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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    3828.4%
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    4,06489.1%
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    441.0%

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HydraLoRA: An Asymmetric LoRA Architecture for Efficient Fine-Tuning

Chunlin Tian, Zhan Shi, Zhijiang Guo, Li Li, Cheng-Zhong Xu

展开摘要

Adapting Large Language Models (LLMs) to new tasks through fine-tuning has been made more efficient by the introduction of Parameter-Efficient Fine-Tuning (PEFT) techniques, such as LoRA. However, these methods often underperform compared to full fine-tuning, particularly in scenarios involving complex datasets. This issue becomes even more pronounced in complex domains, highlighting the need for improved PEFT approaches that can achieve better performance. Through a series of experiments, we have uncovered two critical insights that shed light on the training and parameter inefficiency of LoRA. Building on these insights, we have developed HydraLoRA, a LoRA framework with an asymmetric structure that eliminates the need for domain expertise. Our experiments demonstrate that HydraLoRA outperforms other PEFT approaches, even those that rely on domain knowledge during the training and inference phases. Our anonymous codes are submitted with the paper and will be publicly available. Code is available: https://github.com/Clin0212/HydraLoRA.

Oral
Differentially Private Equivalence Testing for Continuous Distributions and Applications

Or Sheffet, Daniel Omer

展开摘要

We present the first algorithm for testing equivalence between two continuous distributions using differential privacy (DP). Our algorithm is a private version of the algorithm of Diakonikolas et al. The algorithm of Diakonikolas et al uses the data itself to repeatedly discretize the real line so that --- when the two distributions are far apart in ${\cal A}_k$-norm --- one of the discretized distributions exhibits large $L_2$-norm difference; and upon repeated sampling such large gap would be detected. Designing its private analogue poses two difficulties. First, our DP algorithm can not resample new datapoints as a change to a single datapoint may lead to a very large change in the descretization of the real line. In contrast, the (sorted) index of the discretization point changes only by $1$ between neighboring instances, and so we use a novel algorithm that set the discretization points using random Bernoulli noise, resulting in only a few buckets being affected under the right coupling. Second, our algorithm, which doesn't resample data, requires we also revisit the utility analysis of the original algorithm and prove its correctness w.r.t. the original sorted data; a problem we tackle using sampling a subset of Poisson-drawn size from each discretized bin. Lastly, since any distribution can be reduced to a continuous distribution, our algorithm is successfully carried to multiple other families of distributions and thus has numerous applications.

Poster
Spec-Gaussian: Anisotropic View-Dependent Appearance for 3D Gaussian Splatting

Ziyi Yang, Xinyu Gao, Yang-Tian Sun, Yi-Hua Huang, Xiaoyang Lyu, Wen Zhou, Shaohui Jiao, Xiaojuan Qi, Xiaogang Jin

展开摘要

The recent advancements in 3D Gaussian splatting (3D-GS) have not only facilitated real-time rendering through modern GPU rasterization pipelines but have also attained state-of-the-art rendering quality. Nevertheless, despite its exceptional rendering quality and performance on standard datasets, 3D-GS frequently encounters difficulties in accurately modeling specular and anisotropic components. This issue stems from the limited ability of spherical harmonics (SH) to represent high-frequency information. To overcome this challenge, we introduce Spec-Gaussian, an approach that utilizes an anisotropic spherical Gaussian (ASG) appearance field instead of SH for modeling the view-dependent appearance of each 3D Gaussian. Additionally, we have developed a coarse-to-fine training strategy to improve learning efficiency and eliminate floaters caused by overfitting in real-world scenes. Our experimental results demonstrate that our method surpasses existing approaches in terms of rendering quality. Thanks to ASG, we have significantly improved the ability of 3D-GS to model scenes with specular and anisotropic components without increasing the number of 3D Gaussians. This improvement extends the applicability of 3D GS to handle intricate scenarios with specular and anisotropic surfaces.

Poster
Dynamic Neural Regeneration: Enhancing Deep Learning Generalization on Small Datasets

Vijaya Raghavan T Ramkumar, Elahe Arani, Bahram Zonooz

展开摘要

The efficacy of deep learning techniques is contingent upon access to large volumes of data (labeled or unlabeled). However, in practical domains such as medical applications, data availability is often limited. This presents a significant challenge: How can we effectively train deep neural networks on relatively small datasets while improving generalization? Recent works have explored evolutionary or iterative training paradigms, which reinitialize a subset of parameters to enhance generalization performance for small datasets. However, these methods typically rely on randomly selected parameter subsets and maintain fixed masks throughout training, potentially leading to suboptimal outcomes. Inspired by neurogenesis in the brain, we propose a novel iterative training framework, Dynamic Neural Regeneration (DNR), that employs a data-aware dynamic masking scheme to eliminate redundant connections by estimating their significance. This approach increases the model's capacity for further learning through random weight reinitialization. Experimental results demonstrate that our approach outperforms existing methods in accuracy and robustness, highlighting its potential for real-world applications where data collection is challenging.

Poster
FouRA: Fourier Low-Rank Adaptation

Shubhankar Borse, Shreya Kadambi, Nilesh Prasad Pandey, Kartikeya Bhardwaj, Viswanath Ganapathy, Sweta Priyadarshi, Risheek Garrepalli, Rafael Esteves, Munawar Hayat, Fatih Porikli

展开摘要

While Low-Rank Adaptation (LoRA) has proven beneficial for efficiently fine-tuning large models, LoRA fine-tuned text-to-image diffusion models lack diversity in the generated images, as the model tends to copy data from the observed training samples. This effect becomes more pronounced at higher values of adapter strength and for adapters with higher ranks which are fine-tuned on smaller datasets. To address these challenges, we present FouRA, a novel low-rank method that learns projections in the Fourier domain along with learning a flexible input-dependent adapter rank selection strategy. Through extensive experiments and analysis, we show that FouRA successfully solves the problems related to data copying and distribution collapse while significantly improving the generated image quality. We demonstrate that FouRA enhances the generalization of fine-tuned models thanks to its adaptive rank selection. We further show that the learned projections in the frequency domain are decorrelated and prove effective when merging multiple adapters. While FouRA is motivated for vision tasks, we also demonstrate its merits for language tasks on commonsense reasoning and GLUE benchmarks.

Poster
Stealth edits to large language models

Oliver Sutton, Qinghua Zhou, Wei Wang, Desmond Higham, Alexander N. Gorban, Alexander Bastounis, Ivan Y Tyukin

展开摘要

We reveal the theoretical foundations of techniques for editing large language models, and present new methods which can do so without requiring retraining. Our theoretical insights show that a single metric (a measure of the intrinsic dimension of the model's features) can be used to assess a model's editability and reveals its previously unrecognised susceptibility to malicious *stealth attacks*. This metric is fundamental to predicting the success of a variety of editing approaches, and reveals new bridges between disparate families of editing methods. We collectively refer to these as *stealth editing* methods, because they directly update a model's weights to specify its response to specific known hallucinating prompts without affecting other model behaviour. By carefully applying our theoretical insights, we are able to introduce a new *jet-pack* network block which is optimised for highly selective model editing, uses only standard network operations, and can be inserted into existing networks. We also reveal the vulnerability of language models to stealth attacks: a small change to a model's weights which fixes its response to a single attacker-chosen prompt. Stealth attacks are computationally simple, do not require access to or knowledge of the model's training data, and therefore represent a potent yet previously unrecognised threat to redistributed foundation models. Extensive experimental results illustrate and support our methods and their theoretical underpinnings. Demos and source code are available at https://github.com/qinghua-zhou/stealth-edits.

Poster
Small steps no more: Global convergence of stochastic gradient bandits for arbitrary learning rates

Jincheng Mei, Bo Dai, Alekh Agarwal, Sharan Vaswani, Anant Raj, Csaba Szepesvari, Dale Schuurmans

展开摘要

We provide a new understanding of the stochastic gradient bandit algorithm by showing that it converges to a globally optimal policy almost surely using \emph{any} constant learning rate. This result demonstrates that the stochastic gradient algorithm continues to balance exploration and exploitation appropriately even in scenarios where standard smoothness and noise control assumptions break down. The proofs are based on novel findings about action sampling rates and the relationship between cumulative progress and noise, and extend the current understanding of how simple stochastic gradient methods behave in bandit settings.

Poster
FlexPlanner: Flexible 3D Floorplanning via Deep Reinforcement Learning in Hybrid Action Space with Multi-Modality Representation

Ruizhe Zhong, Xingbo Du, Shixiong Kai, Zhentao Tang, Siyuan Xu, Jianye Hao, Mingxuan Yuan, Junchi Yan

展开摘要

In the Integrated Circuit (IC) design flow, floorplanning (FP) determines the position and shape of each block. Serving as a prototype for downstream tasks, it is critical and establishes the upper bound of the final PPA (Power, Performance, Area). However, with the emergence of 3D IC with stacked layers, existing methods are not flexible enough to handle the versatile constraints. Besides, they typically face difficulties in aligning the cross-die modules in 3D ICs due to their heuristic representations, which could potentially result in severe data transfer failures. To address these issues, we propose FlexPlanner, a flexible learning-based method in hybrid action space with multi-modality representation to simultaneously handle position, aspect ratio, and alignment of blocks. To our best knowledge, FlexPlanner is the first learning-based approach to discard heuristic-based search in the 3D FP task. Thus, the solution space is not limited by the heuristic floorplanning representation, allowing for significant improvements in both wirelength and alignment scores. Specifically, FlexPlanner models 3D FP based on multi-modalities, including vision, graph, and sequence. To address the non-trivial heuristic-dependent issue, we design a sophisticated policy network with hybrid action space and asynchronous layer decision mechanism that allow for determining the versatile properties of each block. Experiments on public benchmarks MCNC and GSRC show the effectiveness. We significantly improve the alignment score from 0.474 to 0.940 and achieve an average reduction of 16% in wirelength. Moreover, our method also demonstrates zero-shot transferability on unseen circuits.

Poster
A Simulation Benchmark for Autonomous Racing with Large-Scale Human Data

Adrian Remonda, Nicklas Hansen, Ayoub Raji, Nicola Musiu, Marko Bertogna, Eduardo E. Veas, Xiaolong Wang

展开摘要

Despite the availability of international prize-money competitions, scaled vehicles, and simulation environments, research on autonomous racing and the control of sports cars operating close to the limit of handling has been limited by the high costs of vehicle acquisition and management, as well as the limited physics accuracy of open-source simulators. In this paper, we propose a racing simulation platform based on the simulator Assetto Corsa to test, validate, and benchmark autonomous driving algorithms, including reinforcement learning (RL) and classical Model Predictive Control (MPC), in realistic and challenging scenarios. Our contributions include the development of this simulation platform, several state-of-the-art algorithms tailored to the racing environment, and a comprehensive dataset collected from human drivers. Additionally, we evaluate algorithms in the offline RL setting. All the necessary code (including environment and benchmarks), working examples, and datasets are publicly released and can be found at: https://github.com/dasGringuen/assetto_corsa_gym.

Poster
N-agent Ad Hoc Teamwork

Caroline Wang, Arrasy Rahman, Ishan Durugkar, Elad Liebman, Peter Stone

展开摘要

Current approaches to learning cooperative multi-agent behaviors assume relatively restrictive settings. In standard fully cooperative multi-agent reinforcement learning, the learning algorithm controls *all* agents in the scenario, while in ad hoc teamwork, the learning algorithm usually assumes control over only a *single* agent in the scenario. However, many cooperative settings in the real world are much less restrictive. For example, in an autonomous driving scenario, a company might train its cars with the same learning algorithm, yet once on the road, these cars must cooperate with cars from another company. Towards expanding the class of scenarios that cooperative learning methods may optimally address, we introduce $N$*-agent ad hoc teamwork* (NAHT), where a set of autonomous agents must interact and cooperate with dynamically varying numbers and types of teammates. This paper formalizes the problem, and proposes the *Policy Optimization with Agent Modelling* (POAM) algorithm. POAM is a policy gradient, multi-agent reinforcement learning approach to the NAHT problem, that enables adaptation to diverse teammate behaviors by learning representations of teammate behaviors. Empirical evaluation on tasks from the multi-agent particle environment and StarCraft II shows that POAM improves cooperative task returns compared to baseline approaches, and enables out-of-distribution generalization to unseen teammates.

Poster
Enhancing LLM’s Cognition via Structurization

Kai Liu, Zhihang Fu, Chao Chen, Wei Zhang, Rongxin Jiang, Fan Zhou, Yaowu Chen, Yue Wu, Jieping Ye

展开摘要

When reading long-form text, human cognition is complex and structurized. While large language models (LLMs) process input contexts through a causal and sequential perspective, this approach can potentially limit their ability to handle intricate and complex inputs effectively. To enhance LLM’s cognition capability, this paper presents a novel concept of context structurization. Specifically, we transform the plain, unordered contextual sentences into well-ordered and hierarchically structurized elements. By doing so, LLMs can better grasp intricate and extended contexts through precise attention and information-seeking along the organized structures. Extensive evaluations are conducted across various model architectures and sizes (including a series of auto-regressive LLMs as well as BERT-like masking models) on a diverse set of NLP tasks (e.g., context-based question-answering, exhaustive hallucination evaluation, and passage-level dense retrieval). Empirical results show consistent and significant performance gains afforded by a single-round structurization. In particular, we boost the open-sourced LLaMA2-70B model to achieve comparable performance against GPT-3.5-Turbo as the halluci- nation evaluator. Besides, we show the feasibility of distilling advanced LLMs’ language processing abilities to a smaller yet effective StruXGPT-7B to execute structurization, addressing the practicality of our approach. Code is available at https://github.com/alibaba/struxgpt.

Poster
Self-Play Fine-tuning of Diffusion Models for Text-to-image Generation

Huizhuo Yuan, Zixiang Chen, Kaixuan Ji, Quanquan Gu

展开摘要

Fine-tuning Diffusion Models remains an underexplored frontier in generative artificial intelligence (GenAI), especially when compared with the remarkable progress made in fine-tuning Large Language Models (LLMs). While cutting-edge diffusion models such as Stable Diffusion (SD) and SDXL rely on supervised fine-tuning, their performance inevitably plateaus after seeing a certain volume of data. Recently, reinforcement learning (RL) has been employed to fine-tune diffusion models with human preference data, but it requires at least two images (``winner'' and ``loser'' images) for each text prompt. In this paper, we introduce an innovative technique called self-play fine-tuning for diffusion models (SPIN-Diffusion), where the diffusion model engages in competition with its earlier versions, facilitating an iterative self-improvement process. Our approach offers an alternative to conventional supervised fine-tuning and RL strategies, significantly improving both model performance and alignment. Our experiments on the Pick-a-Pic dataset reveal that SPIN-Diffusion outperforms the existing supervised fine-tuning method in aspects of human preference alignment and visual appeal right from its first iteration. By the second iteration, it exceeds the performance of RLHF-based methods across all metrics, achieving these results with less data. Codes are available at \url{https://github.com/uclaml/SPIN-Diffusion/}.

Poster
Benchmarking Generative Models on Computational Thinking Tests in Elementary Visual Programming

Victor-Alexandru Pădurean, Adish Singla

展开摘要

Generative models have demonstrated human-level proficiency in various benchmarks across domains like programming, natural sciences, and general knowledge. Despite these promising results on competitive benchmarks, they still struggle with seemingly simple problem-solving tasks typically carried out by elementary-level students. How do state-of-the-art models perform on standardized programming-related tests designed to assess computational thinking and problem-solving skills at schools? In this paper, we curate a novel benchmark involving computational thinking tests grounded in elementary visual programming domains. Our initial results show that state-of-the-art models like GPT-4o and Llama3 barely match the performance of an average school student. To further boost the performance of these models, we fine-tune them using a novel synthetic data generation methodology. The key idea is to develop a comprehensive dataset using symbolic methods that capture different skill levels, ranging from recognition of visual elements to multi-choice quizzes to synthesis-style tasks. We showcase how various aspects of symbolic information in synthetic data help improve fine-tuned models' performance. We will release the full implementation and datasets to facilitate further research on enhancing computational thinking in generative models.

Poster
BEACON: Benchmark for Comprehensive RNA Tasks and Language Models

Yuchen Ren, Zhiyuan Chen, Lifeng Qiao, Hongtai Jing, Yuchen Cai, Sheng Xu, Peng Ye, Xinzhu Ma, Siqi Sun, Hongliang Yan, Dong Yuan, Wanli Ouyang, Xihui Liu

展开摘要

RNA plays a pivotal role in translating genetic instructions into functional outcomes, underscoring its importance in biological processes and disease mechanisms. Despite the emergence of numerous deep learning approaches for RNA, particularly universal RNA language models, there remains a significant lack of standardized benchmarks to assess the effectiveness of these methods. In this study, we introduce the first comprehensive RNA benchmark BEACON **BE**nchm**A**rk for **CO**mprehensive R**N**A Task and Language Models). First, BEACON comprises 13 distinct tasks derived from extensive previous work covering structural analysis, functional studies, and engineering applications, enabling a comprehensive assessment of the performance of methods on various RNA understanding tasks. Second, we examine a range of models, including traditional approaches like CNNs, as well as advanced RNA foundation models based on language models, offering valuable insights into the task-specific performances of these models. Third, we investigate the vital RNA language model components from the tokenizer and positional encoding aspects. Notably, our findings emphasize the superiority of single nucleotide tokenization and the effectiveness of Attention with Linear Biases (ALiBi) over traditional positional encoding methods. Based on these insights, a simple yet strong baseline called BEACON-B is proposed, which can achieve outstanding performance with limited data and computational resources. The datasets and source code of our benchmark are available at https://github.com/terry-r123/RNABenchmark.

Poster
NeuralClothSim: Neural Deformation Fields Meet the Thin Shell Theory

Navami Kairanda, Marc Habermann, Christian Theobalt, Vladislav Golyanik

展开摘要

Despite existing 3D cloth simulators producing realistic results, they predominantly operate on discrete surface representations (e.g. points and meshes) with a fixed spatial resolution, which often leads to large memory consumption and resolution-dependent simulations. Moreover, back-propagating gradients through the existing solvers is difficult and they hence cannot be easily integrated into modern neural architectures. In response, this paper re-thinks physically plausible cloth simulation: We propose NeuralClothSim, i.e., a new quasistatic cloth simulator using thin shells, in which surface deformation is encoded in neural network weights in form of a neural field. Our memory-efficient solver operates on a new continuous coordinate-based surface representation called neural deformation fields (NDFs); it supervises NDF equilibria with the laws of the non-linear Kirchhoff-Love shell theory with a non-linear anisotropic material model. NDFs are adaptive: They 1) allocate their capacity to the deformation details and 2) allow surface state queries at arbitrary spatial resolutions without re-training. We show how to train NeuralClothSim while imposing hard boundary conditions and demonstrate multiple applications, such as material interpolation and simulation editing. The experimental results highlight the effectiveness of our continuous neural formulation.

Poster
Pseudo-Private Data Guided Model Inversion Attacks

Xiong Peng, Bo Han, Feng Liu, Tongliang Liu, Mingyuan Zhou

展开摘要

In model inversion attacks (MIAs), adversaries attempt to recover private training data by exploiting access to a well-trained target model. Recent advancements have improved MIA performance using a two-stage generative framework. This approach first employs a generative adversarial network to learn a fixed distributional prior, which is then used to guide the inversion process during the attack. However, in this paper, we observed a phenomenon that such a fixed prior would lead to a low probability of sampling actual private data during the inversion process due to the inherent distribution gap between the prior distribution and the private data distribution, thereby constraining attack performance. To address this limitation, we propose increasing the density around high-quality pseudo-private data—recovered samples through model inversion that exhibit characteristics of the private training data—by slightly tuning the generator. This strategy effectively increases the probability of sampling actual private data that is close to these pseudo-private data during the inversion process. After integrating our method, the generative model inversion pipeline is strengthened, leading to improvements over state-of-the-art MIAs. This paves the way for new research directions in generative MIAs.

Poster
Apathetic or Empathetic? Evaluating LLMs' Emotional Alignments with Humans

Jen-tse Huang, Man Ho LAM, Eric John Li, Shujie Ren, Wenxuan Wang, Wenxiang Jiao, Zhaopeng Tu, Michael Lyu

展开摘要

Evaluating Large Language Models’ (LLMs) anthropomorphic capabilities has become increasingly important in contemporary discourse. Utilizing the emotion appraisal theory from psychology, we propose to evaluate the empathy ability of LLMs, i.e., how their feelings change when presented with specific situations. After a careful and comprehensive survey, we collect a dataset containing over 400 situations that have proven effective in eliciting the eight emotions central to our study. Categorizing the situations into 36 factors, we conduct a human evaluation involving more than 1,200 subjects worldwide. With the human evaluation results as references, our evaluation includes seven LLMs, covering both commercial and open-source models, including variations in model sizes, featuring the latest iterations, such as GPT-4, Mixtral-8x22B, and LLaMA-3.1. We find that, despite several misalignments, LLMs can generally respond appropriately to certain situations. Nevertheless, they fall short in alignment with the emotional behaviors of human beings and cannot establish connections between similar situations. Our collected dataset of situations, the human evaluation results, and the code of our testing framework, i.e., EmotionBench, are publicly available at https://github.com/CUHK-ARISE/EmotionBench.

Poster
Train-Attention: Meta-Learning Where to Focus in Continual Knowledge Learning

Yeongbin Seo, Dongha Lee, Jinyoung Yeo

展开摘要

Previous studies on continual knowledge learning (CKL) in large language models (LLMs) have predominantly focused on approaches such as regularization, architectural modifications, and rehearsal techniques to mitigate catastrophic forgetting. However, these methods naively inherit the inefficiencies of standard training procedures, indiscriminately applying uniform weight across all tokens, which can lead to unnecessary parameter updates and increased forgetting. To address these shortcomings, we propose a novel CKL approach termed Train-Attention-Augmented Language Model (TAALM), which enhances learning efficiency by dynamically predicting and applying weights to tokens based on their usefulness. This method employs a meta-learning framework that optimizes token importance predictions, facilitating targeted knowledge updates and minimizing forgetting. Also, we observe that existing benchmarks do not clearly exhibit the trade-off between learning and retaining, therefore we propose a new benchmark, LAMA-ckl, to address this issue. Through experiments conducted on both newly introduced and established CKL benchmarks, TAALM proves the state-of-the-art performance upon the baselines, and also shows synergistic compatibility when integrated with previous CKL approaches. The code and the dataset are available online.

Poster
Abstracted Shapes as Tokens - A Generalizable and Interpretable Model for Time-series Classification

Yunshi Wen, Tengfei Ma, Tsui-Wei Weng, Lam M. Nguyen, Anak Agung Julius

展开摘要

In time-series analysis, many recent works seek to provide a unified view and representation for time-series across multiple domains, leading to the development of foundation models for time-series data. Despite diverse modeling techniques, existing models are black boxes and fail to provide insights and explanations about their representations. In this paper, we present VQShape, a pre-trained, generalizable, and interpretable model for time-series representation learning and classification. By introducing a novel representation for time-series data, we forge a connection between the latent space of VQShape and shape-level features. Using vector quantization, we show that time-series from different domains can be described using a unified set of low-dimensional codes, where each code can be represented as an abstracted shape in the time domain. On classification tasks, we show that the representations of VQShape can be utilized to build interpretable classifiers, achieving comparable performance to specialist models. Additionally, in zero-shot learning, VQShape and its codebook can generalize to previously unseen datasets and domains that are not included in the pre-training process. The code and pre-trained weights are available at https://github.com/YunshiWen/VQShape.

Poster
Achieving $\tilde{O}(1/\epsilon)$ Sample Complexity for Constrained Markov Decision Process

Jiashuo Jiang, Yinyu Ye

展开摘要

We consider the reinforcement learning problem for the constrained Markov decision process (CMDP), which plays a central role in satisfying safety or resource constraints in sequential learning and decision-making. In this problem, we are given finite resources and a MDP with unknown transition probabilities. At each stage, we take an action, collecting a reward and consuming some resources, all assumed to be unknown and need to be learned over time. In this work, we take the first step towards deriving optimal problem-dependent guarantees for the CMDP problems. We derive a logarithmic regret bound, which translates into a $O(\frac{1}{\Delta\cdot\epsilon}\cdot\log^2(1/\epsilon))$ sample complexity bound, with $\Delta$ being a problem-dependent parameter, yet independent of $\epsilon$. Our sample complexity bound improves upon the state-of-art $O(1/\epsilon^2)$ sample complexity for CMDP problems established in the previous literature, in terms of the dependency on $\epsilon$. To achieve this advance, we develop a new framework for analyzing CMDP problems. To be specific, our algorithm operates in the primal space and we resolve the primal LP for the CMDP problem at each period in an online manner, with \textit{adaptive} remaining resource capacities. The key elements of our algorithm are: i) a characterization of the instance hardness via LP basis, ii) an eliminating procedure that identifies one optimal basis of the primal LP, and; iii) a resolving procedure that is adaptive to the remaining resources and sticks to the characterized optimal basis.

Poster