NeurIPS 2024 Papers

Conference on Neural Information Processing Systems

Decision breakdown

4,562papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    721.6%
  • Spotlight
    3828.4%
  • Poster
    4,06489.1%
  • Other / unlabeled
    441.0%

Browse all papers

Faster Diffusion: Rethinking the Role of the Encoder for Diffusion Model Inference

Senmao Li, taihang Hu, Joost van de weijer, Fahad Khan, Tao Liu, Linxuan Li, Shiqi Yang, Yaxing Wang, Ming-Ming Cheng, Jian Yang

Expand abstract

One of the main drawback of diffusion models is the slow inference time for image generation. Among the most successful approaches to addressing this problem are distillation methods. However, these methods require considerable computational resources. In this paper, we take another approach to diffusion model acceleration. We conduct a comprehensive study of the UNet encoder and empirically analyze the encoder features. This provides insights regarding their changes during the inference process. In particular, we find that encoder features change minimally, whereas the decoder features exhibit substantial variations across different time-steps. This insight motivates us to omit encoder computation at certain adjacent time-steps and reuse encoder features of previous time-steps as input to the decoder in multiple time-steps. Importantly, this allows us to perform decoder computation in parallel, further accelerating the denoising process. Additionally, we introduce a prior noise injection method to improve the texture details in the generated image. Besides the standard text-to-image task, we also validate our approach on other tasks: text-to-video, personalized generation and reference-guided generation. Without utilizing any knowledge distillation technique, our approach accelerates both the Stable Diffusion (SD) and DeepFloyd-IF model sampling by 41$\%$ and 24$\%$ respectively, and DiT model sampling by 34$\%$, while maintaining high-quality generation performance. Our code will be publicly released.

Poster
Abstract Reward Processes: Leveraging State Abstraction for Consistent Off-Policy Evaluation

Shreyas Chaudhari, Ameet Deshpande, Bruno Castro da Silva, Philip S. Thomas

Expand abstract

Evaluating policies using off-policy data is crucial for applying reinforcement learning to real-world problems such as healthcare and autonomous driving. Previous methods for *off-policy evaluation* (OPE) generally suffer from high variance or irreducible bias, leading to unacceptably high prediction errors. In this work, we introduce STAR, a framework for OPE that encompasses a broad range of estimators -- which include existing OPE methods as special cases -- that achieve lower mean squared prediction errors. STAR leverages state abstraction to distill complex, potentially continuous problems into compact, discrete models which we call *abstract reward processes* (ARPs). Predictions from ARPs estimated from off-policy data are provably consistent (asymptotically correct). Rather than proposing a specific estimator, we present a new framework for OPE and empirically demonstrate that estimators within STAR outperform existing methods. The best STAR estimator outperforms baselines in all twelve cases studied, and even the median STAR estimator surpasses the baselines in seven out of the twelve cases.

Poster
Benchmarking PtO and PnO Methods in the Predictive Combinatorial Optimization Regime

Haoyu Geng, Hang Ruan, Runzhong Wang, Yang Li, Yang Wang, Lei Chen, Junchi Yan

Expand abstract

Predictive combinatorial optimization, where the parameters of combinatorial optimization (CO) are unknown at the decision-making time, is the precise modeling of many real-world applications, including energy cost-aware scheduling and budget allocation on advertising. Tackling such a problem usually involves a prediction model and a CO solver. These two modules are integrated into the predictive CO pipeline following two design principles: ''Predict-then-Optimize (PtO)'', which learns predictions by supervised training and subsequently solves CO using predicted coefficients, while the other, named ''Predict-and-Optimize (PnO)'', directly optimizes towards the ultimate decision quality and claims to yield better decisions than traditional PtO approaches. However, there lacks a systematic benchmark of both approaches, including the specific design choices at the module level, as well as an evaluation dataset that covers representative real-world scenarios. To this end, we develop a modular framework to benchmark 11 existing PtO/PnO methods on 8 problems, including a new industrial dataset for combinatorial advertising that will be released. Our study shows that PnO approaches are better than PtO on 7 out of 8 benchmarks, but there is no silver bullet found for the specific design choices of PnO. A comprehensive categorization of current approaches and integration of typical scenarios are provided under a unified benchmark. Therefore, this paper could serve as a comprehensive benchmark for future PnO approach development and also offer fast prototyping for application-focused development. The code is available at \url{https://github.com/Thinklab-SJTU/PredictiveCO-Benchmark}.

Poster
Extracting Training Data from Molecular Pre-trained Models

Renhong Huang, Jiarong Xu, Zhiming Yang, Xiang Si, Xin Jiang, Hanyang Yuan, Chunping Wang, Yang Yang

Expand abstract

Graph Neural Networks (GNNs) have significantly advanced the field of drug discovery, enhancing the speed and efficiency of molecular identification. However, training these GNNs demands vast amounts of molecular data, which has spurred the emergence of collaborative model-sharing initiatives. These initiatives facilitate the sharing of molecular pre-trained models among organizations without exposing proprietary training data. Despite the benefits, these molecular pre-trained models may still pose privacy risks. For example, malicious adversaries could perform data extraction attack to recover private training data, thereby threatening commercial secrets and collaborative trust. This work, for the first time, explores the risks of extracting private training molecular data from molecular pre-trained models. This task is nontrivial as the molecular pre-trained models are non-generative and exhibit a diversity of model architectures, which differs significantly from language and image models. To address these issues, we introduce a molecule generation approach and propose a novel, model-independent scoring function for selecting promising molecules. To efficiently reduce the search space of potential molecules, we further introduce a Molecule Extraction Policy Network for molecule extraction. Our experiments demonstrate that even with only query access to molecular pre-trained models, there is a considerable risk of extracting training data, challenging the assumption that model sharing alone provides adequate protection against data extraction attacks. Our codes are publicly available at: \url{https://github.com/renH2/Molextract}.

Poster
On Statistical Rates and Provably Efficient Criteria of Latent Diffusion Transformers (DiTs)

Jerry Yao-Chieh Hu, Weimin Wu, Zhuoru Li, Sophia Pi, Zhao Song, Han Liu

Expand abstract

We investigate the statistical and computational limits of latent **Di**ffusion **T**ransformers (**DiTs**) under the low-dimensional linear latent space assumption. Statistically, we study the universal approximation and sample complexity of the DiTs score function, as well as the distribution recovery property of the initial data. Specifically, under mild data assumptions, we derive an approximation error bound for the score network of latent DiTs, which is sub-linear in the latent space dimension. Additionally, we derive the corresponding sample complexity bound and show that the data distribution generated from the estimated score function converges toward a proximate area of the original one. Computationally, we characterize the hardness of both forward inference and backward computation of latent DiTs, assuming the Strong Exponential Time Hypothesis (SETH). For forward inference, we identify efficient criteria for all possible latent DiTs inference algorithms and showcase our theory by pushing the efficiency toward almost-linear time inference. For backward computation, we leverage the low-rank structure within the gradient computation of DiTs training for possible algorithmic speedup. Specifically, we show that such speedup achieves almost-linear time latent DiTs training by casting the DiTs gradient as a series of chained low-rank approximations with bounded error. Under the low-dimensional assumption, we show that the statistical rates and the computational efficiency are all dominated by the dimension of the subspace, suggesting that latent DiTs have the potential to bypass the challenges associated with the high dimensionality of initial data.

Poster
Are Multiple Instance Learning Algorithms Learnable for Instances?

Jaeseok Jang, Hyuk-Yoon Kwon

Expand abstract

Multiple Instance Learning (MIL) has been increasingly adopted to mitigate the high costs and complexity associated with labeling individual instances, learning instead from bags of instances labeled at the bag level and enabling instance-level labeling. While existing research has primarily focused on the learnability of MIL at the bag level, there is an absence of theoretical exploration to check if a given MIL algorithm is learnable at the instance level. This paper proposes a theoretical framework based on probably approximately correct (PAC) learning theory to assess the instance-level learnability of deep multiple instance learning (Deep MIL) algorithms. Our analysis exposes significant gaps between current Deep MIL algorithms, highlighting the theoretical conditions that must be satisfied by MIL algorithms to ensure instance-level learnability. With these conditions, we interpret the learnability of the representative Deep MIL algorithms and validate them through empirical studies.

Poster
Learning Truncated Causal History Model for Video Restoration

Amirhosein Ghasemabadi, Muhammad Kamran Janjua, Mohammad Salameh, Di Niu

Expand abstract

One key challenge to video restoration is to model the transition dynamics of video frames governed by motion. In this work, we propose Turtle to learn the truncated causal history model for efficient and high-performing video restoration. Unlike traditional methods that process a range of contextual frames in parallel, Turtle enhances efficiency by storing and summarizing a truncated history of the input frame latent representation into an evolving historical state. This is achieved through a sophisticated similarity-based retrieval mechanism that implicitly accounts for inter-frame motion and alignment. The causal design in Turtle enables recurrence in inference through state-memorized historical features while allowing parallel training by sampling truncated video clips. We report new state-of-the-art results on a multitude of video restoration benchmark tasks, including video desnowing, nighttime video deraining, video raindrops and rain streak removal, video super-resolution, real-world and synthetic video deblurring, and blind video denoising while reducing the computational cost compared to existing best contextual methods on all these tasks.

Poster
Causal discovery with endogenous context variables

Wiebke Günther, Oana-Iuliana Popescu, Martin Rabel, Urmi Ninad, Andreas Gerhardus, Jakob Runge

Expand abstract

Systems with variations of the underlying generating mechanism between different contexts, i.e., different environments or internal states in which the system operates, are common in the real world, such as soil moisture regimes in Earth science. Besides understanding the shared properties of the system, in practice, the question of context-specific properties, i.e., the change in causal relationships between contexts, arises. For real-world data, contexts are often driven by system variables, e.g., precipitation highly influences soil moisture. Nevertheless, this setup needs to be studied more. To account for such endogenous contexts in causal discovery, our work proposes a constraint-based method that can efficiently discover context-specific causal graphs using an adaptive testing approach. Our approach tests conditional independence on the pooled datasets to infer the dependence between system variables, including the context, to avoid introducing selection bias. To yield context-specific insights, conditional independence is tested on context-specific data. We work out the theoretical framework for this adaptive testing approach and give a detailed discussion of the connection to structural causal models, including sufficiency assumptions, which allow to prove the soundness of our algorithm and to interpret the results causally. A simulation study to evaluate numerical properties shows that our approach behaves as expected, but also leads to a further understanding of current limitations and viable extensions.

Poster
Distributional regression: CRPS-error bounds for model fitting, model selection and convex aggregation

Dombry Clement, Ahmed Zaoui

Expand abstract

Distributional regression aims at estimating the conditional distribution of a target variable given explanatory co-variates. It is a crucial tool for forecasting when a precise uncertainty quantification is required. A popular methodology consists in fitting a parametric model via empirical risk minimization where the risk is measured by the Continuous Rank Probability Score (CRPS). For independent and identically distributed observations, we provide a concentration result for the estimation error and an upper bound for its expectation. Furthermore, we consider model selection performed by minimization of the validation error and provide a concentration bound for the regret. A similar result is proved for convex aggregation of models. Finally, we show that our results may be applied to various models such as EMOS, distributional regression networks, distributional nearest neighbours or distributional random forests and we illustrate our findings on two data sets (QSAR aquatic toxicity and Airfoil self-noise).

Poster
Training-Free Adaptive Diffusion with Bounded Difference Approximation Strategy

Hancheng Ye, Jiakang Yuan, Renqiu Xia, Xiangchao Yan, Tao Chen, Junchi Yan, Botian Shi, Bo Zhang

Expand abstract

Diffusion models have recently achieved great success in the synthesis of high-quality images and videos. However, the existing denoising techniques in diffusion models are commonly based on step-by-step noise predictions, which suffers from high computation cost, resulting in a prohibitive latency for interactive applications. In this paper, we propose AdaptiveDiffusion to relieve this bottleneck by adaptively reducing the noise prediction steps during the denoising process. Our method considers the potential of skipping as many noise prediction steps as possible while keeping the final denoised results identical to the original full-step ones. Specifically, the skipping strategy is guided by the third-order latent difference that indicates the stability between timesteps during the denoising process, which benefits the reusing of previous noise prediction results. Extensive experiments on image and video diffusion models demonstrate that our method can significantly speed up the denoising process while generating identical results to the original process, achieving up to an average 2-5x speedup without quality degradation. The code is available at https://github.com/UniModal4Reasoning/AdaptiveDiffusion

Poster
Generative Forests

Richard Nock, Mathieu Guillame-Bert

Expand abstract

We focus on generative AI for a type of data that still represent one of the most prevalent form of data: tabular data. We introduce a new powerful class of forest-based models fit for such tasks and a simple training algorithm with strong convergence guarantees in a boosting model that parallels that of the original weak / strong supervised learning setting. This algorithm can be implemented by a few tweaks to the most popular induction scheme for decision tree induction (*i.e. supervised learning*) with two classes. Experiments on the quality of generated data display substantial improvements compared to the state of the art. The losses our algorithm minimize and the structure of our models make them practical for related tasks that require fast estimation of a density given a generative model and an observation (even partially specified): such tasks include missing data imputation and density estimation. Additional experiments on these tasks reveal that our models can be notably good contenders to diverse state of the art methods, relying on models as diverse as (or mixing elements of) trees, neural nets, kernels or graphical models.

Poster
Credit Attribution and Stable Compression

Roi Livni, Shay Moran, Kobbi Nissim, Chirag Pabbaraju

Expand abstract

Credit attribution is crucial across various fields. In academic research, proper citation acknowledges prior work and establishes original contributions. Similarly, in generative models, such as those trained on existing artworks or music, it is important to ensure that any generated content influenced by these works appropriately credits the original creators. We study credit attribution by machine learning algorithms. We propose new definitions--relaxations of Differential Privacy--that weaken the stability guarantees for a designated subset of $k$ datapoints. These $k$ datapoints can be used non-stably with permission from their owners, potentially in exchange for compensation. Meanwhile, the remaining datapoints are guaranteed to have no significant influence on the algorithm's output. Our framework extends well-studied notions of stability, including Differential Privacy ($k = 0$), differentially private learning with public data (where the $k$ public datapoints are fixed in advance), and stable sample compression (where the $k$ datapoints are selected adaptively by the algorithm). We examine the expressive power of these stability notions within the PAC learning framework, provide a comprehensive characterization of learnability for algorithms adhering to these principles, and propose directions and questions for future research.

Poster
A Hitchhiker's Guide to Fine-Grained Face Forgery Detection Using Common Sense Reasoning

Niki Foteinopoulou, Enjie Ghorbel, Djamila Aouada

Expand abstract

Explainability in artificial intelligence is crucial for restoring trust, particularly in areas like face forgery detection, where viewers often struggle to distinguish between real and fabricated content. Vision and Large Language Models (VLLM) bridge computer vision and natural language, offering numerous applications driven by strong common-sense reasoning. Despite their success in various tasks, the potential of vision and language remains underexplored in face forgery detection, where they hold promise for enhancing explainability by leveraging the intrinsic reasoning capabilities of language to analyse fine-grained manipulation areas. For that reason, few works have recently started to frame the problem of deepfake detection as a Visual Question Answering (VQA) task, nevertheless omitting the realistic and informative open-ended multi-label setting. With the rapid advances in the field of VLLM, an exponential rise of investigations in that direction is expected. As such, there is a need for a clear experimental methodology that converts face forgery detection to a Visual Question Answering (VQA) task to systematically and fairly evaluate different VLLM architectures. Previous evaluation studies in deepfake detection have mostly focused on the simpler binary task, overlooking evaluation protocols for multi-label fine-grained detection and text-generative models. We propose a multi-staged approach that diverges from the traditional binary evaluation protocol and conducts a comprehensive evaluation study to compare the capabilities of several VLLMs in this context. In the first stage, we assess the models' performance on the binary task and their sensitivity to given instructions using several prompts. In the second stage, we delve deeper into fine-grained detection by identifying areas of manipulation in a multiple-choice VQA setting. In the third stage, we convert the fine-grained detection to an open-ended question and compare several matching strategies for the multi-label classification task. Finally, we qualitatively evaluate the fine-grained responses of the VLLMs included in the benchmark. We apply our benchmark to several popular models, providing a detailed comparison of binary, multiple-choice, and open-ended VQA evaluation across seven datasets. \url{https://nickyfot.github.io/hitchhickersguide.github.io/}

Poster
Robust Reinforcement Learning from Corrupted Human Feedback

Alexander Bukharin, Ilgee Hong, Haoming Jiang, Zichong Li, Qingru Zhang, Zixuan Zhang, Tuo Zhao

Expand abstract

Reinforcement learning from human feedback (RLHF) provides a principled framework for aligning AI systems with human preference data. For various reasons, e.g., personal bias, context ambiguity, lack of training, etc, human annotators may give incorrect or inconsistent preference labels. To tackle this challenge, we propose a robust RLHF approach -- $R^3M$, which models the potentially corrupted preference label as sparse outliers. Accordingly, we formulate the robust reward learning as an $\ell_1$-regularized maximum likelihood estimation problem. Computationally, we develop an efficient alternating optimization algorithm, which only incurs negligible computational overhead compared with the standard RLHF approach. Theoretically, we prove that under proper regularity conditions, $R^3M$ can consistently learn the underlying reward and identify outliers, provided that the number of outlier labels scales sublinearly with the preference sample size. Furthermore, we remark that $R^3M$ is versatile and can be extended to various preference optimization methods, including direct preference optimization (DPO). Our experiments on robotic control and natural language generation with large language models (LLMs) show that $R^3M$ improves robustness of the reward against several types of perturbations to the preference data.

Poster
Improving Deep Reinforcement Learning by Reducing the Chain Effect of Value and Policy Churn

Hongyao Tang, Glen Berseth

Expand abstract

Deep neural networks provide Reinforcement Learning (RL) powerful function approximators to address large-scale decision-making problems. However, these approximators introduce challenges due to the non-stationary nature of RL training. One source of the challenges in RL is that output predictions can churn, leading to uncontrolled changes after each batch update for states not included in the batch. Although such a churn phenomenon exists in each step of network training, it remains under-explored on how churn occurs and impacts RL. In this work, we start by characterizing churn in a view of Generalized Policy Iteration with function approximation, and we discover a chain effect of churn that leads to a cycle where the churns in value estimation and policy improvement compound and bias the learning dynamics throughout the iteration. Further, we concretize the study and focus on the learning issues caused by the chain effect in different settings, including greedy action deviation in value-based methods, trust region violation in proximal policy optimization, and dual bias of policy value in actor-critic methods. We then propose a method to reduce the chain effect across different settings, called Churn Approximated ReductIoN (CHAIN), which can be easily plugged into most existing DRL algorithms. Our experiments demonstrate the effectiveness of our method in both reducing churn and improving learning performance across online and offline, value-based and policy-based RL settings.

Poster
Private Geometric Median

Mahdi Haghifam, Thomas Steinke, Jonathan Ullman

Expand abstract

In this paper, we study differentially private (DP) algorithms for computing the geometric median (GM) of a dataset: Given $n$ points, $x_1,\dots,x_n$ in $\mathbb{R}^d$, the goal is to find a point $\theta$ that minimizes the sum of the Euclidean distances to these points, i.e., $\sum_{i=1}^{n} \lVert|\theta - x_i\rVert_2$. Off-the-shelf methods, such as DP-GD, require strong a priori knowledge locating the data within a ball of radius $R$, and the excess risk of the algorithm depends linearly on $R$. In this paper, we ask: can we design an efficient and private algorithm with an excess error guarantee that scales with the (unknown) radius containing the majority of the datapoints? Our main contribution is a pair of polynomial-time DP algorithms for the task of private GM with an excess error guarantee that scales with the effective diameter of the datapoints. Additionally, we propose an inefficient algorithm based on the inverse smooth sensitivity mechanism, which satisfies the more restrictive notion of pure DP. We complement our results with a lower bound and demonstrate the optimality of our polynomial-time algorithms in terms of sample complexity.

Poster
Text-Guided Attention is All You Need for Zero-Shot Robustness in Vision-Language Models

Lu Yu, Haiyang Zhang, Changsheng Xu

Expand abstract

Due to the impressive zero-shot capabilities, pre-trained vision-language models (e.g. CLIP), have attracted widespread attention and adoption across various domains. Nonetheless, CLIP has been observed to be susceptible to adversarial examples. Through experimental analysis, we have observed a phenomenon wherein adversarial perturbations induce shifts in text-guided attention. Building upon this observation, we propose a simple yet effective strategy: Text-Guided Attention for Zero-Shot Robustness (TGA-ZSR). This framework incorporates two components: the Attention Refinement module and the Attention-based Model Constraint module. Our goal is to maintain the generalization of the CLIP model and enhance its adversarial robustness: The Attention Refinement module aligns the text-guided attention obtained from the target model via adversarial examples with the text-guided attention acquired from the original model via clean examples. This alignment enhances the model’s robustness. Additionally, the Attention-based Model Constraint module acquires text-guided attention from both the target and original models using clean examples. Its objective is to maintain model performance on clean samples while enhancing overall robustness. The experiments validate that our method yields a 9.58% enhancement in zero-shot robust accuracy over the current state-of-the-art techniques across 16 datasets. Our code is available at https://github.com/zhyblue424/TGA-ZSR.

Poster
PACE: Marrying generalization in PArameter-efficient fine-tuning with Consistency rEgularization

Yao Ni, Shan Zhang, Piotr Koniusz

Expand abstract

Parameter-Efficient Fine-Tuning (PEFT) effectively adapts pre-trained transformers to downstream tasks. However, the optimization of tasks performance often comes at the cost of generalizability in fine-tuned models. To address this issue, we theoretically connect smaller weight gradient norms during training and larger datasets to the improvements in model generalization. Motivated by this connection, we propose reducing gradient norms for enhanced generalization and aligning fine-tuned model with the pre-trained counterpart to retain knowledge from large-scale pre-training data. Yet, naive alignment does not guarantee gradient reduction and can potentially cause gradient explosion, complicating efforts to manage gradients. To address such an issue, we propose PACE, marrying generalization of PArameter-efficient fine-tuning with Consistency rEgularization. We perturb features learned from the adapter with the multiplicative noise and ensure the fine-tuned model remains consistent for same sample under different perturbations. Theoretical analysis shows that PACE not only implicitly regularizes gradients for enhanced generalization, but also implicitly aligns the fine-tuned and pre-trained models to retain knowledge. Experimental evidence supports our theories. PACE surpasses existing PEFT methods in visual adaptation tasks (VTAB-1k, FGVC, few-shot learning, domain adaptation) showcasing its potential for resource-efficient fine-tuning. It also improves LoRA in text classification (GLUE) and mathematical reasoning (GSM-8K).

Spotlight
One-to-Multiple: A Progressive Style Transfer Unsupervised Domain-Adaptive Framework for Kidney Tumor Segmentation

Kai Hu, Jinhao Li, Yuan Zhang, Xiongjun Ye, Xieping Gao

Expand abstract

In multi-sequence Magnetic Resonance Imaging (MRI), the accurate segmentation of the kidney and tumor based on traditional supervised methods typically necessitates detailed annotation for each sequence, which is both time-consuming and labor-intensive. Unsupervised Domain Adaptation (UDA) methods can effectively mitigate inter-domain differences by aligning cross-modal features, thereby reducing the annotation burden. However, most existing UDA methods are limited to one-to-one domain adaptation, which tends to be inefficient and resource-intensive when faced with multi-target domain transfer tasks. To address this challenge, we propose a novel and efficient One-to-Multiple Progressive Style Transfer Unsupervised Domain-Adaptive (PSTUDA) framework for kidney and tumor segmentation in multi-sequence MRI. Specifically, we develop a multi-level style dictionary to explicitly store the style information of each target domain at various stages, which alleviates the burden of a single generator in a multi-target transfer task and enables effective decoupling of content and style. Concurrently, we employ multiple cascading style fusion modules that utilize point-wise instance normalization to progressively recombine content and style features, which enhances cross-modal alignment and structural consistency. Experiments conducted on the private MSKT and public KiTS19 datasets demonstrate the superiority of the proposed PSTUDA over comparative methods in multi-sequence kidney and tumor segmentation. The average Dice Similarity Coefficients are increased by at least 1.8% and 3.9%, respectively. Impressively, our PSTUDA not only significantly reduces the floating-point computation by approximately 72% but also reduces the number of model parameters by about 50%, bringing higher efficiency and feasibility to practical clinical applications.

Poster
Stopping Bayesian Optimization with Probabilistic Regret Bounds

James T. Wilson

Expand abstract

Bayesian optimization is a popular framework for efficiently tackling black-box search problems. As a rule, these algorithms operate by iteratively choosing what to evaluate next until some predefined budget has been exhausted. We investigate replacing this de facto stopping rule with criteria based on the probability that a point satisfies a given set of conditions. We focus on the prototypical example of an $(\epsilon, \delta)$-criterion: stop when a solution has been found whose value is within $\epsilon > 0$ of the optimum with probability at least $1 - \delta$ under the model. For Gaussian process priors, we show that Bayesian optimization satisfies this criterion under mild technical assumptions. Further, we give a practical algorithm for evaluating Monte Carlo stopping rules in a manner that is both sample efficient and robust to estimation error. These findings are accompanied by empirical results which demonstrate the strengths and weaknesses of the proposed approach.

Poster