arXiv subjects

Tianbao Yang

Publications and source records attributed to Tianbao Yang.

At least 91 records · Page 5Linked to original sources

arXiv2023

Large-scale Stochastic Optimization of NDCG Surrogates for Deep Learning with Provable Convergence

NDCG, namely Normalized Discounted Cumulative Gain, is a widely used ranking metric in information retrieval and machine learning. However, efficient and provable stochastic methods for maximizing NDCG are still lacking, especially for deep models. In this paper, we propose a principled approach to optimize NDCG and its top-$K$ variant. First, we formulate a novel compositional optimization problem for optimizing the NDCG surrogate, and a novel bilevel compositional optimization problem for optimizing the top-$K$ NDCG surrogate. Then, we develop efficient stochastic algorithms with provable convergence guarantees for the non-convex objectives. Different from existing NDCG optimization methods, the per-iteration complexity of our algorithms scales with the mini-batch size instead of the number of total items. To improve the effectiveness for deep learning, we further propose practical strategies by using initial warm-up and stop gradient operator. Experimental results on multiple datasets demonstrate that our methods outperform prior ranking approaches in terms of NDCG. To the best of our knowledge, this is the first time that stochastic algorithms are proposed to optimize NDCG with a provable convergence guarantee. Our proposed methods are implemented in the LibAUC library at https://libauc.org/.

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arXiv2022

Multi-block-Single-probe Variance Reduced Estimator for Coupled Compositional Optimization

Variance reduction techniques such as SPIDER/SARAH/STORM have been extensively studied to improve the convergence rates of stochastic non-convex optimization, which usually maintain and update a sequence of estimators for a single function across iterations. What if we need to track multiple functional mappings across iterations but only with access to stochastic samples of $\mathcal{O}(1)$ functional mappings at each iteration? There is an important application in solving an emerging family of coupled compositional optimization problems in the form of $\sum_{i=1}^m f_i(g_i(\mathbf{w}))$, where $g_i$ is accessible through a stochastic oracle. The key issue is to track and estimate a sequence of $\mathbf g(\mathbf{w})=(g_1(\mathbf{w}), \ldots, g_m(\mathbf{w}))$ across iterations, where $\mathbf g(\mathbf{w})$ has $m$ blocks and it is only allowed to probe $\mathcal{O}(1)$ blocks to attain their stochastic values and Jacobians. To improve the complexity for solving these problems, we propose a novel stochastic method named Multi-block-Single-probe Variance Reduced (MSVR) estimator to track the sequence of $\mathbf g(\mathbf{w})$. It is inspired by STORM but introduces a customized error correction term to alleviate the noise not only in stochastic samples for the selected blocks but also in those blocks that are not sampled. With the help of the MSVR estimator, we develop several algorithms for solving the aforementioned compositional problems with improved complexities across a spectrum of settings with non-convex/convex/strongly convex/Polyak-Łojasiewicz (PL) objectives. Our results improve upon prior ones in several aspects, including the order of sample complexities and dependence on the strong convexity parameter. Empirical studies on multi-task deep AUC maximization demonstrate the better performance of using the new estimator.

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arXiv2022

Multi-block Min-max Bilevel Optimization with Applications in Multi-task Deep AUC Maximization

In this paper, we study multi-block min-max bilevel optimization problems, where the upper level is non-convex strongly-concave minimax objective and the lower level is a strongly convex objective, and there are multiple blocks of dual variables and lower level problems. Due to the intertwined multi-block min-max bilevel structure, the computational cost at each iteration could be prohibitively high, especially with a large number of blocks. To tackle this challenge, we present a single-loop randomized stochastic algorithm, which requires updates for only a constant number of blocks at each iteration. Under some mild assumptions on the problem, we establish its sample complexity of $O(1/ε^4)$ for finding an $ε$-stationary point. This matches the optimal complexity for solving stochastic nonconvex optimization under a general unbiased stochastic oracle model. Moreover, we provide two applications of the proposed method in multi-task deep AUC (area under ROC curve) maximization and multi-task deep partial AUC maximization. Experimental results validate our theory and demonstrate the effectiveness of our method on problems with hundreds of tasks.

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arXiv2022

Large-scale Optimization of Partial AUC in a Range of False Positive Rates

The area under the ROC curve (AUC) is one of the most widely used performance measures for classification models in machine learning. However, it summarizes the true positive rates (TPRs) over all false positive rates (FPRs) in the ROC space, which may include the FPRs with no practical relevance in some applications. The partial AUC, as a generalization of the AUC, summarizes only the TPRs over a specific range of the FPRs and is thus a more suitable performance measure in many real-world situations. Although partial AUC optimization in a range of FPRs had been studied, existing algorithms are not scalable to big data and not applicable to deep learning. To address this challenge, we cast the problem into a non-smooth difference-of-convex (DC) program for any smooth predictive functions (e.g., deep neural networks), which allowed us to develop an efficient approximated gradient descent method based on the Moreau envelope smoothing technique, inspired by recent advances in non-smooth DC optimization. To increase the efficiency of large data processing, we used an efficient stochastic block coordinate update in our algorithm. Our proposed algorithm can also be used to minimize the sum of ranked range loss, which also lacks efficient solvers. We established a complexity of $\tilde O(1/ε^6)$ for finding a nearly $ε$-critical solution. Finally, we numerically demonstrated the effectiveness of our proposed algorithms for both partial AUC maximization and sum of ranked range loss minimization.

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arXiv2022

Optimal Algorithms for Stochastic Multi-Level Compositional Optimization

In this paper, we investigate the problem of stochastic multi-level compositional optimization, where the objective function is a composition of multiple smooth but possibly non-convex functions. Existing methods for solving this problem either suffer from sub-optimal sample complexities or need a huge batch size. To address these limitations, we propose a Stochastic Multi-level Variance Reduction method (SMVR), which achieves the optimal sample complexity of $\mathcal{O}\left(1 / ε^{3}\right)$ to find an $ε$-stationary point for non-convex objectives. Furthermore, when the objective function satisfies the convexity or Polyak-Łojasiewicz (PL) condition, we propose a stage-wise variant of SMVR and improve the sample complexity to $\mathcal{O}\left(1 / ε^{2}\right)$ for convex functions or $\mathcal{O}\left(1 /\left(με\right)\right)$ for non-convex functions satisfying the $μ$-PL condition. The latter result implies the same complexity for $μ$-strongly convex functions. To make use of adaptive learning rates, we also develop Adaptive SMVR, which achieves the same complexities but converges faster in practice. All our complexities match the lower bounds not only in terms of $ε$ but also in terms of $μ$ (for PL or strongly convex functions), without using a large batch size in each iteration.

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arXiv2022

Fairness via Adversarial Attribute Neighbourhood Robust Learning

Improving fairness between privileged and less-privileged sensitive attribute groups (e.g, {race, gender}) has attracted lots of attention. To enhance the model performs uniformly well in different sensitive attributes, we propose a principled \underline{R}obust \underline{A}dversarial \underline{A}ttribute \underline{N}eighbourhood (RAAN) loss to debias the classification head and promote a fairer representation distribution across different sensitive attribute groups. The key idea of RAAN is to mitigate the differences of biased representations between different sensitive attribute groups by assigning each sample an adversarial robust weight, which is defined on the representations of adversarial attribute neighbors, i.e, the samples from different protected groups. To provide efficient optimization algorithms, we cast the RAAN into a sum of coupled compositional functions and propose a stochastic adaptive (Adam-style) and non-adaptive (SGD-style) algorithm framework SCRAAN with provable theoretical guarantee. Extensive empirical studies on fairness-related benchmark datasets verify the effectiveness of the proposed method.

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arXiv2022

Provable Stochastic Optimization for Global Contrastive Learning: Small Batch Does Not Harm Performance

In this paper, we study contrastive learning from an optimization perspective, aiming to analyze and address a fundamental issue of existing contrastive learning methods that either rely on a large batch size or a large dictionary of feature vectors. We consider a global objective for contrastive learning, which contrasts each positive pair with all negative pairs for an anchor point. From the optimization perspective, we explain why existing methods such as SimCLR require a large batch size in order to achieve a satisfactory result. In order to remove such requirement, we propose a memory-efficient Stochastic Optimization algorithm for solving the Global objective of Contrastive Learning of Representations, named SogCLR. We show that its optimization error is negligible under a reasonable condition after a sufficient number of iterations or is diminishing for a slightly different global contrastive objective. Empirically, we demonstrate that SogCLR with small batch size (e.g., 256) can achieve similar performance as SimCLR with large batch size (e.g., 8192) on self-supervised learning task on ImageNet-1K. We also attempt to show that the proposed optimization technique is generic and can be applied to solving other contrastive losses, e.g., two-way contrastive losses for bimodal contrastive learning. The proposed method is implemented in our open-sourced library LibAUC (www.libauc.org).

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arXiv2022

AUC Maximization in the Era of Big Data and AI: A Survey

Area under the ROC curve, a.k.a. AUC, is a measure of choice for assessing the performance of a classifier for imbalanced data. AUC maximization refers to a learning paradigm that learns a predictive model by directly maximizing its AUC score. It has been studied for more than two decades dating back to late 90s and a huge amount of work has been devoted to AUC maximization since then. Recently, stochastic AUC maximization for big data and deep AUC maximization for deep learning have received increasing attention and yielded dramatic impact for solving real-world problems. However, to the best our knowledge there is no comprehensive survey of related works for AUC maximization. This paper aims to address the gap by reviewing the literature in the past two decades. We not only give a holistic view of the literature but also present detailed explanations and comparisons of different papers from formulations to algorithms and theoretical guarantees. We also identify and discuss remaining and emerging issues for deep AUC maximization, and provide suggestions on topics for future work.

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arXiv2022

Benchmarking Deep AUROC Optimization: Loss Functions and Algorithmic Choices

The area under the ROC curve (AUROC) has been vigorously applied for imbalanced classification and moreover combined with deep learning techniques. However, there is no existing work that provides sound information for peers to choose appropriate deep AUROC maximization techniques. In this work, we fill this gap from three aspects. (i) We benchmark a variety of loss functions with different algorithmic choices for deep AUROC optimization problem. We study the loss functions in two categories: pairwise loss and composite loss, which includes a total of 10 loss functions. Interestingly, we find composite loss, as an innovative loss function class, shows more competitive performance than pairwise loss from both training convergence and testing generalization perspectives. Nevertheless, data with more corrupted labels favors a pairwise symmetric loss. (ii) Moreover, we benchmark and highlight the essential algorithmic choices such as positive sampling rate, regularization, normalization/activation, and optimizers. Key findings include: higher positive sampling rate is likely to be beneficial for deep AUROC maximization; different datasets favors different weights of regularizations; appropriate normalization techniques, such as sigmoid and $\ell_2$ score normalization, could improve model performance. (iii) For optimization aspect, we benchmark SGD-type, Momentum-type, and Adam-type optimizers for both pairwise and composite loss. Our findings show that although Adam-type method is more competitive from training perspective, but it does not outperform others from testing perspective.

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arXiv2022

GraphFM: Improving Large-Scale GNN Training via Feature Momentum

Training of graph neural networks (GNNs) for large-scale node classification is challenging. A key difficulty lies in obtaining accurate hidden node representations while avoiding the neighborhood explosion problem. Here, we propose a new technique, named feature momentum (FM), that uses a momentum step to incorporate historical embeddings when updating feature representations. We develop two specific algorithms, known as GraphFM-IB and GraphFM-OB, that consider in-batch and out-of-batch data, respectively. GraphFM-IB applies FM to in-batch sampled data, while GraphFM-OB applies FM to out-of-batch data that are 1-hop neighborhood of in-batch data. We provide a convergence analysis for GraphFM-IB and some theoretical insight for GraphFM-OB. Empirically, we observe that GraphFM-IB can effectively alleviate the neighborhood explosion problem of existing methods. In addition, GraphFM-OB achieves promising performance on multiple large-scale graph datasets.

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arXiv2022

Smoothed Online Convex Optimization Based on Discounted-Normal-Predictor

In this paper, we investigate an online prediction strategy named as Discounted-Normal-Predictor (Kapralov and Panigrahy, 2010) for smoothed online convex optimization (SOCO), in which the learner needs to minimize not only the hitting cost but also the switching cost. In the setting of learning with expert advice, Daniely and Mansour (2019) demonstrate that Discounted-Normal-Predictor can be utilized to yield nearly optimal regret bounds over any interval, even in the presence of switching costs. Inspired by their results, we develop a simple algorithm for SOCO: Combining online gradient descent (OGD) with different step sizes sequentially by Discounted-Normal-Predictor. Despite its simplicity, we prove that it is able to minimize the adaptive regret with switching cost, i.e., attaining nearly optimal regret with switching cost on every interval. By exploiting the theoretical guarantee of OGD for dynamic regret, we further show that the proposed algorithm can minimize the dynamic regret with switching cost in every interval.

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arXiv2022

Momentum Accelerates the Convergence of Stochastic AUPRC Maximization

In this paper, we study stochastic optimization of areas under precision-recall curves (AUPRC), which is widely used for combating imbalanced classification tasks. Although a few methods have been proposed for maximizing AUPRC, stochastic optimization of AUPRC with convergence guarantee remains an undeveloped territory. A state-of-the-art complexity is $O(1/ε^5)$ for finding an $ε$-stationary solution. In this paper, we further improve the stochastic optimization of AURPC by (i) developing novel stochastic momentum methods with a better iteration complexity of $O(1/ε^4)$ for finding an $ε$-stationary solution; and (ii) designing a novel family of stochastic adaptive methods with the same iteration complexity, which enjoy faster convergence in practice. To this end, we propose two innovative techniques that are critical for improving the convergence: (i) the biased estimators for tracking individual ranking scores are updated in a randomized coordinate-wise manner; and (ii) a momentum update is used on top of the stochastic gradient estimator for tracking the gradient of the objective. The novel analysis of Adam-style updates is also one main contribution. Extensive experiments on various data sets demonstrate the effectiveness of the proposed algorithms. Of independent interest, the proposed stochastic momentum and adaptive algorithms are also applicable to a class of two-level stochastic dependent compositional optimization problems.

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arXiv2021

A Novel Convergence Analysis for Algorithms of the Adam Family

Since its invention in 2014, the Adam optimizer has received tremendous attention. On one hand, it has been widely used in deep learning and many variants have been proposed, while on the other hand their theoretical convergence property remains to be a mystery. It is far from satisfactory in the sense that some studies require strong assumptions about the updates, which are not necessarily applicable in practice, while other studies still follow the original problematic convergence analysis of Adam, which was shown to be not sufficient to ensure convergence. Although rigorous convergence analysis exists for Adam, they impose specific requirements on the update of the adaptive step size, which are not generic enough to cover many other variants of Adam. To address theses issues, in this extended abstract, we present a simple and generic proof of convergence for a family of Adam-style methods (including Adam, AMSGrad, Adabound, etc.). Our analysis only requires an increasing or large "momentum" parameter for the first-order moment, which is indeed the case used in practice, and a boundness condition on the adaptive factor of the step size, which applies to all variants of Adam under mild conditions of stochastic gradients. We also establish a variance diminishing result for the used stochastic gradient estimators. Indeed, our analysis of Adam is so simple and generic that it can be leveraged to establish the convergence for solving a broader family of non-convex optimization problems, including min-max, compositional, and bilevel optimization problems. For the full (earlier) version of this extended abstract, please refer to arXiv:2104.14840.

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arXiv2021

Simple Stochastic and Online Gradient Descent Algorithms for Pairwise Learning

Pairwise learning refers to learning tasks where the loss function depends on a pair of instances. It instantiates many important machine learning tasks such as bipartite ranking and metric learning. A popular approach to handle streaming data in pairwise learning is an online gradient descent (OGD) algorithm, where one needs to pair the current instance with a buffering set of previous instances with a sufficiently large size and therefore suffers from a scalability issue. In this paper, we propose simple stochastic and online gradient descent methods for pairwise learning. A notable difference from the existing studies is that we only pair the current instance with the previous one in building a gradient direction, which is efficient in both the storage and computational complexity. We develop novel stability results, optimization, and generalization error bounds for both convex and nonconvex as well as both smooth and nonsmooth problems. We introduce novel techniques to decouple the dependency of models and the previous instance in both the optimization and generalization analysis. Our study resolves an open question on developing meaningful generalization bounds for OGD using a buffering set with a very small fixed size. We also extend our algorithms and stability analysis to develop differentially private SGD algorithms for pairwise learning which significantly improves the existing results.

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arXiv2021

An Online Method for A Class of Distributionally Robust Optimization with Non-Convex Objectives

In this paper, we propose a practical online method for solving a class of distributionally robust optimization (DRO) with non-convex objectives, which has important applications in machine learning for improving the robustness of neural networks. In the literature, most methods for solving DRO are based on stochastic primal-dual methods. However, primal-dual methods for DRO suffer from several drawbacks: (1) manipulating a high-dimensional dual variable corresponding to the size of data is time expensive; (2) they are not friendly to online learning where data is coming sequentially. To address these issues, we consider a class of DRO with an KL divergence regularization on the dual variables, transform the min-max problem into a compositional minimization problem, and propose practical duality-free online stochastic methods without requiring a large mini-batch size. We establish the state-of-the-art complexities of the proposed methods with and without a Polyak-Łojasiewicz (PL) condition of the objective. Empirical studies on large-scale deep learning tasks (i) demonstrate that our method can speed up the training by more than 2 times than baseline methods and save days of training time on a large-scale dataset with $\sim$ 265K images, and (ii) verify the supreme performance of DRO over Empirical Risk Minimization (ERM) on imbalanced datasets. Of independent interest, the proposed method can be also used for solving a family of stochastic compositional problems with state-of-the-art complexities.

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arXiv2021

Deep AUC Maximization for Medical Image Classification: Challenges and Opportunities

In this extended abstract, we will present and discuss opportunities and challenges brought about by a new deep learning method by AUC maximization (aka \underline{\bf D}eep \underline{\bf A}UC \underline{\bf M}aximization or {\bf DAM}) for medical image classification. Since AUC (aka area under ROC curve) is a standard performance measure for medical image classification, hence directly optimizing AUC could achieve a better performance for learning a deep neural network than minimizing a traditional loss function (e.g., cross-entropy loss). Recently, there emerges a trend of using deep AUC maximization for large-scale medical image classification. In this paper, we will discuss these recent results by highlighting (i) the advancements brought by stochastic non-convex optimization algorithms for DAM; (ii) the promising results on various medical image classification problems. Then, we will discuss challenges and opportunities of DAM for medical image classification from three perspectives, feature learning, large-scale optimization, and learning trustworthy AI models.

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arXiv2021

Federated Deep AUC Maximization for Heterogeneous Data with a Constant Communication Complexity

Deep AUC (area under the ROC curve) Maximization (DAM) has attracted much attention recently due to its great potential for imbalanced data classification. However, the research on Federated Deep AUC Maximization (FDAM) is still limited. Compared with standard federated learning (FL) approaches that focus on decomposable minimization objectives, FDAM is more complicated due to its minimization objective is non-decomposable over individual examples. In this paper, we propose improved FDAM algorithms for heterogeneous data by solving the popular non-convex strongly-concave min-max formulation of DAM in a distributed fashion, which can also be applied to a class of non-convex strongly-concave min-max problems. A striking result of this paper is that the communication complexity of the proposed algorithm is a constant independent of the number of machines and also independent of the accuracy level, which improves an existing result by orders of magnitude. The experiments have demonstrated the effectiveness of our FDAM algorithm on benchmark datasets, and on medical chest X-ray images from different organizations. Our experiment shows that the performance of FDAM using data from multiple hospitals can improve the AUC score on testing data from a single hospital for detecting life-threatening diseases based on chest radiographs. The proposed method is implemented in our open-sourced library LibAUC (www.libauc.org) whose github address is https://github.com/Optimization-AI/ICML2021_FedDeepAUC_CODASCA.

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arXiv2021

Large-scale Robust Deep AUC Maximization: A New Surrogate Loss and Empirical Studies on Medical Image Classification

Deep AUC Maximization (DAM) is a new paradigm for learning a deep neural network by maximizing the AUC score of the model on a dataset. Most previous works of AUC maximization focus on the perspective of optimization by designing efficient stochastic algorithms, and studies on generalization performance of large-scale DAM on difficult tasks are missing. In this work, we aim to make DAM more practical for interesting real-world applications (e.g., medical image classification). First, we propose a new margin-based min-max surrogate loss function for the AUC score (named as AUC min-max-margin loss or simply AUC margin loss for short). It is more robust than the commonly used AUC square loss, while enjoying the same advantage in terms of large-scale stochastic optimization. Second, we conduct extensive empirical studies of our DAM method on four difficult medical image classification tasks, namely (i) classification of chest x-ray images for identifying many threatening diseases, (ii) classification of images of skin lesions for identifying melanoma, (iii) classification of mammogram for breast cancer screening, and (iv) classification of microscopic images for identifying tumor tissue. Our studies demonstrate that the proposed DAM method improves the performance of optimizing cross-entropy loss by a large margin, and also achieves better performance than optimizing the existing AUC square loss on these medical image classification tasks. Specifically, our DAM method has achieved the 1st place on Stanford CheXpert competition on Aug. 31, 2020. To the best of our knowledge, this is the first work that makes DAM succeed on large-scale medical image datasets. We also conduct extensive ablation studies to demonstrate the advantages of the new AUC margin loss over the AUC square loss on benchmark datasets. The proposed method is implemented in our open-sourced library LibAUC (www.libauc.org).

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