Sample Efficient Graph-Based Optimization with Noisy Observations
Queensland University of Technology（昆士兰科技大学）；Stanford University（斯坦福大学）；Adobe Research（奥多比研究中心）；Google Research（谷歌研究中心）
Tan Nguyen, Ali Shameli, Yasin Abbasi-Yadkori, Anup Rao, Branislav Kveton
备注：
The first version of this paper appeared in AISTATS 2019. Thank to community feedback, some typos and a minor issue have been identified. Specifically, on page 4, column 2, line 18, the statement $Δ_{1,s} \ge (1+m)^{S-1-s} Δ_1$ is not valid, and in the proof of Theorem 2, "By Lemma 1" should be "By Definition 2". These problems are fixed in this updated version published here on arxiv
We study sample complexity of optimizing "hill-climbing friendly" functions defined on a graph under noisy observations. We define a notion of convexity, and we show that a variant of best-arm identification can find a near-optimal solution after a small number of queries that is independent of the size of the graph. For functions that have local minima and are nearly convex, we show a sample complexity for the classical simulated annealing under noisy observations. We show effectiveness of the greedy algorithm with restarts and the simulated annealing on problems of graph-based nearest neighbor classification as well as a web document re-ranking application.
Indian Institute of Technology Madras（印度理工学院马德拉斯分校）
We introduce biased gradient oracles to capture a setting where the function measurements have an estimation error that can be controlled through a batch size parameter. Our proposed oracles are appealing in several practical contexts, for instance, risk measure estimation from a batch of independent and identically distributed (i.i.d.) samples, or simulation optimization, where the function measurements are `biased' due to computational constraints. In either case, increasing the batch size reduces the estimation error. We highlight the applicability of our biased gradient oracles in a risk-s…
UAV Trajectory Optimization via Improved Noisy Deep Q-Network
Dept. of Computer Science（计算机科学系）；Wenzhou-Kean University（温州市凯恩大学）；School of Electrical and Computer Engineering（电气与计算机工程学院）；University of Tehran（伊朗塔里班大学）；School of Computer Science and Info. Eng.（计算机科学与信息工程学院）；Qilu Institute of Technology（青岛理工学院）
Learning in Quantum Control: High-Dimensional Global Optimization for Noisy Quantum Dynamics
University of Calgary（卡尔加里大学）；ICFO-The Institute of Photonic Sciences（光子科学研究所（ICFO））；Canadian Institute for Advanced Research（加拿大高等研究院）；University of Science and Technology of China（中国科学技术大学）
Bosch Center for Artificial Intelligence（博世人工智能中心）；ETH Zürich（苏黎世联邦理工学院）
We consider the problem of robust optimization within the well-established Bayesian optimization (BO) framework. While BO is intrinsically robust to noisy evaluations of the objective function, standard approaches do not consider the case of uncertainty about the input parameters. In this paper, we propose Noisy-Input Entropy Search (NES), a novel information-theoretic acquisition function that is designed to find robust optima for problems with both input and measurement noise. NES is based on the key insight that the robust objective in many cases can be modeled as a Gaussian process, howeve…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Carnegie Mellon University（卡内基梅隆大学）
We study the problem of black-box optimization of a noisy function in the presence of low-cost approximations or fidelities, which is motivated by problems like hyper-parameter tuning. In hyper-parameter tuning evaluating the black-box function at a point involves training a learning algorithm on a large data-set at a particular hyper-parameter and evaluating the validation error. Even a single such evaluation can be prohibitively expensive. Therefore, it is beneficial to use low-cost approximations, like training the learning algorithm on a sub-sampled version of the whole data-set. These low…
Many existing fairness criteria for machine learning involve equalizing some metric across protected groups such as race or gender. However, practitioners trying to audit or enforce such group-based criteria can easily face the problem of noisy or biased protected group information. First, we study the consequences of naively relying on noisy protected group labels: we provide an upper bound on the fairness violations on the true groups G when the fairness criteria are satisfied on noisy groups $\hat{G}$. Second, we introduce two new approaches using robust optimization that, unlike the naive …
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error. Bayesian optimization is a promising technique for efficiently optimizing multiple continuous parameters, but existing approaches degrade in performance when the noise level is high, limiting its applicability to many randomized experiments. We derive an expression for expected improvement under greedy batch optimization with noisy observations and noisy co…
Deep neural networks (DNNs) trained on large-scale datasets have exhibited significant performance in image classification. Many large-scale datasets are collected from websites, however they tend to contain inaccurate labels that are termed as noisy labels. Training on such noisy labeled datasets causes performance degradation because DNNs easily overfit to noisy labels. To overcome this problem, we propose a joint optimization framework of learning DNN parameters and estimating true labels. Our framework can correct labels during training by alternating update of network parameters and label…
University of Alberta（阿尔伯塔大学）；Indian Institute of Technology Madras（马德拉斯印度理工学院）；Imperial College London（伦敦帝国理工学院）
Algorithms for bandit convex optimization and online learning often rely on constructing noisy gradient estimates, which are then used in appropriately adjusted first-order algorithms, replacing actual gradients. Depending on the properties of the function to be optimized and the nature of ``noise'' in the bandit feedback, the bias and variance of gradient estimates exhibit various tradeoffs. In this paper we propose a novel framework that replaces the specific gradient estimation methods with an abstract oracle. With the help of the new framework we unify previous works, reproducing their res…
Deep neural networks (DNNs) suffer from noisy-labeled data because of the risk of overfitting. To avoid the risk, in this paper, we propose a novel DNN training method with sample selection based on adaptive k-set selection, which selects k (< n) clean sample candidates from the whole n noisy training samples at each epoch. It has a strong advantage of guaranteeing the performance of the selection theoretically. Roughly speaking, a regret, which is defined by the difference between the actual selection and the best selection, of the proposed method is theoretically bounded, even though the bes…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Parallel surrogate optimization algorithms have proven to be efficient methods for solving expensive noisy optimization problems. In this work we develop a new parallel surrogate optimization algorithm (ProSRS), using a novel tree-based "zoom strategy" to improve the efficiency of the algorithm. We prove that if ProSRS is run for sufficiently long, with probability converging to one there will be at least one point among all the evaluations that will be arbitrarily close to the global minimum. We compare our algorithm to several state-of-the-art Bayesian optimization algorithms on a suite of s…
The Chinese University of Hong Kong（香港中文大学）；Tencent（腾讯）
Noisy labels are ubiquitous in real-world datasets, which poses a challenge for robustly training deep neural networks (DNNs) since DNNs can easily overfit to the noisy labels. Most recent efforts have been devoted to defending noisy labels by discarding noisy samples from the training set or assigning weights to training samples, where the weight associated with a noisy sample is expected to be small. Thereby, these previous efforts result in a waste of samples, especially those assigned with small weights. The input $x$ is always useful regardless of whether its observed label $y$ is clean. …
Pohang University of Science and Technology（浦项科技大学）；Seoul National University of Science and Technology (SeoulTech)（首尔国立科技大学（首尔科技大学））
Because deep learning is vulnerable to noisy labels, sample selection techniques, which train networks with only clean labeled data, have attracted a great attention. However, if the labels are dominantly corrupted by few classes, these noisy samples are called dominant-noisy-labeled samples, the network also learns dominant-noisy-labeled samples rapidly via content-aware optimization. In this study, we propose a compelling criteria to penalize dominant-noisy-labeled samples intensively through class-wise penalty labels. By averaging prediction confidences for the each observed label, we obtai…
Implicit feedback data is extensively explored in recommendation as it is easy to collect and generally applicable. However, predicting users' preference on implicit feedback data is a challenging task since we can only observe positive (voted) samples and unvoted samples. It is difficult to distinguish between the negative samples and unlabeled positive samples from the unvoted ones. Existing works, such as Bayesian Personalized Ranking (BPR), sample unvoted items as negative samples uniformly, therefore suffer from a critical noisy-label issue. To address this gap, we design an adaptive samp…
This paper is concerned with low-rank matrix optimization, which has found a wide range of applications in machine learning. This problem in the special case of matrix sensing has been studied extensively through the notion of Restricted Isometry Property (RIP), leading to a wealth of results on the geometric landscape of the problem and the convergence rate of common algorithms. However, the existing results can handle the problem in the case with a general objective function subject to noisy data only when the RIP constant is close to 0. In this paper, we develop a new mathematical framework…
One-step abductive multi-target learning (OSAMTL) was proposed to handle complex noisy labels. In this paper, giving definition of diverse noisy label samples (DNLS), we propose one-step abductive multi-target learning with DNLS (OSAMTL-DNLS) to expand the methodology of original OSAMTL to better handle complex noisy labels.
In black-box optimization problems, we aim to maximize an unknown objective function, where the function is only accessible through feedbacks of an evaluation or simulation oracle. In real-life, the feedbacks of such oracles are often noisy and available after some unknown delay that may depend on the computation time of the oracle. Additionally, if the exact evaluations are expensive but coarse approximations are available at a lower cost, the feedbacks can have multi-fidelity. In order to address this problem, we propose a generic extension of hierarchical optimistic tree search (HOO), calle…
University of California, Berkeley（加州大学伯克利分校）；Columbia University（哥伦比亚大学）；University of Michigan（密歇根大学）
Causal inference from observational datasets often relies on measuring and adjusting for covariates. In practice, measurements of the covariates can often be noisy and/or biased, or only measurements of their proxies may be available. Directly adjusting for these imperfect measurements of the covariates can lead to biased causal estimates. Moreover, without additional assumptions, the causal effects are not point-identifiable due to the noise in these measurements. To this end, we study the partial identification of causal effects given noisy covariates, under a user-specified assumption on th…
Center for Advanced Medical Computing and Analysis, Massachusetts General Hospital and Harvard Medical School（麻省总医院与哈佛医学院高级医学计算与分析中心）；Gordon Center for Medical Imaging, Massachusetts General Hospital and Harvard Medical School（麻省总医院与哈佛医学院戈登医学成像中心）
Deep neural networks have been proved efficient for medical image denoising. Current training methods require both noisy and clean images. However, clean images cannot be acquired for many practical medical applications due to naturally noisy signal, such as dynamic imaging, spectral computed tomography, arterial spin labeling magnetic resonance imaging, etc. In this paper we proposed a training method which learned denoising neural networks from noisy training samples only. Training data in the acquisition domain was split to two subsets and the network was trained to map one noisy set to the…
Modern deep neural networks (DNNs) become frail when the datasets contain noisy (incorrect) class labels. Robust techniques in the presence of noisy labels can be categorized into two folds: developing noise-robust functions or using noise-cleansing methods by detecting the noisy data. Recently, noise-cleansing methods have been considered as the most competitive noisy-label learning algorithms. Despite their success, their noisy label detectors are often based on heuristics more than a theory, requiring a robust classifier to predict the noisy data with loss values. In this paper, we propose …
Optimization plays a key role in the training of deep neural networks. Deciding when to stop training can have a substantial impact on the performance of the network during inference. Under certain conditions, the generalization error can display a double descent pattern during training: the learning curve is non-monotonic and seemingly diverges before converging again after additional epochs. This optimization pattern can lead to early stopping procedures to stop training before the second convergence and consequently select a suboptimal set of parameters for the network, with worse performan…
Massachusetts Institute of Technology（麻省理工学院）；South China University of Technology（华南理工大学）；Takeda Pharmaceuticals Co., Ltd.（武田药品工业株式会社）
Data lies at the core of modern deep learning. The impressive performance of supervised learning is built upon a base of massive accurately labeled data. However, in some real-world applications, accurate labeling might not be viable; instead, multiple noisy labels (instead of one accurate label) are provided by several annotators for each data sample. Learning a classifier on such a noisy training dataset is a challenging task. Previous approaches usually assume that all data samples share the same set of parameters related to annotator errors, while we demonstrate that label error learning s…
SGD does not produce robust results on datasets with label noise. Because the gradients calculated according to the losses of the noisy samples cause the optimization process to go in the wrong direction. In this paper, as an alternative to SGD, we recommend using samples with loss less than a threshold value determined during the optimization process, instead of using all samples in the mini-batch. Our proposed method, Adaptive-k, aims to exclude label noise samples from the optimization process and make the process robust. On noisy datasets, we found that using a threshold-based approach, su…
Harvard University（哈佛大学）；Vector Institute for Artificial Intelligence（矢量人工智能研究所）；University of Toronto（多伦多大学）；Atinary Technologies Sàrl（阿蒂纳里技术有限公司）
Research challenges encountered across science, engineering, and economics can frequently be formulated as optimization tasks. In chemistry and materials science, recent growth in laboratory digitization and automation has sparked interest in optimization-guided autonomous discovery and closed-loop experimentation. Experiment planning strategies based on off-the-shelf optimization algorithms can be employed in fully autonomous research platforms to achieve desired experimentation goals with the minimum number of trials. However, the experiment planning strategy that is most suitable to a scien…
Machine Learning Department, Carnegie Mellon University（卡内基梅隆大学机器学习系）；Department of Statistics and Data Science, Carnegie Mellon University（卡内基梅隆大学统计与数据科学系）
We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy evaluations of function values at the queried points (i.e. the algorithm has access to zeroth-order information). Optimization performance is evaluated by the expected difference of function values at the estimated optimum and the true optimum. In contrast to the classical optimization setup, first-order information like gradients are not directly accessibl…
Learning with Imbalanced Noisy Data by Preventing Bias in Sample Selection
School of Computer Science and Engineering, Nanjing University of Science and Technology（南京理工大学计算机科学与工程学院）；Terminus Group（特步集团）；School of Electronic and Information Engineering, Tongji University（同济大学电子与信息工程学院）
Chung-Ang University（中央大学）；University of Copenhagen（哥本哈根大学）
Regularization is essential for avoiding over-fitting to training data in network optimization, leading to better generalization of the trained networks. The label noise provides a strong implicit regularization by replacing the target ground truth labels of training examples by uniform random labels. However, it can cause undesirable misleading gradients due to the large loss associated with incorrect labels. We propose a first-order optimization method (Label-Noised Trim-SGD) that uses the label noise with the example trimming in order to remove the outliers based on the loss. The proposed a…
Optimizing multiple competing black-box objectives is a challenging problem in many fields, including science, engineering, and machine learning. Multi-objective Bayesian optimization (MOBO) is a sample-efficient approach for identifying the optimal trade-offs between the objectives. However, many existing methods perform poorly when the observations are corrupted by noise. We propose a novel acquisition function, NEHVI, that overcomes this important practical limitation by applying a Bayesian treatment to the popular expected hypervolume improvement (EHVI) criterion and integrating over this …
We investigate the effectiveness of convex relaxation and nonconvex optimization in solving bilinear systems of equations under two different designs (i.e.$~$a sort of random Fourier design and Gaussian design). Despite the wide applicability, the theoretical understanding about these two paradigms remains largely inadequate in the presence of random noise. The current paper makes two contributions by demonstrating that: (1) a two-stage nonconvex algorithm attains minimax-optimal accuracy within a logarithmic number of iterations. (2) convex relaxation also achieves minimax-optimal statistical…
Nanjing University（南京大学）；Tencent AI Lab（腾讯人工智能实验室）
Learning with Noisy Labels (LNL) has attracted significant attention from the research community. Many recent LNL methods rely on the assumption that clean samples tend to have "small loss". However, this assumption always fails to generalize to some real-world cases with imbalanced subpopulations, i.e., training subpopulations varying in sample size or recognition difficulty. Therefore, recent LNL methods face the risk of misclassifying those "informative" samples (e.g., hard samples or samples in the tail subpopulations) into noisy samples, leading to poor generalization performance. To addr…
Imperial College London（帝国理工学院）；National University of Singapore（新加坡国立大学）
We consider the problem of Bayesian optimization of a one-dimensional Brownian motion in which the $T$ adaptively chosen observations are corrupted by Gaussian noise. We show that as the smallest possible expected cumulative regret and the smallest possible expected simple regret scale as $Ω(σ\sqrt{T / \log (T)}) \cap \mathcal{O}(σ\sqrt{T} \cdot \log T)$ and $Ω(σ/ \sqrt{T \log (T)}) \cap \mathcal{O}(σ\log T / \sqrt{T})$ respectively, where $σ^2$ is the noise variance. Thus, our upper and lower bounds are tight up to a factor of $\mathcal{O}( (\log T)^{1.5} )$. The upper bound uses an algorithm…
Deargen Inc.（Deargen公司）；Deargen USA Inc.（Deargen美国公司）
The standard empirical risk minimization (ERM) can underperform on certain minority groups (i.e., waterbirds in lands or landbirds in water) due to the spurious correlation between the input and its label. Several studies have improved the worst-group accuracy by focusing on the high-loss samples. The hypothesis behind this is that such high-loss samples are \textit{spurious-cue-free} (SCF) samples. However, these approaches can be problematic since the high-loss samples may also be samples with noisy labels in the real-world scenarios. To resolve this issue, we utilize the predictive uncertai…
Samples with ground truth labels may not always be available in numerous domains. While learning from crowdsourcing labels has been explored, existing models can still fail in the presence of sparse, unreliable, or diverging annotations. Co-teaching methods have shown promising improvements for computer vision problems with noisy labels by employing two classifiers trained on each others' confident samples in each batch. Inspired by the idea of separating confident and uncertain samples during the training process, we extend it for the crowdsourcing problem. Our model, CrowdTeacher, uses the i…
Robust Federated Learning against Noisy Clients via Masked Optimization
Institute of Computing Technology, Chinese Academy of Sciences & University of Chinese Academy of Sciences（计算技术研究所，中国科学院及中国科学院大学）；Department of Electronic Engineering, The Chinese University of Hong Kong（电子工程系，香港中文大学）；Institute of Computing Technology, Chinese Academy of Sciences（计算技术研究所，中国科学院）
