model Training

The reward model has become increasingly important in alignment, assessment, and data construction for large language models (LLMs). Most existing researchers focus on enhancing reward models through data improvements, following the conventional training framework for reward models that directly optimizes the predicted rewards. In this paper, we propose a hybrid alignment framework HaF-RM for reward model training by introducing an additional constraint on token-level policy probabilities in addition to the reward score. It can simultaneously supervise the internal preference model at the token level and optimize the mapping layer of the reward model at the sequence level. Theoretical justifications and experiment results on five datasets show the validity and effectiveness of our proposed hybrid framework for training a high-quality reward model. By decoupling the reward modeling procedure and incorporating hybrid supervision, our HaF-RM framework offers a principled and effective approach to enhancing the performance and alignment of reward models, a critical component in the responsible development of powerful language models. We release our code at https://haf-rm.github.io.

Optimal Matrix Sketching over Sliding Windows

Matrix sketching, aimed at approximating a matrix $\boldsymbol{A} \in \mathbb{R}^{N\times d}$ consisting of vector streams of length $N$ with a smaller sketching matrix $\boldsymbol{B} \in \mathbb{R}^{\ell\times d}, \ell \ll N$, has garnered increasing attention in fields such as large-scale data analytics and machine learning. A well-known deterministic matrix sketching method is the Frequent Directions algorithm, which achieves the optimal $O\left(\frac{d}{\varepsilon}\right)$ space bound and provides a covariance error guarantee of $\varepsilon = \lVert \boldsymbol{A}^\top \boldsymbol{A} - \boldsymbol{B}^\top \boldsymbol{B} \rVert_2/\lVert \boldsymbol{A} \rVert_F^2$. The matrix sketching problem becomes particularly interesting in the context of sliding windows, where the goal is to approximate the matrix $\boldsymbol{A}_W$, formed by input vectors over the most recent $N$ time units. However, despite recent efforts, whether achieving the optimal $O\left(\frac{d}{\varepsilon}\right)$ space bound on sliding windows is possible has remained an open question. In this paper, we introduce the DS-FD algorithm, which achieves the optimal $O\left(\frac{d}{\varepsilon}\right)$ space bound for matrix sketching over row-normalized, sequence-based sliding windows. We also present matching upper and lower space bounds for time-based and unnormalized sliding windows, demonstrating the generality and optimality of \dsfd across various sliding window models. This conclusively answers the open question regarding the optimal space bound for matrix sketching over sliding windows. Furthermore, we conduct extensive experiments with both synthetic and real-world datasets, validating our theoretical claims and thus confirming the correctness and effectiveness of our algorithm, both theoretically and empirically.

StructComp: Substituting propagation with Structural Compression in Training Graph Contrastive Learning

Graph contrastive learning (GCL) has become a powerful tool for learning graph data, but its scalability remains a significant challenge. In this work, we propose a simple yet effective training framework called Structural Compression (StructComp) to address this issue. Inspired by a sparse low-rank approximation on the diffusion matrix, StructComp trains the encoder with the compressed nodes. This allows the encoder not to perform any message passing during the training stage, and significantly reduces the number of sample pairs in the contrastive loss. We theoretically prove that the original GCL loss can be approximated with the contrastive loss computed by StructComp. Moreover, StructComp can be regarded as an additional regularization term for GCL models, resulting in a more robust encoder. Empirical studies on seven benchmark datasets show that StructComp greatly reduces the time and memory consumption while improving model performance compared to the vanilla GCL models and scalable training methods.

Understanding Community Bias Amplification in Graph Representation Learning

In this work, we discover a phenomenon of community bias amplification in graph representation learning, which refers to the exacerbation of performance bias between different classes by graph representation learning. We conduct an in-depth theoretical study of this phenomenon from a novel spectral perspective. Our analysis suggests that structural bias between communities results in varying local convergence speeds for node embeddings. This phenomenon leads to bias amplification in the classification results of downstream tasks. Based on the theoretical insights, we propose random graph coarsening, which is proved to be effective in dealing with the above issue. Finally, we propose a novel graph contrastive learning model called Random Graph Coarsening Contrastive Learning (RGCCL), which utilizes random coarsening as data augmentation and mitigates community bias by contrasting the coarsened graph with the original graph. Extensive experiments on various datasets demonstrate the advantage of our method when dealing with community bias amplification.

Adversarially Robust Distributed Count Tracking via Partial Differential Privacy

We study the distributed tracking model, also known as distributed functional monitoring. This model involves $k$ sites each receiving a stream of items and communicating with the central server. The server's task is to track a function of all items received thus far continuously, with minimum communication cost. For count tracking, it is known that there is a $\sqrt{k}$ gap in communication between deterministic and randomized algorithms. However, existing randomized algorithms assume an "oblivious adversary" who constructs the entire input streams before the algorithm starts. Here we consider adaptive adversaries who can choose new items based on previous answers from the algorithm. Deterministic algorithms are trivially robust to adaptive adversaries, while randomized ones may not. Therefore, we investigate whether the $\sqrt{k}$ advantage of randomized algorithms is from randomness itself or the oblivious adversary assumption. We provide an affirmative answer to this question by giving a robust algorithm with optimal communication. Existing robustification techniques do not yield optimal bounds due to the inherent challenges of the distributed nature of the problem. To address this, we extend the differential privacy framework by introducing "partial differential privacy" and proving a new generalization theorem. This theorem may have broader applications beyond robust count tracking, making it of independent interest.

Rethinking Semi-Supervised Imbalanced Node Classification from Bias-Variance Decomposition

This paper introduces a new approach to address the issue of class imbalance in graph neural networks (GNNs) for learning on graph-structured data. Our approach integrates imbalanced node classification and Bias-Variance Decomposition, establishing a theoretical framework that closely relates data imbalance to model variance. We also leverage graph augmentation technique to estimate the variance, and design a regularization term to alleviate the impact of imbalance. Exhaustive tests are conducted on multiple benchmarks, including naturally imbalanced datasets and public-split class-imbalanced datasets, demonstrating that our approach outperforms state-of-the-art methods in various imbalanced scenarios. This work provides a novel theoretical perspective for addressing the problem of imbalanced node classification in GNNs.