NeurIPS 2024 论文列表

Conference on Neural Information Processing Systems

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4,562篇论文

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    4,06489.1%
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Achieving Near-Optimal Convergence for Distributed Minimax Optimization with Adaptive Stepsizes

Yan Huang, Xiang Li, Yipeng Shen, Niao He, Jinming Xu

展开摘要

In this paper, we show that applying adaptive methods directly to distributed minimax problems can result in non-convergence due to inconsistency in locally computed adaptive stepsizes. To address this challenge, we propose D-AdaST, a Distributed Adaptive minimax method with Stepsize Tracking. The key strategy is to employ an adaptive stepsize tracking protocol involving the transmission of two extra (scalar) variables. This protocol ensures the consistency among stepsizes of nodes, eliminating the steady-state error due to the lack of coordination of stepsizes among nodes that commonly exists in vanilla distributed adaptive methods, and thus guarantees exact convergence. For nonconvex-strongly-concave distributed minimax problems, we characterize the specific transient times that ensure time-scale separation of stepsizes and quasi-independence of networks, leading to a near-optimal convergence rate of $\tilde{\mathcal{O}} \left( \epsilon ^{-\left( 4+\delta \right)} \right)$ for any small $\delta > 0$, matching that of the centralized counterpart. To our best knowledge, D-AdaST is the *first* distributed adaptive method achieving near-optimal convergence without knowing any problem-dependent parameters for nonconvex minimax problems. Extensive experiments are conducted to validate our theoretical results.

Poster
Hyper-SD: Trajectory Segmented Consistency Model for Efficient Image Synthesis

Yuxi Ren, Xin Xia, Yanzuo Lu, JiaCheng Zhang, Jie Wu, Pan Xie, Xing Wang, Xuefeng Xiao

展开摘要

Recently, a series of diffusion-aware distillation algorithms have emerged to alleviate the computational overhead associated with the multi-step inference process of Diffusion Models (DMs). Current distillation techniques often dichotomize into two distinct aspects: i) ODE Trajectory Preservation; and ii) ODE Trajectory Reformulation. However, these approaches suffer from severe performance degradation or domain shifts. To address these limitations, we propose Hyper-SD, a novel framework that synergistically amalgamates the advantages of ODE Trajectory Preservation and Reformulation, while maintaining near-lossless performance during step compression. Firstly, we introduce Trajectory Segmented Consistency Distillation to progressively perform consistent distillation within pre-defined time-step segments, which facilitates the preservation of the original ODE trajectory from a higher-order perspective. Secondly, we incorporate human feedback learning to boost the performance of the model in a low-step regime and mitigate the performance loss incurred by the distillation process. Thirdly, we integrate score distillation to further improve the low-step generation capability of the model and offer the first attempt to leverage a unified LoRA to support the inference process at all steps. Extensive experiments and user studies demonstrate that Hyper-SD achieves SOTA performance from 1 to 8 inference steps for both SDXL and SD1.5. For example, Hyper-SDXL surpasses SDXL-Lightning by +0.68 in CLIP Score and +0.51 in Aes Score in the 1-step inference.

Poster
How to Continually Adapt Text-to-Image Diffusion Models for Flexible Customization?

Jiahua Dong, Wenqi Liang, Hongliu Li, Duzhen Zhang, Meng Cao, Henghui Ding, Salman Khan, Fahad Khan

展开摘要

Custom diffusion models (CDMs) have attracted widespread attention due to their astonishing generative ability for personalized concepts. However, most existing CDMs unreasonably assume that personalized concepts are fixed and cannot change over time. Moreover, they heavily suffer from catastrophic forgetting and concept neglect on old personalized concepts when continually learning a series of new concepts. To address these challenges, we propose a novel Concept-Incremental text-to-image Diffusion Model (CIDM), which can resolve catastrophic forgetting and concept neglect to learn new customization tasks in a concept-incremental manner. Specifically, to surmount the catastrophic forgetting of old concepts, we develop a concept consolidation loss and an elastic weight aggregation module. They can explore task-specific and task-shared knowledge during training, and aggregate all low-rank weights of old concepts based on their contributions during inference. Moreover, in order to address concept neglect, we devise a context-controllable synthesis strategy that leverages expressive region features and noise estimation to control the contexts of generated images according to user conditions. Experiments validate that our CIDM surpasses existing custom diffusion models. The source codes are available at https://github.com/JiahuaDong/CIFC.

Poster
Pseudo-Siamese Blind-spot Transformers for Self-Supervised Real-World Denoising

Yuhui Quan, Tianxiang Zheng, Hui Ji

展开摘要

Real-world image denoising remains a challenge task. This paper studies self-supervised image denoising, requiring only noisy images captured in a single shot. We revamping the blind-spot technique by leveraging the transformer’s capability for long-range pixel interactions, which is crucial for effectively removing noise dependence in relating pixel–a requirement for achieving great performance for the blind-spot technique. The proposed method integrates these elements with two key innovations: a directional self-attention (DSA) module using a half-plane grid for self-attention, creating a sophisticated blind-spot structure, and a Siamese architecture with mutual learning to mitigate the performance impacts from the restricted attention grid in DSA. Experiments on benchmark datasets demonstrate that our method outperforms existing self-supervised and clean-image-free methods. This combination of blind-spot and transformer techniques provides a natural synergy for tackling real-world image denoising challenges.

Poster
On the Comparison between Multi-modal and Single-modal Contrastive Learning

Wei Huang, Andi Han, Yongqiang Chen, Yuan Cao, zhiqiang xu, Taiji Suzuki

展开摘要

Multi-modal contrastive learning with language supervision has presented a paradigm shift in modern machine learning. By pre-training on a web-scale dataset, multi-modal contrastive learning can learn high-quality representations that exhibit impressive robustness and transferability. Despite its empirical success, the theoretical understanding is still in its infancy, especially regarding its comparison with single-modal contrastive learning. In this work, we introduce a feature learning theory framework that provides a theoretical foundation for understanding the differences between multi-modal and single-modal contrastive learning. Based on a data generation model consisting of signal and noise, our analysis is performed on a ReLU network trained with the InfoMax objective function. Through a trajectory-based optimization analysis and generalization characterization on downstream tasks, we identify the critical factor, which is the signal-to-noise ratio (SNR), that impacts the generalizability in downstream tasks of both multi-modal and single-modal contrastive learning. Through the cooperation between the two modalities, multi-modal learning can achieve better feature learning, leading to improvements in performance in downstream tasks compared to single-modal learning. Our analysis provides a unified framework that can characterize the optimization and generalization of both single-modal and multi-modal contrastive learning. Empirical experiments on both synthetic and real-world datasets further consolidate our theoretical findings.

Poster
Graphcode: Learning from multiparameter persistent homology using graph neural networks

Florian Russold, Michael Kerber

展开摘要

We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale parameters. Such multi-parameter topological summaries are usually based on complicated theoretical foundations and difficult to compute; in contrast, graphcodes yield an informative and interpretable summary and can be computed as efficient as one-parameter summaries. Moreover, a graphcode is simply an embedded graph and can therefore be readily integrated in machine learning pipelines using graph neural networks. We describe such a pipeline and demonstrate that graphcodes achieve better classification accuracy than state-of-the-art approaches on various datasets.

Poster
On scalable oversight with weak LLMs judging strong LLMs

Zachary Kenton, Noah Yamamoto Siegel, Janos Kramar, Jonah Brown-Cohen, Samuel Albanie, Jannis Bulian, Rishabh Agarwal, David Lindner, Yunhao Tang, Noah Goodman, Rohin Shah

展开摘要

Scalable oversight protocols aim to enable humans to accurately supervise superhuman AI. In this paper we study debate, where two AI's compete to convince a judge; consultancy, where a single AI tries to convince a judge that asks questions; and compare to a baseline of direct question-answering, where the judge just answers outright without the AI. We use large language models (LLMs) as both AI agents and as stand-ins for human judges, taking the judge models to be weaker than agent models. We benchmark on a diverse range of asymmetries between judges and agents, extending previous work on a single extractive QA task with information asymmetry, to also include mathematics, coding, logic and multimodal reasoning asymmetries. We find that debate outperforms consultancy across all tasks when the consultant is randomly assigned to argue for the correct/incorrect answer. Comparing debate to direct question answering, the results depend on the type of task: in extractive QA tasks with information asymmetry debate outperforms direct question answering, but in other tasks without information asymmetry the results are mixed. Previous work assigned debaters/consultants an answer to argue for. When we allow them to instead choose which answer to argue for, we find judges are less frequently convinced by the wrong answer in debate than in consultancy. Further, we find that stronger debater models increase judge accuracy, though more modestly than in previous studies.

Poster
Mobile-Agent-v2: Mobile Device Operation Assistant with Effective Navigation via Multi-Agent Collaboration

Junyang Wang, Haiyang Xu, Haitao Jia, Xi Zhang, Ming Yan, Weizhou Shen, Ji Zhang, Fei Huang, Jitao Sang

展开摘要

Mobile device operation tasks are increasingly becoming a popular multi-modal AI application scenario. Current Multi-modal Large Language Models (MLLMs), constrained by their training data, lack the capability to function effectively as operation assistants. Instead, MLLM-based agents, which enhance capabilities through tool invocation, are gradually being applied to this scenario. However, the two major navigation challenges in mobile device operation tasks — task progress navigation and focus content navigation — are difficult to effectively solve under the single-agent architecture of existing work. This is due to the overly long token sequences and the interleaved text-image data format, which limit performance. To address these navigation challenges effectively, we propose Mobile-Agent-v2, a multi-agent architecture for mobile device operation assistance. The architecture comprises three agents: planning agent, decision agent, and reflection agent. The planning agent condenses lengthy, interleaved image-text history operations and screens summaries into a pure-text task progress, which is then passed on to the decision agent. This reduction in context length makes it easier for decision agent to navigate the task progress. To retain focus content, we design a memory unit that updates with task progress by decision agent. Additionally, to correct erroneous operations, the reflection agent observes the outcomes of each operation and handles any mistake accordingly. Experimental results indicate that Mobile-Agent-v2 achieves over a 30% improvement in task completion compared to the single-agent architecture of Mobile-Agent. The code is open-sourced at https://github.com/X-PLUG/MobileAgent.

Poster
How Diffusion Models Learn to Factorize and Compose

Qiyao Liang, Ziming Liu, Mitchell Ostrow, Ila R Fiete

展开摘要

Diffusion models are capable of generating photo-realistic images that combine elements which do not appear together in natural images, demonstrating their ability to compositionally generalize. Nonetheless, the precise mechanism of compositionality and how it is acquired through training remains elusive. Here, we consider a highly reduced setting to examine whether diffusion models learn semantically meaningful and fully factorized representations of composable features. We performed extensive controlled experiments on conditional DDPMs trained to generate various forms of 2D Gaussian data. We demonstrate that the models learn factorized, semi-continuous manifold representations that are orthogonal in underlying continuous latent features of independent variations but are not aligned for different values of the same feature. With such representations, models demonstrate superior compositionality but have limited ability to interpolate over unseen values of a given feature. Our experimental results further demonstrate that diffusion models can attain compositionality with a small amount of compositional examples, suggesting a novel way to train DDPMs. Finally, we connect manifold formation in diffusion models to percolation theory in physics, thereby offering insights into the sudden onset of factorized representation learning. Our thorough toy experiments thus contribute a deeper understanding of how diffusion models capture compositional structure in data, paving the way for future research aimed at enhancing factorization and compositional generalization in generative models for real-world applications.

Poster
UrbanKGent: A Unified Large Language Model Agent Framework for Urban Knowledge Graph Construction

Yansong Ning, Hao Liu

展开摘要

Urban knowledge graph has recently worked as an emerging building block to distill critical knowledge from multi-sourced urban data for diverse urban application scenarios. Despite its promising benefits, urban knowledge graph construction (UrbanKGC) still heavily relies on manual effort, hindering its potential advancement. This paper presents UrbanKGent, a unified large language model agent framework, for urban knowledge graph construction. Specifically, we first construct the knowledgeable instruction set for UrbanKGC tasks (such as relational triplet extraction and knowledge graph completion) via heterogeneity-aware and geospatial-infused instruction generation. Moreover, we propose a tool-augmented iterative trajectory refinement module to enhance and refine the trajectories distilled from GPT-4. Through hybrid instruction fine-tuning with augmented trajectories on Llama 2 and Llama 3 family, we obtain UrbanKGC agent family, consisting of UrbanKGent-7/8/13B version. We perform a comprehensive evaluation on two real-world datasets using both human and GPT-4 self-evaluation. The experimental results demonstrate that UrbanKGent family can not only significantly outperform 31 baselines in UrbanKGC tasks, but also surpass the state-of-the-art LLM, GPT-4, by more than 10% with approximately 20 times lower cost. Compared with the existing benchmark, the UrbanKGent family could help construct an UrbanKG with hundreds of times richer relationships using only one-fifth of the data. Our data and code are available at https://github.com/usail-hkust/UrbanKGent.

Poster
Reinforcement Learning with Euclidean Data Augmentation for State-Based Continuous Control

Jinzhu Luo, Dingyang Chen, Qi Zhang

展开摘要

Data augmentation creates new data points by transforming the original ones for an reinforcement learning (RL) agent to learn from, which has been shown to be effective for the objective of improving data efficiency of RL for continuous control. Prior work towards this objective has been largely restricted to perturbation-based data augmentation where new data points are created by perturbing the original ones, which has been impressively effective for tasks where the RL agent observe control states as images with perturbations including random cropping, shifting, etc. This work focuses on state-based control, where the RL agent can directly observe raw kinematic and task features, and considers an alternative data augmentation applied to these features based on Euclidean symmetries under transformations like rotations. We show that the default state features used in exiting benchmark tasks that are based on joint configurations are not amenable to Euclidean transformations. We therefore advocate using state features based on configurations of the limbs (i.e., rigid bodies connected by joints) that instead provides rich augmented data under Euclidean transformations. With minimal hyperparameter tuning, we show this new Euclidean data augmentation strategy significantly improve both data efficiency and asymptotic performance of RL on a wide range of continuous control tasks.

Poster
Streaming Bayes GFlowNets

Tiago Silva, Daniel Augusto de Souza, Diego Mesquita

展开摘要

Bayes' rule naturally allows for inference refinement in a streaming fashion, without the need to recompute posteriors from scratch whenever new data arrives. In principle, Bayesian streaming is straightforward: we update our prior with the available data and use the resulting posterior as a prior when processing the next data chunk. In practice, however, this recipe entails i) approximating an intractable posterior at each time step; and ii) encapsulating results appropriately to allow for posterior propagation. For continuous state spaces, variational inference (VI) is particularly convenient due to its scalability and the tractability of variational posteriors, For discrete state spaces, however, state-of-the-art VI results in analytically intractable approximations that are ill-suited for streaming settings. To enable streaming Bayesian inference over discrete parameter spaces, we propose streaming Bayes GFlowNets (abbreviated as SB-GFlowNets) by leveraging the recently proposed GFlowNets --- a powerful class of amortized samplers for discrete compositional objects. Notably, SB-GFlowNet approximates the initial posterior using a standard GFlowNet and subsequently updates it using a tailored procedure that requires only the newly observed data. Our case studies in linear preference learning and phylogenetic inference showcase the effectiveness of SB-GFlowNets in sampling from an unnormalized posterior in a streaming setting. As expected, we also observe that SB-GFlowNets is significantly faster than repeatedly training a GFlowNet from scratch to sample from the full posterior.

Poster
Breaking Semantic Artifacts for Generalized AI-generated Image Detection

Chende Zheng, Chenhao Lin, Zhengyu Zhao, Hang Wang, Xu Guo, Shuai Liu, Chao Shen

展开摘要

With the continuous evolution of AI-generated images, the generalized detection of them has become a crucial aspect of AI security. Existing detectors have focused on cross-generator generalization, while it remains unexplored whether these detectors can generalize across different image scenes, e.g., images from different datasets with different semantics. In this paper, we reveal that existing detectors suffer from substantial Accuracy drops in such cross-scene generalization. In particular, we attribute their failures to ''semantic artifacts'' in both real and generated images, to which detectors may overfit. To break such ''semantic artifacts'', we propose a simple yet effective approach based on conducting an image patch shuffle and then training an end-to-end patch-based classifier. We conduct a comprehensive open-world evaluation on 31 test sets, covering 7 Generative Adversarial Networks, 18 (variants of) Diffusion Models, and another 6 CNN-based generative models. The results demonstrate that our approach outperforms previous approaches by 2.08\% (absolute) on average regarding cross-scene detection Accuracy. We also notice the superiority of our approach in open-world generalization, with an average Accuracy improvement of 10.59\% (absolute) across all test sets. Our code is available at *https://github.com/Zig-HS/FakeImageDetection*.

Poster
Seeing the Image: Prioritizing Visual Correlation by Contrastive Alignment

Xin Xiao, Bohong Wu, Jiacong Wang, Chunyuan Li, zhou Xun, Haoyuan Guo

展开摘要

Existing image-text modality alignment in Vision Language Models (VLMs) treats each text token equally in an autoregressive manner. Despite being simple and effective, this method results in sub-optimal cross-modal alignment by over-emphasizing the text tokens that are less correlated with or even contradictory with the input images. In this paper, we advocate for distinct contributions for each text token based on its visual correlation. Specifically, we present by contrasting image inputs, the difference in prediction logits on each text token provides strong guidance of visual correlation. We therefore introduce Contrastive Alignment (CAL), a simple yet effective re-weighting strategy that prioritizes training visually correlated tokens. Our experimental results demonstrate that CAL consistently improves different types of VLMs across different resolutions and model sizes on various benchmark datasets. Importantly, our method incurs minimal additional computational overhead, rendering it highly efficient compared to alternative data scaling strategies.

Poster
Motion Consistency Model: Accelerating Video Diffusion with Disentangled Motion-Appearance Distillation

Yuanhao Zhai, Kevin Lin, Zhengyuan Yang, Linjie Li, Jianfeng Wang, Chung-Ching Lin, David Doermann, Junsong Yuan, Lijuan Wang

展开摘要

Image diffusion distillation achieves high-fidelity generation with very few sampling steps. However, directly applying these techniques to video models results in unsatisfied frame quality. This issue arises from the limited frame appearance quality in public video datasets, affecting the performance of both teacher and student video diffusion models. Our study aims to improve video diffusion distillation and meanwhile enabling the student model to improve frame appearance using the abundant high-quality image data. To this end, we propose motion consistency models (MCM), a single-stage video diffusion distillation method that disentangles motion and appearance learning. Specifically, MCM involves a video consistency model that distills motion from the video teacher model, and an image discriminator that boosts frame appearance to match high-quality image data. However, directly combining these components leads to two significant challenges: a conflict in frame learning objectives, where video distillation learns from low-quality video frames while the image discriminator targets high-quality images, and training-inference discrepancies due to the differing quality of video samples used during training and inference. To address these challenges, we introduce disentangled motion distillation and mixed trajectory distillation. The former applies the distillation objective solely to the motion representation, while the latter mitigates training-inference discrepancies by mixing distillation trajectories from both the low- and high-quality video domains. Extensive experiments show that our MCM achieves state-of-the-art video diffusion distillation performance. Additionally, our method can enhance frame quality in video diffusion models, producing frames with high aesthetic value or specific styles.

Poster
GaussianCut: Interactive segmentation via graph cut for 3D Gaussian Splatting

Umangi Jain, Ashkan Mirzaei, Igor Gilitschenski

展开摘要

We introduce GaussianCut, a new method for interactive multiview segmentation of scenes represented as 3D Gaussians. Our approach allows for selecting the objects to be segmented by interacting with a single view. It accepts intuitive user input, such as point clicks, coarse scribbles, or text. Using 3D Gaussian Splatting (3DGS) as the underlying scene representation simplifies the extraction of objects of interest which are considered to be a subset of the scene's Gaussians. Our key idea is to represent the scene as a graph and use the graph-cut algorithm to minimize an energy function to effectively partition the Gaussians into foreground and background. To achieve this, we construct a graph based on scene Gaussians and devise a segmentation-aligned energy function on the graph to combine user inputs with scene properties. To obtain an initial coarse segmentation, we leverage 2D image/video segmentation models and further refine these coarse estimates using our graph construction. Our empirical evaluations show the adaptability of GaussianCut across a diverse set of scenes. GaussianCut achieves competitive performance with state-of-the-art approaches for 3D segmentation without requiring any additional segmentation-aware training

Poster
ANAH-v2: Scaling Analytical Hallucination Annotation of Large Language Models

Yuzhe Gu, Ziwei Ji, Wenwei Zhang, Chengqi Lyu, Dahua Lin, Kai Chen

展开摘要

Large language models (LLMs) exhibit hallucinations in long-form question-answering tasks across various domains and wide applications. Current hallucination detection and mitigation datasets are limited in domain and size, which struggle to scale due to prohibitive labor costs and insufficient reliability of existing hallucination annotators. To facilitate the scalable oversight of LLM hallucinations, this paper introduces an iterative self-training framework that simultaneously and progressively scales up the annotation dataset and improves the accuracy of the annotator. Based on the Expectation Maximization algorithm, in each iteration, the framework first applies an automatic hallucination annotation pipeline for a scaled dataset and then trains a more accurate annotator on the dataset. This new annotator is adopted in the annotation pipeline for the next iteration. Extensive experimental results demonstrate that the finally obtained hallucination annotator with only 7B parameters surpasses GPT-4 and obtains new state-of-the-art hallucination detection results on HaluEval and HalluQA by zero-shot inference. Such an annotator can not only evaluate the hallucination levels of various LLMs on the large-scale dataset but also help to mitigate the hallucination of LLMs generations, with the Natural Language Inference metric increasing from 25% to 37% on HaluEval.

Poster
DACO: Towards Application-Driven and Comprehensive Data Analysis via Code Generation

Xueqing Wu, Rui Zheng, Jingzhen Sha, Te-Lin Wu, Hanyu Zhou, Tang Mohan, Kai-Wei Chang, Nanyun Peng, Haoran Huang

展开摘要

Data analysis is a crucial analytical process essential for deriving insights from real-world databases. As shown in Figure 1, the need for data analysis typically arises from specific application scenarios, and requires diverse reasoning skills including mathematical reasoning, logical reasoning, and strategic reasoning. Existing work often focus on simple factual retrieval or arithmetic resolutions and thus are insufficient for addressing complex real-world queries. This work aims to propose new resources and benchmarks on this crucial yet challenging and under-explored task. Due to the prohibitively high cost of collecting expert annotations, we use large language models (LLMs) enhanced by code generation to automatically generate high-quality data analysis, which will later be refined by human annotators. We construct the **DACO dataset**, containing (1) 440 databases (of tabular data) collected from real-world scenarios, (2) ~2k automatically generated query-answer pairs that can serve as weak supervision for model training, and (3) a concentrated but high-quality test set with human refined annotations that serves as our main evaluation benchmark. Experiments show that while LLMs like GPT-4 exhibit promising data analysis capabilities, they are still evaluated as less helpful than human-written analysis on 58.1% cases. Leveraging our weak supervision data, we experiment with various fine-tuning methods, including supervised fine-tuning (SFT) and reinforcement learning from human feedback (RLHF). Our trained model outperforms existing baselines for table question answering, and RLHF further boosts the helpfulness of generated analysis on 58.5% cases. Data and code are released at https://github.com/shirley-wu/daco.

Poster
Occupancy-based Policy Gradient: Estimation, Convergence, and Optimality

Audrey Huang, Nan Jiang

展开摘要

Occupancy functions play an instrumental role in reinforcement learning (RL) for guiding exploration, handling distribution shift, and optimizing general objectives beyond the expected return. Yet, computationally efficient policy optimization methods that use (only) occupancy functions are virtually non-existent. In this paper, we establish the theoretical foundations of model-free policy gradient (PG) methods that compute the gradient through the occupancy for both online and offline RL, without modeling value functions. Our algorithms reduce gradient estimation to squared-loss regression and are computationally oracle-efficient. We characterize the sample complexities of both local and global convergence, accounting for both finite-sample estimation error and the roles of exploration (online) and data coverage (offline). Occupancy-based PG naturally handles arbitrary offline data distributions, and, with one-line algorithmic changes, can be adapted to optimize any differentiable objective functional.

Poster
No-Regret M${}^{\natural}$-Concave Function Maximization: Stochastic Bandit Algorithms and NP-Hardness of Adversarial Full-Information Setting

Taihei Oki, Shinsaku Sakaue

展开摘要

M${}^{\natural}$-concave functions, a.k.a. gross substitute valuation functions, play a fundamental role in many fields, including discrete mathematics and economics. In practice, perfect knowledge of M${}^{\natural}$-concave functions is often unavailable a priori, and we can optimize them only interactively based on some feedback. Motivated by such situations, we study online M${}^{\natural}$-concave function maximization problems, which are interactive versions of the problem studied by Murota and Shioura (1999). For the stochastic bandit setting, we present $O(T^{-1/2})$-simple regret and $O(T^{2/3})$-regret algorithms under $T$ times access to unbiased noisy value oracles of M${}^{\natural}$-concave functions. A key to proving these results is the robustness of the greedy algorithm to local errors in M${}^{\natural}$-concave function maximization, which is one of our main technical results. While we obtain those positive results for the stochastic setting, another main result of our work is an impossibility in the adversarial setting. We prove that, even with full-information feedback, no algorithms that run in polynomial time per round can achieve $O(T^{1-c})$ regret for any constant $c > 0$ unless $\mathsf{P} = \mathsf{NP}$. Our proof is based on a reduction from the matroid intersection problem for three matroids, which would be a novel idea in the context of online learning.

Poster