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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In this paper, we propose a new zero order optimization method called minibatch stochastic three points (MiSTP) method to solve an unconstrained minimization problem in a setting where only an approximation of the objective function evaluation is possible. It is based on the recently proposed stochastic three points (STP) method (Bergou et al., 2020). At each iteration, MiSTP generates a random search direction in a similar manner to STP, but chooses the next iterate based solely on the approximation of the objective function rather than its exact evaluations. We also analyze our method's complexity in the nonconvex and convex cases and evaluate its performance on multiple machine learning tasks.
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 //libauc.org/.
In cross-device Federated Learning (FL), clients with low computational power train a common\linebreak[4] machine model by exchanging parameters via updates instead of potentially private data. Federated Dropout (FD) is a technique that improves the communication efficiency of a FL session by selecting a \emph{subset} of model parameters to be updated in each training round. However, compared to standard FL, FD produces considerably lower accuracy and faces a longer convergence time. In this paper, we leverage \textit{coding theory} to enhance FD by allowing different sub-models to be used at each client. We also show that by carefully tuning the server learning rate hyper-parameter, we can achieve higher training speed while also achieving up to the same final accuracy as the no dropout case. For the EMNIST dataset, our mechanism achieves 99.6\% of the final accuracy of the no dropout case while requiring $2.43\times$ less bandwidth to achieve this level of accuracy.
Multiple-objective optimization (MOO) aims to simultaneously optimize multiple conflicting objectives and has found important applications in machine learning, such as minimizing classification loss and discrepancy in treating different populations for fairness. At optimality, further optimizing one objective will necessarily harm at least another objective, and decision-makers need to comprehensively explore multiple optima (called Pareto front) to pinpoint one final solution. We address the efficiency of finding the Pareto front. First, finding the front from scratch using stochastic multi-gradient descent (SMGD) is expensive with large neural networks and datasets. We propose to explore the Pareto front as a manifold from a few initial optima, based on a predictor-corrector method. Second, for each exploration step, the predictor solves a large-scale linear system that scales quadratically in the number of model parameters and requires one backpropagation to evaluate a second-order Hessian-vector product per iteration of the solver. We propose a Gauss-Newton approximation that only scales linearly, and that requires only first-order inner-product per iteration. This also allows for a choice between the MINRES and conjugate gradient methods when approximately solving the linear system. The innovations make predictor-corrector possible for large networks. Experiments on multi-objective (fairness and accuracy) misinformation detection tasks show that 1) the predictor-corrector method can find Pareto fronts better than or similar to SMGD with less time; and 2) the proposed first-order method does not harm the quality of the Pareto front identified by the second-order method, while further reduce running time.
Despite the success of large-scale empirical risk minimization (ERM) at achieving high accuracy across a variety of machine learning tasks, fair ERM is hindered by the incompatibility of fairness constraints with stochastic optimization. We consider the problem of fair classification with discrete sensitive attributes and potentially large models and data sets, requiring stochastic solvers. Existing in-processing fairness algorithms are either impractical in the large-scale setting because they require large batches of data at each iteration or they are not guaranteed to converge. In this paper, we develop the first stochastic in-processing fairness algorithm with guaranteed convergence. For demographic parity, equalized odds, and equal opportunity notions of fairness, we provide slight variations of our algorithm--called FERMI--and prove that each of these variations converges in stochastic optimization with any batch size. Empirically, we show that FERMI is amenable to stochastic solvers with multiple (non-binary) sensitive attributes and non-binary targets, performing well even with minibatch size as small as one. Extensive experiments show that FERMI achieves the most favorable tradeoffs between fairness violation and test accuracy across all tested setups compared with state-of-the-art baselines for demographic parity, equalized odds, equal opportunity. These benefits are especially significant with small batch sizes and for non-binary classification with large number of sensitive attributes, making FERMI a practical fairness algorithm for large-scale problems.
Standard contrastive learning approaches usually require a large number of negatives for effective unsupervised learning and often exhibit slow convergence. We suspect this behavior is due to the suboptimal selection of negatives used for offering contrast to the positives. We counter this difficulty by taking inspiration from support vector machines (SVMs) to present max-margin contrastive learning (MMCL). Our approach selects negatives as the sparse support vectors obtained via a quadratic optimization problem, and contrastiveness is enforced by maximizing the decision margin. As SVM optimization can be computationally demanding, especially in an end-to-end setting, we present simplifications that alleviate the computational burden. We validate our approach on standard vision benchmark datasets, demonstrating better performance in unsupervised representation learning over state-of-the-art, while having better empirical convergence properties.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Self-supervised learning has been widely used to obtain transferrable representations from unlabeled images. Especially, recent contrastive learning methods have shown impressive performances on downstream image classification tasks. While these contrastive methods mainly focus on generating invariant global representations at the image-level under semantic-preserving transformations, they are prone to overlook spatial consistency of local representations and therefore have a limitation in pretraining for localization tasks such as object detection and instance segmentation. Moreover, aggressively cropped views used in existing contrastive methods can minimize representation distances between the semantically different regions of a single image. In this paper, we propose a spatially consistent representation learning algorithm (SCRL) for multi-object and location-specific tasks. In particular, we devise a novel self-supervised objective that tries to produce coherent spatial representations of a randomly cropped local region according to geometric translations and zooming operations. On various downstream localization tasks with benchmark datasets, the proposed SCRL shows significant performance improvements over the image-level supervised pretraining as well as the state-of-the-art self-supervised learning methods.
Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.
This paper presents SimCLR: a simple framework for contrastive learning of visual representations. We simplify recently proposed contrastive self-supervised learning algorithms without requiring specialized architectures or a memory bank. In order to understand what enables the contrastive prediction tasks to learn useful representations, we systematically study the major components of our framework. We show that (1) composition of data augmentations plays a critical role in defining effective predictive tasks, (2) introducing a learnable nonlinear transformation between the representation and the contrastive loss substantially improves the quality of the learned representations, and (3) contrastive learning benefits from larger batch sizes and more training steps compared to supervised learning. By combining these findings, we are able to considerably outperform previous methods for self-supervised and semi-supervised learning on ImageNet. A linear classifier trained on self-supervised representations learned by SimCLR achieves 76.5% top-1 accuracy, which is a 7% relative improvement over previous state-of-the-art, matching the performance of a supervised ResNet-50. When fine-tuned on only 1% of the labels, we achieve 85.8% top-5 accuracy, outperforming AlexNet with 100X fewer labels.
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