ICLR 2025 论文列表

International Conference on Learning Representations

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3,703篇论文

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  • Spotlight
    38010.3%
  • Poster
    3,11084.0%

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Training One-Dimensional Graph Neural Networks is NP-Hard

Robert Ganian, Mathis Rocton, Simon Wietheger

展开摘要

We initiate the study of the computational complexity of training graph neural networks (GNNs). We consider the classical node classification setting; there, the intractability of training multidimensonal GNNs immediately follows from known lower bounds for training classical neural networks (and holds even for trivial GNNs). However, one-dimensional GNNs form a crucial case of interest: the computational complexity of training such networks depends on both the graphical structure of the network and the properties of the involved activation and aggregation functions. As our main result, we establish the NP-hardness of training ReLU-activated one-dimensional GNNs via a highly non-trivial reduction. We complement this result with algorithmic upper bounds for the training problem in the ReLU-activated and linearly-activated settings.

Poster
Regretful Decisions under Label Noise

Sujay Nagaraj, Yang Liu, Flavio Calmon, Berk Ustun

展开摘要

Machine learning models are routinely used to support decisions that affect individuals -- be it to screen a patient for a serious illness or to gauge their response to treatment. In these tasks, we are limited to learning models from datasets with noisy labels. In this paper, we study the instance-level impact of learning under label noise. We introduce a notion of regret for this regime, which measures the number of unforeseen mistakes due to noisy labels. We show that standard approaches to learning under label noise can return models that perform well at a population-level while subjecting individuals to a lottery of mistakes. We present a versatile approach to estimate the likelihood of mistakes at the individual-level from a noisy dataset by training models over plausible realizations of datasets without label noise. This is supported by a comprehensive empirical study of label noise in clinical prediction tasks. Our results reveal how failure to anticipate mistakes can compromise model reliability and adoption -- we demonstrate how we can address these challenges by anticipating and avoiding regretful decisions.

Poster
Graph Sparsification via Mixture of Graphs

Guibin Zhang, Xiangguo Sun, Yanwei Yue, Chonghe Jiang, Kun Wang, Tianlong Chen, Shirui Pan

展开摘要

Graph Neural Networks (GNNs) have demonstrated superior performance across various graph learning tasks but face significant computational challenges when applied to large-scale graphs. One effective approach to mitigate these challenges is graph sparsification, which involves removing non-essential edges to reduce computational overhead. However, previous graph sparsification methods often rely on a single global sparsity setting and uniform pruning criteria, failing to provide customized sparsification schemes for each node's complex local context. In this paper, we introduce Mixture-of-Graphs (MoG), leveraging the concept of Mixture-of-Experts (MoE), to dynamically select tailored pruning solutions for each node. Specifically, MoG incorporates multiple sparsifier experts, each characterized by unique sparsity levels and pruning criteria, and selects the appropriate experts for each node. Subsequently, MoG performs a mixture of the sparse graphs produced by different experts on the Grassmann manifold to derive an optimal sparse graph. One notable property of MoG is its entirely local nature, as it depends on the specific circumstances of each individual node. Extensive experiments on four large-scale OGB datasets and two superpixel datasets, equipped with five GNN backbones, demonstrate that MoG (I) identifies subgraphs at higher sparsity levels ($8.67\\%\sim 50.85\\%$), with performance equal to or better than the dense graph, (II) achieves $1.47-2.62\times$ speedup in GNN inference with negligible performance drop, and (III) boosts ``top-student'' GNN performance ($1.02\\%\uparrow$ on RevGNN+\textsc{ogbn-proteins} and $1.74\\%\\uparrow$ on DeeperGCN+\textsc{ogbg-ppa}). The source code is available at \url{https://github.com/yanweiyue/MoG}.

Spotlight
Bad-PFL: Exploiting Backdoor Attacks against Personalized Federated Learning

Mingyuan Fan, Zhanyi Hu, Fuyi Wang, Cen Chen

展开摘要

Data heterogeneity and backdoor attacks rank among the most significant challenges facing federated learning (FL). For data heterogeneity, personalized federated learning (PFL) enables each client to maintain a private personalized model to cater to client-specific knowledge. Meanwhile, vanilla FL has proven vulnerable to backdoor attacks. However, recent advancements in PFL community have demonstrated a potential immunity against such attacks. This paper explores this intersection further, revealing that existing federated backdoor attacks fail in PFL because backdoors about manually designed triggers struggle to survive in personalized models. To tackle this, we degisn Bad-PFL, which employs features from natural data as our trigger. As long as the model is trained on natural data, it inevitably embeds the backdoor associated with our trigger, ensuring its longevity in personalized models. Moreover, our trigger undergoes mutual reinforcement training with the model, further solidifying the backdoor's durability and enhancing attack effectiveness. The large-scale experiments across three benchmark datasets demonstrate the superior performance of Bad-PFL against various PFL methods, even when equipped with state-of-the-art defense mechanisms.

Poster
Small-to-Large Generalization: Training Data Influences Models Consistently Across Scale

Alaa Khaddaj, Logan Engstrom, Aleksander Madry

展开摘要

Choice of training data distribution greatly influences model behavior. Yet, in large-scale settings, precisely characterizing *how* changes in training data affects predictions is often difficult due to model training costs. Current practice is to instead extrapolate from scaled down, inexpensive-to-train proxy models. However, changes in data do not influence smaller and larger models identically. Therefore, understanding how choice of data affects large-scale models raises the question: how does training data distribution influence model behavior across compute scale? We find that small- and large-scale language model predictions (generally) *do* highly correlate across choice of training data. Equipped with these findings, we characterize how proxy scale affects effectiveness in two downstream proxy model applications: data attribution and dataset selection.

Poster
MADGEN: Mass-Spec attends to De Novo Molecular generation

Yinkai Wang, Xiaohui Chen, Liping Liu, Soha Hassoun

展开摘要

The annotation (assigning structural chemical identities) of MS/MS spectra remains a significant challenge due to the enormous molecular diversity in biological samples and the limited scope of reference databases. Currently, the vast majority of spectral measurements remain in the "dark chemical space" without structural annotations. To improve annotation, we propose MADGEN (Mass-spec Attends to De Novo Molecular GENeration), a scaffold-based method for de novo molecular structure generation guided by mass spectrometry data. MADGEN operates in two stages: scaffold retrieval and spectra-conditioned molecular generation starting with the scaffold. In the first stage, given an MS/MS spectrum, we formulate scaffold retrieval as a ranking problem and employ contrastive learning to align mass spectra with candidate molecular scaffolds. In the second stage, starting from the retrieved scaffold, we employ the MS/MS spectrum to guide an attention-based generative model to generate the final molecule. Our approach constrains the molecular generation search space, reducing its complexity and improving generation accuracy. We evaluate MADGEN on three datasets (NIST23, CANOPUS, and MassSpecGym) and evaluate MADGEN's performance with a predictive scaffold retriever and with an oracle retriever. We demonstrate the effectiveness of using attention to integrate spectral information throughout the generation process to achieve strong results with the oracle retriever.

Poster
When Attention Sink Emerges in Language Models: An Empirical View

Xiangming Gu, Tianyu Pang, Chao Du, Qian Liu, Fengzhuo Zhang, Cunxiao Du, Ye Wang, Min Lin

展开摘要

Auto-regressive language Models (LMs) assign significant attention to the first token, even if it is not semantically important, which is known as **attention sink**. This phenomenon has been widely adopted in applications such as streaming/long context generation, KV cache optimization, inference acceleration, model quantization, and others. Despite its widespread use, a deep understanding of attention sink in LMs is still lacking. In this work, we first demonstrate that attention sinks exist universally in auto-regressive LMs with various inputs, even in small models. Furthermore, attention sink is observed to emerge during the LM pre-training, motivating us to investigate how *optimization*, *data distribution*, *loss function*, and *model architecture* in LM pre-training influence its emergence. We highlight that attention sink emerges after effective optimization on sufficient training data. The sink position is highly correlated with the loss function and data distribution. Most importantly, we find that attention sink acts more like key biases, *storing extra attention scores*, which could be non-informative and not contribute to the value computation. We also observe that this phenomenon (at least partially) stems from tokens' inner dependence on attention scores as a result of softmax normalization. After relaxing such dependence by replacing softmax attention with other attention operations, such as sigmoid attention without normalization, attention sinks do not emerge in LMs up to 1B parameters. The code is available at https://github.com/sail-sg/Attention-Sink.

Spotlight
On the Adversarial Risk of Test Time Adaptation: An Investigation into Realistic Test-Time Data Poisoning

Yongyi Su, Yushu Li, Nanqing Liu, Kui Jia, Xulei Yang, Chuan-Sheng Foo, Xun Xu

展开摘要

Test-time adaptation (TTA) updates the model weights during the inference stage using testing data to enhance generalization. However, this practice exposes TTA to adversarial risks. Existing studies have shown that when TTA is updated with crafted adversarial test samples, also known as test-time poisoned data, the performance on benign samples can deteriorate. Nonetheless, the perceived adversarial risk may be overstated if the poisoned data is generated under overly strong assumptions. In this work, we first review realistic assumptions for test-time data poisoning, including white-box versus grey-box attacks, access to benign data, attack order, and more. We then propose an effective and realistic attack method that better produces poisoned samples without access to benign samples, and derive an effective in-distribution attack objective. We also design two TTA-aware attack objectives. Our benchmarks of existing attack methods reveal that the TTA methods are more robust than previously believed. In addition, we analyze effective defense strategies to help develop adversarially robust TTA methods. The source code is available at https://github.com/Gorilla-Lab-SCUT/RTTDP.

Poster
Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models

Yinlam Chow, Guy Tennenholtz, Izzeddin Gur, Vincent Zhuang, Bo Dai, Aviral Kumar, Rishabh Agarwal, Sridhar Thiagarajan, Craig Boutilier, Aleksandra Faust

展开摘要

Recent studies indicate that effectively utilizing inference-time compute is crucial for attaining good performance from large language models (LLMs). Specifically, the Best-of-N (BoN) inference strategy, where an LLM generates multiple responses and a verifier selects the best, has shown strong empirical performance. Motivated by this, we develop a novel inference-aware fine-tuning paradigm, which encompasses the BoN-aware inference framework as a special case. We devise the first imitation learning and reinforcement learning (RL) methods for fine-tuning LLMs using BoN, overcoming the challenging, non-differentiable argmax operator in BoN. We empirically demonstrate that our BoN-aware models implicitly learn a per-example "meta-strategy", which interleaves best responses with more diverse responses that might be better suited to a test-time input—a process reminiscent of the exploration-exploitation trade-off in RL. Our experiments demonstrate the effectiveness of BoN-aware fine-tuning in terms of improved performance and inference-time compute. In particular, we show that our methods improve the BoN performance of Gemma 2B on Hendrycks MATH from 26.8% to 30.8%, and Pass@K from 60% to 67%.

Poster
Multi-Label Test-Time Adaptation with Bound Entropy Minimization

Xiangyu Wu, Feng Yu, Yang Yang, Qing-Guo Chen, Jianfeng Lu

展开摘要

Mainstream test-time adaptation (TTA) techniques endeavor to mitigate distribution shifts via entropy minimization for multi-class classification, inherently increasing the probability of the most confident class. However, when encountering multi-label instances, the primary challenge stems from the varying number of labels per image, and prioritizing only the highest probability class inevitably undermines the adaptation of other positive labels. To address this issue, we investigate TTA within multi-label scenario (ML--TTA), developing Bound Entropy Minimization (BEM) objective to simultaneously increase the confidence of multiple top predicted labels. Specifically, to determine the number of labels for each augmented view, we retrieve a paired caption with yielded textual labels for that view. These labels are allocated to both the view and caption, called weak label set and strong label set with the same size k. Following this, the proposed BEM considers the highest top-k predicted labels from view and caption as a single entity, respectively, learning both view and caption prompts concurrently. By binding top-k predicted labels, BEM overcomes the limitation of vanilla entropy minimization, which exclusively optimizes the most confident class. Across the MSCOCO, VOC, and NUSWIDE multi-label datasets, our ML--TTA framework equipped with BEM exhibits superior performance compared to the latest SOTA methods, across various model architectures, prompt initialization, and varying label scenarios. The code is available at https://github.com/Jinx630/ML-TTA.

Poster
Wayward Concepts In Multimodal Models

Brandon Trabucco, Max A Gurinas, Kyle Doherty, Russ Salakhutdinov

展开摘要

Large multimodal models such as Stable Diffusion can generate, detect, and classify new visual concepts after optimizing just the prompt. How are prompt embeddings for visual concepts found by prompt tuning methods different from typical discrete prompts? We conduct a large-scale analysis on three state-of-the-art models in text-to-image generation, open-set object detection, and zero-shot classification, and find that prompts optimized to represent new visual concepts are akin to an adversarial attack on the text encoder. Across 4,800 new embeddings trained for 40 diverse visual concepts on four standard datasets, we find perturbations within an $\epsilon$-ball to any prompt that reprogram models to generate, detect, and classify arbitrary subjects. These perturbations target the final-layers in text encoders, and steer pooling tokens towards the subject. We explore the transferability of these prompts, and find that perturbations reprogramming multimodal models are initialization-specific, and model-specific. Code for reproducing our work is available at the following site: https://wayward-concepts.github.io.

Poster
LaGeM: A Large Geometry Model for 3D Representation Learning and Diffusion

Biao Zhang, Peter Wonka

展开摘要

This paper introduces a novel hierarchical autoencoder that maps 3D models into a highly compressed latent space. The hierarchical autoencoder is specifically designed to tackle the challenges arising from large-scale datasets and generative modeling using diffusion. Different from previous approaches that only work on a regular image or volume grid, our hierarchical autoencoder operates on unordered sets of vectors. Each level of the autoencoder controls different geometric levels of detail. We show that the model can be used to represent a wide range of 3D models while faithfully representing high-resolution geometry details. The training of the new architecture takes 0.70x time and 0.58x memory compared to the baseline. We also explore how the new representation can be used for generative modeling. Specifically, we propose a cascaded diffusion framework where each stage is conditioned on the previous stage. Our design extends existing cascaded designs for image and volume grids to vector sets.

Poster
TabWak: A Watermark for Tabular Diffusion Models

Chaoyi Zhu, Jiayi Tang, Jeroen M. Galjaard, Pin-Yu Chen, Robert Birke, Cornelis Bos, Lydia Y. Chen

展开摘要

Synthetic data offers alternatives for data augmentation and sharing. Till date, it remains unknown how to use watermarking techniques to trace and audit synthetic tables generated by tabular diffusion models to mitigate potential misuses. In this paper, we design TabWak, the first watermarking method to embed invisible signatures that control the sampling of Gaussian latent codes used to synthesize table rows via the diffusion backbone. TabWak has two key features. Different from existing image watermarking techniques, TabWak uses self-cloning and shuffling to embed the secret key in positional information of random seeds that control the Gaussian latents, allowing to use different seeds at each row for high inter-row diversity and enabling row-wise detectability. To further boost the robustness of watermark detection against post-editing attacks, TabWak uses a valid-bit mechanism that focuses on the tail of the latent code distribution for superior noise resilience. We provide theoretical guarantees on the row diversity and effectiveness of detectability. We evaluate TabWak on five datasets against baselines to show that the quality of watermarked tables remains nearly indistinguishable from non-watermarked tables while achieving high detectability in the presence of strong post-editing attacks, with a 100% true positive rate at a 0.1% false positive rate on synthetic tables with fewer than 300 rows. Our code is available at the following anonymized repository https://github.com/chaoyitud/TabWak.

Spotlight
Mini-Monkey: Alleviating the Semantic Sawtooth Effect for Lightweight MLLMs via Complementary Image Pyramid

Mingxin Huang, Yuliang Liu, Dingkang Liang, Lianwen Jin, Xiang Bai

展开摘要

Recently, scaling images to high resolution has received much attention in multimodal large language models (MLLMs). Most existing practices adopt a sliding-window-style cropping strategy to adapt to resolution increase. Such a cropping strategy, however, can easily cut off objects and connected regions, which introduces semantic discontinuity and therefore impedes MLLMs from recognizing small or irregularly shaped objects or text, leading to a phenomenon we call the semantic sawtooth effect. This effect is particularly evident in lightweight MLLMs. To address this issue, we introduce a Complementary Image Pyramid (CIP), a simple, effective, and plug-and-play solution designed to mitigate semantic discontinuity during high-resolution image processing. In particular, CIP dynamically constructs an image pyramid to provide complementary semantic information for the cropping-based MLLMs, enabling it rich acquire semantics at all levels. Furthermore, we introduce a Scale Compression Mechanism (SCM) to reduce the additional computational overhead by compressing the redundant visual tokens. Our experiments demonstrate that CIP can consistently enhance the performance across diverse architectures (e.g., MiniCPM-V-2, InternVL2, and LLaVA-OneVision), various model capacity (1B$\rightarrow$8B), and different usage configurations (training-free and fine-tuning). Leveraging the proposed CIP and SCM, we introduce a lightweight MLLM, Mini-Monkey, which achieves remarkable performance in both general multimodal understanding and document understanding. On the OCRBench, the 2B-version Mini-Monkey even surpasses the 8B model InternVL2-8B by 12 score. Additionally, training Mini-Monkey is cheap, requiring only eight RTX 3090 GPUs. Code and models are available at https://github.com/Yuliang-Liu/Monkey.

Poster
ScienceAgentBench: Toward Rigorous Assessment of Language Agents for Data-Driven Scientific Discovery

Ziru Chen, Shijie Chen, Yuting Ning, Qianheng Zhang, Boshi Wang, Botao Yu, Yifei Li, Zeyi Liao, Chen Wei, Zitong Lu, Vishal Dey, Mingyi Xue, Frazier N. Baker, Benjamin Burns, Daniel Adu-Ampratwum, Xuhui Huang, Xia Ning, Song Gao, Yu Su, Huan Sun

展开摘要

The advancements of language language models (LLMs) have piqued growing interest in developing LLM-based language agents to automate scientific discovery end-to-end, which has sparked both excitement and skepticism about the true capabilities of such agents. In this work, we argue that for an agent to fully automate scientific discovery, it must be able to complete all essential tasks in the workflow. Thus, we call for rigorous assessment of agents on individual tasks in a scientific workflow before making bold claims on end-to-end automation. To this end, we present ScienceAgentBench, a new benchmark for evaluating language agents for data-driven scientific discovery. To ensure the scientific authenticity and real-world relevance of our benchmark, we extract 102 tasks from 44 peer-reviewed publications in four disciplines and engage nine subject matter experts to validate them. We unify the target output for every task to a self-contained Python program file and employ an array of evaluation metrics to examine the generated programs, execution results, and costs. Each task goes through multiple rounds of manual validation by annotators and subject matter experts to ensure its annotation quality and scientific plausibility. We also propose two effective strategies to mitigate data contamination concerns. Using our benchmark, we evaluate five open-weight and proprietary LLMs, each with three frameworks: direct prompting, OpenHands, and self-debug. Given three attempts for each task, the best-performing agent can only solve 32.4% of the tasks independently and 34.3% with expert-provided knowledge. These results underscore the limited capacities of current language agents in generating code for data-driven discovery, let alone end-to-end automation for scientific research.

Poster
Episodic Memories Generation and Evaluation Benchmark for Large Language Models

Alexis Huet, Zied Ben Houidi, Dario Rossi

展开摘要

Episodic memory -- the ability to recall specific events grounded in time and space -- is a cornerstone of human cognition, enabling not only coherent storytelling, but also planning and decision-making. Despite their remarkable capabilities, Large Language Models (LLMs) lack a robust mechanism for episodic memory: we argue that integrating episodic memory capabilities into LLM is essential for advancing AI towards human-like cognition, increasing their potential to reason consistently and ground their output in real-world episodic events, hence avoiding confabulations. To address this challenge, we introduce a comprehensive framework to model and evaluate LLM episodic memory capabilities. Drawing inspiration from cognitive science, we develop a structured approach to represent episodic events, encapsulating temporal and spatial contexts, involved entities, and detailed descriptions. We synthesize a unique episodic memory benchmark, free from contamination, and release open source code and datasets to assess LLM performance across various recall and episodic reasoning tasks. Our evaluation of state-of-the-art models, including GPT-4 and Claude variants, Llama 3.1, and o1-mini, reveals that even the most advanced LLMs struggle with episodic memory tasks, particularly when dealing with multiple related events or complex spatio-temporal relationships -- even in contexts as short as 10k-100k tokens.

Poster
Towards Foundation Models for Mixed Integer Linear Programming

Sirui Li, Janardhan Kulkarni, Ishai Menache, Cathy Wu, Beibin Li

展开摘要

Mixed Integer Linear Programming (MILP) is essential for modeling complex decision-making problems but faces challenges in computational tractability and interpretability. Current deep learning approaches for MILP focus on specific problem classes and do not generalize to unseen classes. To address this shortcoming, we take a foundation model training approach, where we train a single deep learning model on a diverse set of MILP problems to generalize across problem classes. As existing datasets for MILP lack diversity and volume, we introduce MILP-Evolve, a novel LLM-based evolutionary framework that is capable of generating a large set of diverse MILP classes with an unlimited amount of instances. We study our methodology on three key learning tasks that capture diverse aspects of MILP: (1) integrality gap prediction, (2) learning to branch, and (3) a new task of aligning MILP instances with natural language descriptions. Our empirical results show that models trained on the data generated by MILP-Evolve achieve significant improvements on unseen problems, including MIPLIB benchmarks. Our work highlights the potential of moving towards a foundation model approach for MILP that can generalize to a broad range of MILP problem classes. Our code and data are publicly available at https://github.com/microsoft/OptiGuide.

Poster
A Multiscale Frequency Domain Causal Framework for Enhanced Pathological Analysis

Xiaoyu Cui, Weixing Chen, Jiandong Su

展开摘要

Multiple Instance Learning (MIL) in digital pathology Whole Slide Image (WSI) analysis has shown significant progress. However, due to data bias and unobservable confounders, this paradigm still faces challenges in terms of performance and interpretability. Existing MIL methods might identify patches that do not have true diagnostic significance, leading to false correlations, and experience difficulties in integrating multi-scale features and handling unobservable confounders. To address these issues, we propose a new Multi-Scale Frequency Domain Causal framework (MFC). This framework employs an adaptive memory module to estimate the overall data distribution through multi-scale frequency-domain information during training and simulates causal interventions based on this distribution to mitigate confounders in pathological diagnosis tasks. The framework integrates the Multi-scale Spatial Representation Module (MSRM), Frequency Domain Structure Representation Module (FSRM), and Causal Memory Intervention Module (CMIM) to enhance the model's performance and interpretability. Furthermore, the plug-and-play nature of this framework allows it to be broadly applied across various models. Experimental results on Camelyon16 and TCGA-NSCLC dataset show that, compared to previous work, our method has significantly improved accuracy and generalization ability, providing a new theoretical perspective for medical image analysis and potentially advancing the field further. The code will be released at https://github.com/WissingChen/MFC-MIL.

Poster
Divergence-enhanced Knowledge-guided Context Optimization for Visual-Language Prompt Tuning

Yilun Li, Miaomiao Cheng, XU HAN, Wei Song

展开摘要

Prompt tuning vision-language models like CLIP has shown great potential in learning transferable representations for various downstream tasks. The main issue is how to mitigate the over-fitting problem on downstream tasks with limited training samples. While knowledge-guided context optimization has been proposed by constructing consistency constraints to handle catastrophic forgetting in the pre-trained backbone, it also introduces a bias toward pre-training. This paper proposes a novel and simple Divergence-enhanced Knowledge-guided Prompt Tuning (DeKg) method to address this issue. The key insight is that the bias toward pre-training can be alleviated by encouraging the independence between the learnable and the crafted prompt. Specifically, DeKg employs the Hilbert-Schmidt Independence Criterion (HSIC) to regularize the learnable prompts, thereby reducing their dependence on prior general knowledge, and enabling divergence induced by target knowledge. Comprehensive evaluations demonstrate that DeKg serves as a plug-and-play module can seamlessly integrate with existing knowledge-guided context optimization methods and achieves superior performance in three challenging benchmarks. We make our code available at https://github.com/cnunlp/DeKg.

Poster
Gap-Dependent Bounds for Q-Learning using Reference-Advantage Decomposition

Zhong Zheng, Haochen Zhang, Lingzhou Xue

展开摘要

We study the gap-dependent bounds of two important algorithms for on-policy $Q$-learning for finite-horizon episodic tabular Markov Decision Processes (MDPs): UCB-Advantage (Zhang et al. 2020) and Q-EarlySettled-Advantage (Li et al. 2021). UCB-Advantage and Q-EarlySettled-Advantage improve upon the results based on Hoeffding-type bonuses and achieve the {almost optimal} $\sqrt{T}$-type regret bound in the worst-case scenario, where $T$ is the total number of steps. However, the benign structures of the MDPs such as a strictly positive suboptimality gap can significantly improve the regret. While gap-dependent regret bounds have been obtained for $Q$-learning with Hoeffding-type bonuses, it remains an open question to establish gap-dependent regret bounds for $Q$-learning using variance estimators in their bonuses and reference-advantage decomposition for variance reduction. We develop a novel error decomposition framework to prove gap-dependent regret bounds of UCB-Advantage and Q-EarlySettled-Advantage that are logarithmic in $T$ and improve upon existing ones for $Q$-learning algorithms. Moreover, we establish the gap-dependent bound for the policy switching cost of UCB-Advantage and improve that under the worst-case MDPs. To our knowledge, this paper presents the first gap-dependent regret analysis for $Q$-learning using variance estimators and reference-advantage decomposition and also provides the first gap-dependent analysis on policy switching cost for $Q$-learning.

Spotlight