arXiv subjects

Tianbao Yang

Publications and source records attributed to Tianbao Yang.

At least 55 records · Page 3Linked to original sources

arXiv2024

Stochastic Approximation Approaches to Group Distributionally Robust Optimization and Beyond

This paper investigates group distributionally robust optimization (GDRO) with the goal of learning a model that performs well over $m$ different distributions. First, we formulate GDRO as a stochastic convex-concave saddle-point problem, which is then solved by stochastic mirror descent (SMD) with $m$ samples in each iteration, and attain a nearly optimal sample complexity. To reduce the number of samples required in each round from $m$ to 1, we cast GDRO as a two-player game, where one player conducts SMD and the other executes an online algorithm for non-oblivious multi-armed bandits, maintaining the same sample complexity. Next, we extend GDRO to address scenarios involving imbalanced data and heterogeneous distributions. In the first scenario, we introduce a weighted variant of GDRO, enabling distribution-dependent convergence rates that rely on the number of samples from each distribution. We design two strategies to meet the sample budget: one integrates non-uniform sampling into SMD, and the other employs the stochastic mirror-prox algorithm with mini-batches, both of which deliver faster rates for distributions with more samples. In the second scenario, we propose to optimize the average top-$k$ risk instead of the maximum risk, thereby mitigating the impact of outlier distributions. Similar to the case of vanilla GDRO, we develop two stochastic approaches: one uses $m$ samples per iteration via SMD, and the other consumes $k$ samples per iteration through an online algorithm for non-oblivious combinatorial semi-bandits.

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arXiv2024

Single-Loop Stochastic Algorithms for Difference of Max-Structured Weakly Convex Functions

In this paper, we study a class of non-smooth non-convex problems in the form of $\min_{x}[\max_{y\in Y}ϕ(x, y) - \max_{z\in Z}ψ(x, z)]$, where both $Φ(x) = \max_{y\in Y}ϕ(x, y)$ and $Ψ(x)=\max_{z\in Z}ψ(x, z)$ are weakly convex functions, and $ϕ(x, y), ψ(x, z)$ are strongly concave functions in terms of $y$ and $z$, respectively. It covers two families of problems that have been studied but are missing single-loop stochastic algorithms, i.e., difference of weakly convex functions and weakly convex strongly-concave min-max problems. We propose a stochastic Moreau envelope approximate gradient method dubbed SMAG, the first single-loop algorithm for solving these problems, and provide a state-of-the-art non-asymptotic convergence rate. The key idea of the design is to compute an approximate gradient of the Moreau envelopes of $Φ, Ψ$ using only one step of stochastic gradient update of the primal and dual variables. Empirically, we conduct experiments on positive-unlabeled (PU) learning and partial area under ROC curve (pAUC) optimization with an adversarial fairness regularizer to validate the effectiveness of our proposed algorithms.

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arXiv2024

Communication-Efficient Federated Group Distributionally Robust Optimization

Federated learning faces challenges due to the heterogeneity in data volumes and distributions at different clients, which can compromise model generalization ability to various distributions. Existing approaches to address this issue based on group distributionally robust optimization (GDRO) often lead to high communication and sample complexity. To this end, this work introduces algorithms tailored for communication-efficient Federated Group Distributionally Robust Optimization (FGDRO). Our contributions are threefold: Firstly, we introduce the FGDRO-CVaR algorithm, which optimizes the average top-K losses while reducing communication complexity to $O(1/ε^4)$, where $ε$ denotes the desired precision level. Secondly, our FGDRO-KL algorithm is crafted to optimize KL regularized FGDRO, cutting communication complexity to $O(1/ε^3)$. Lastly, we propose FGDRO-KL-Adam to utilize Adam-type local updates in FGDRO-KL, which not only maintains a communication cost of $O(1/ε^3)$ but also shows potential to surpass SGD-type local steps in practical applications. The effectiveness of our algorithms has been demonstrated on a variety of real-world tasks, including natural language processing and computer vision.

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arXiv2024

An Efficient Contrastive Unimodal Pretraining Method for EHR Time Series Data

Machine learning has revolutionized the modeling of clinical timeseries data. Using machine learning, a Deep Neural Network (DNN) can be automatically trained to learn a complex mapping of its input features for a desired task. This is particularly valuable in Electronic Health Record (EHR) databases, where patients often spend extended periods in intensive care units (ICUs). Machine learning serves as an efficient method for extract meaningful information. However, many state-of-the-art (SOTA) methods for training DNNs demand substantial volumes of labeled data, posing significant challenges for clinics in terms of cost and time. Self-supervised learning offers an alternative by allowing practitioners to extract valuable insights from data without the need for costly labels. Yet, current SOTA methods often necessitate large data batches to achieve optimal performance, increasing computational demands. This presents a challenge when working with long clinical timeseries data. To address this, we propose an efficient method of contrastive pretraining tailored for long clinical timeseries data. Our approach utilizes an estimator for negative pair comparison, enabling effective feature extraction. We assess the efficacy of our pretraining using standard self-supervised tasks such as linear evaluation and semi-supervised learning. Additionally, our model demonstrates the ability to impute missing measurements, providing clinicians with deeper insights into patient conditions. We demonstrate that our pretraining is capable of achieving better performance as both the size of the model and the size of the measurement vocabulary scale. Finally, we externally validate our model, trained on the MIMIC-III dataset, using the eICU dataset. We demonstrate that our model is capable of learning robust clinical information that is transferable to other clinics.

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arXiv2024

FastCLIP: A Suite of Optimization Techniques to Accelerate CLIP Training with Limited Resources

Existing studies of training state-of-the-art Contrastive Language-Image Pretraining (CLIP) models on large-scale data involve hundreds of or even thousands of GPUs due to the requirement of a large batch size. However, such a large amount of resources is not accessible to most people. While advanced compositional optimization techniques for optimizing global contrastive losses have been demonstrated effective for removing the requirement of large batch size, their performance on large-scale data remains underexplored and not optimized. To bridge the gap, this paper explores several aspects of CLIP training with limited resources (e.g., up to tens of GPUs). First, we introduce FastCLIP, a general CLIP training framework built on advanced compositional optimization techniques while designed and optimized for the distributed setting. Our framework is equipped with an efficient gradient reduction strategy to reduce communication overhead. Second, to further boost training efficiency, we investigate three components of the framework from an optimization perspective: the schedule of the inner learning rate, the update rules of the temperature parameter and the model parameters, respectively. Experiments on different strategies for each component shed light on how to conduct CLIP training more efficiently. Finally, we benchmark the performance of FastCLIP and the state-of-the-art training baseline (OpenCLIP) on different compute scales up to 32 GPUs on 8 nodes, and three data scales ranging from 2.7 million, 9.1 million to 315 million image-text pairs to demonstrate the significant improvement of FastCLIP in the resource-limited setting. We release the code of FastCLIP at https://github.com/Optimization-AI/fast_clip .

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arXiv2024

Non-Smooth Weakly-Convex Finite-sum Coupled Compositional Optimization

This paper investigates new families of compositional optimization problems, called $\underline{\bf n}$on-$\underline{\bf s}$mooth $\underline{\bf w}$eakly-$\underline{\bf c}$onvex $\underline{\bf f}$inite-sum $\underline{\bf c}$oupled $\underline{\bf c}$ompositional $\underline{\bf o}$ptimization (NSWC FCCO). There has been a growing interest in FCCO due to its wide-ranging applications in machine learning and AI, as well as its ability to address the shortcomings of stochastic algorithms based on empirical risk minimization. However, current research on FCCO presumes that both the inner and outer functions are smooth, limiting their potential to tackle a more diverse set of problems. Our research expands on this area by examining non-smooth weakly-convex FCCO, where the outer function is weakly convex and non-decreasing, and the inner function is weakly-convex. We analyze a single-loop algorithm and establish its complexity for finding an $ε$-stationary point of the Moreau envelop of the objective function. Additionally, we also extend the algorithm to solving novel non-smooth weakly-convex tri-level finite-sum coupled compositional optimization problems, which feature a nested arrangement of three functions. Lastly, we explore the applications of our algorithms in deep learning for two-way partial AUC maximization and multi-instance two-way partial AUC maximization, using empirical studies to showcase the effectiveness of the proposed algorithms.

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arXiv2024

Deterministic and Stochastic Accelerated Gradient Method for Convex Semi-Infinite Optimization

This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint parameters, a momentum gradient ascend step to update the dual variables, and a gradient descend step to update the primal variables. Our approach also extends to scenarios where gradients and function values are accessible solely through stochastic oracles. This method extends the recent primal-dual methods, for example, Hamedani and Aybat (2021); Boob et al. (2022), for optimization with a finite number of constraints. We show the iteration complexity of the proposed method for finding an $ε$-optimal solution under different convexity and concavity assumptions on the functions.

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arXiv2024

Efficient and Effective Implicit Dynamic Graph Neural Network

Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the oversmoothing of learned embeddings and long-range dependency being more pronounced in dynamic graphs, as features are aggregated both across neighborhood and time, no prior work has proposed an implicit graph neural model in a dynamic setting. In this paper, we present Implicit Dynamic Graph Neural Network (IDGNN) a novel implicit neural network for dynamic graphs which is the first of its kind. A key characteristic of IDGNN is that it demonstrably is well-posed, i.e., it is theoretically guaranteed to have a fixed-point representation. We then demonstrate that the standard iterative algorithm often used to train implicit models is computationally expensive in our dynamic setting as it involves computing gradients, which themselves have to be estimated in an iterative manner. To overcome this, we pose an equivalent bilevel optimization problem and propose an efficient single-loop training algorithm that avoids iterative computation by maintaining moving averages of key components of the gradients. We conduct extensive experiments on real-world datasets on both classification and regression tasks to demonstrate the superiority of our approach over the state-of-the-art baselines. We also demonstrate that our bi-level optimization framework maintains the performance of the expensive iterative algorithm while obtaining up to \textbf{1600x} speed-up.

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arXiv2024

To Cool or not to Cool? Temperature Network Meets Large Foundation Models via DRO

The temperature parameter plays a profound role during training and/or inference with large foundation models (LFMs) such as large language models (LLMs) and CLIP models. Particularly, it adjusts the logits in the softmax function in LLMs, which is crucial for next token generation, and it scales the similarities in the contrastive loss for training CLIP models. A significant question remains: Is it viable to learn a neural network to predict a personalized temperature of any input data for enhancing LFMs"? In this paper, we present a principled framework for learning a small yet generalizable temperature prediction network (TempNet) to improve LFMs. Our solution is composed of a novel learning framework with a robust loss underpinned by constrained distributionally robust optimization (DRO), and a properly designed TempNet with theoretical inspiration. TempNet can be trained together with a large foundation model from scratch or learned separately given a pretrained foundation model. It is not only useful for predicting personalized temperature to promote the training of LFMs but also generalizable and transferable to new tasks. Our experiments on LLMs and CLIP models demonstrate that TempNet greatly improves the performance of existing solutions or models, e.g. Table 1. The code to reproduce the experimental results in this paper can be found at https://github.com/zhqiu/TempNet.

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arXiv2024

Provable Optimization for Adversarial Fair Self-supervised Contrastive Learning

This paper studies learning fair encoders in a self-supervised learning (SSL) setting, in which all data are unlabeled and only a small portion of them are annotated with sensitive attribute. Adversarial fair representation learning is well suited for this scenario by minimizing a contrastive loss over unlabeled data while maximizing an adversarial loss of predicting the sensitive attribute over the data with sensitive attribute. Nevertheless, optimizing adversarial fair representation learning presents significant challenges due to solving a non-convex non-concave minimax game. The complexity deepens when incorporating a global contrastive loss that contrasts each anchor data point against all other examples. A central question is ``{\it can we design a provable yet efficient algorithm for solving adversarial fair self-supervised contrastive learning}?'' Building on advanced optimization techniques, we propose a stochastic algorithm dubbed SoFCLR with a convergence analysis under reasonable conditions without requring a large batch size. We conduct extensive experiments to demonstrate the effectiveness of the proposed approach for downstream classification with eight fairness notions.

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arXiv2024

Adaptive Preference Scaling for Reinforcement Learning with Human Feedback

Reinforcement learning from human feedback (RLHF) is a prevalent approach to align AI systems with human values by learning rewards from human preference data. Due to various reasons, however, such data typically takes the form of rankings over pairs of trajectory segments, which fails to capture the varying strengths of preferences across different pairs. In this paper, we propose a novel adaptive preference loss, underpinned by distributionally robust optimization (DRO), designed to address this uncertainty in preference strength. By incorporating an adaptive scaling parameter into the loss for each pair, our method increases the flexibility of the reward function. Specifically, it assigns small scaling parameters to pairs with ambiguous preferences, leading to more comparable rewards, and large scaling parameters to those with clear preferences for more distinct rewards. Computationally, our proposed loss function is strictly convex and univariate with respect to each scaling parameter, enabling its efficient optimization through a simple second-order algorithm. Our method is versatile and can be readily adapted to various preference optimization frameworks, including direct preference optimization (DPO). Our experiments with robotic control and natural language generation with large language models (LLMs) show that our method not only improves policy performance but also aligns reward function selection more closely with policy optimization, simplifying the hyperparameter tuning process.

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arXiv2024

Federated Compositional Deep AUC Maximization

Federated learning has attracted increasing attention due to the promise of balancing privacy and large-scale learning; numerous approaches have been proposed. However, most existing approaches focus on problems with balanced data, and prediction performance is far from satisfactory for many real-world applications where the number of samples in different classes is highly imbalanced. To address this challenging problem, we developed a novel federated learning method for imbalanced data by directly optimizing the area under curve (AUC) score. In particular, we formulate the AUC maximization problem as a federated compositional minimax optimization problem, develop a local stochastic compositional gradient descent ascent with momentum algorithm, and provide bounds on the computational and communication complexities of our algorithm. To the best of our knowledge, this is the first work to achieve such favorable theoretical results. Finally, extensive experimental results confirm the efficacy of our method.

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arXiv2024

Relative Error Bound Analysis for Nuclear Norm Regularized Matrix Completion

In this paper, we develop a relative error bound for nuclear norm regularized matrix completion, with the focus on the completion of full-rank matrices. Under the assumption that the top eigenspaces of the target matrix are incoherent, we derive a relative upper bound for recovering the best low-rank approximation of the unknown matrix. Although multiple works have been devoted to analyzing the recovery error of full-rank matrix completion, their error bounds are usually additive, making it impossible to obtain the perfect recovery case and more generally difficult to leverage the skewed distribution of eigenvalues. Our analysis is built upon the optimality condition of the regularized formulation and existing guarantees for low-rank matrix completion. To the best of our knowledge, this is the first relative bound that has been proved for the regularized formulation of matrix completion.

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arXiv2023

Multimodal Pretraining of Medical Time Series and Notes

Within the intensive care unit (ICU), a wealth of patient data, including clinical measurements and clinical notes, is readily available. This data is a valuable resource for comprehending patient health and informing medical decisions, but it also contains many challenges in analysis. Deep learning models show promise in extracting meaningful patterns, but they require extensive labeled data, a challenge in critical care. To address this, we propose a novel approach employing self-supervised pretraining, focusing on the alignment of clinical measurements and notes. Our approach combines contrastive and masked token prediction tasks during pretraining. Semi-supervised experiments on the MIMIC-III dataset demonstrate the effectiveness of our self-supervised pretraining. In downstream tasks, including in-hospital mortality prediction and phenotyping, our pretrained model outperforms baselines in settings where only a fraction of the data is labeled, emphasizing its ability to enhance ICU data analysis. Notably, our method excels in situations where very few labels are available, as evidenced by an increase in the AUC-ROC for in-hospital mortality by 0.17 and in AUC-PR for phenotyping by 0.1 when only 1% of labels are accessible. This work advances self-supervised learning in the healthcare domain, optimizing clinical insights from abundant yet challenging ICU data.

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arXiv2023

Stability and Generalization of Stochastic Compositional Gradient Descent Algorithms

Many machine learning tasks can be formulated as a stochastic compositional optimization (SCO) problem such as reinforcement learning, AUC maximization, and meta-learning, where the objective function involves a nested composition associated with an expectation. While a significant amount of studies has been devoted to studying the convergence behavior of SCO algorithms, there is little work on understanding their generalization, i.e., how these learning algorithms built from training examples would behave on future test examples. In this paper, we provide the stability and generalization analysis of stochastic compositional gradient descent algorithms through the lens of algorithmic stability in the framework of statistical learning theory. Firstly, we introduce a stability concept called compositional uniform stability and establish its quantitative relation with generalization for SCO problems. Then, we establish the compositional uniform stability results for two popular stochastic compositional gradient descent algorithms, namely SCGD and SCSC. Finally, we derive dimension-independent excess risk bounds for SCGD and SCSC by trade-offing their stability results and optimization errors. To the best of our knowledge, these are the first-ever-known results on stability and generalization analysis of stochastic compositional gradient descent algorithms.

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arXiv2023

Algorithmic Foundations of Empirical X-risk Minimization

This manuscript introduces a new optimization framework for machine learning and AI, named {\bf empirical X-risk minimization (EXM)}. X-risk is a term introduced to represent a family of compositional measures or objectives, in which each data point is compared with a large number of items explicitly or implicitly for defining a risk function. It includes surrogate objectives of many widely used measures and non-decomposable losses, e.g., AUROC, AUPRC, partial AUROC, NDCG, MAP, precision/recall at top $K$ positions, precision at a certain recall level, listwise losses, p-norm push, top push, global contrastive losses, etc. While these non-decomposable objectives and their optimization algorithms have been studied in the literature of machine learning, computer vision, information retrieval, and etc, optimizing these objectives has encountered some unique challenges for deep learning. In this paper, we present recent rigorous efforts for EXM with a focus on its algorithmic foundations and its applications. We introduce a class of algorithmic techniques for solving EXM with smooth non-convex objectives. We formulate EXM into three special families of non-convex optimization problems belonging to non-convex compositional optimization, non-convex min-max optimization and non-convex bilevel optimization, respectively. For each family of problems, we present some strong baseline algorithms and their complexities, which will motivate further research for improving the existing results. Discussions about the presented results and future studies are given at the end. Efficient algorithms for optimizing a variety of X-risks are implemented in the LibAUC library at \url{www.libauc.org}.

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arXiv2023

SpatialRank: Urban Event Ranking with NDCG Optimization on Spatiotemporal Data

The problem of urban event ranking aims at predicting the top-k most risky locations of future events such as traffic accidents and crimes. This problem is of fundamental importance to public safety and urban administration especially when limited resources are available. The problem is, however, challenging due to complex and dynamic spatio-temporal correlations between locations, uneven distribution of urban events in space, and the difficulty to correctly rank nearby locations with similar features. Prior works on event forecasting mostly aim at accurately predicting the actual risk score or counts of events for all the locations. Rankings obtained as such usually have low quality due to prediction errors. Learning-to-rank methods directly optimize measures such as Normalized Discounted Cumulative Gain (NDCG), but cannot handle the spatiotemporal autocorrelation existing among locations. In this paper, we bridge the gap by proposing a novel spatial event ranking approach named SpatialRank. SpatialRank features adaptive graph convolution layers that dynamically learn the spatiotemporal dependencies across locations from data. In addition, the model optimizes through surrogates a hybrid NDCG loss with a spatial component to better rank neighboring spatial locations. We design an importance-sampling with a spatial filtering algorithm to effectively evaluate the loss during training. Comprehensive experiments on three real-world datasets demonstrate that SpatialRank can effectively identify the top riskiest locations of crimes and traffic accidents and outperform state-of-art methods in terms of NDCG by up to 12.7%.

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arXiv2023

AUC-mixup: Deep AUC Maximization with Mixup

While deep AUC maximization (DAM) has shown remarkable success on imbalanced medical tasks, e.g., chest X-rays classification and skin lesions classification, it could suffer from severe overfitting when applied to small datasets due to its aggressive nature of pushing prediction scores of positive data away from that of negative data. This paper studies how to improve generalization of DAM by mixup data augmentation -- an approach that is widely used for improving generalization of the cross-entropy loss based deep learning methods. %For overfitting issues arising from limited data, the common approach is to employ mixup data augmentation to boost the models' generalization performance by enriching the training data. However, AUC is defined over positive and negative pairs, which makes it challenging to incorporate mixup data augmentation into DAM algorithms. To tackle this challenge, we employ the AUC margin loss and incorporate soft labels into the formulation to effectively learn from data generated by mixup augmentation, which is referred to as the AUC-mixup loss. Our experimental results demonstrate the effectiveness of the proposed AUC-mixup methods on imbalanced benchmark and medical image datasets compared to standard DAM training methods.

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