AdaBatchGrad: Combining Adaptive Batch Size and Adaptive Step Size

This paper presents a novel adaptation of the Stochastic Gradient Descent (SGD), termed AdaBatchGrad. This modification seamlessly integrates an adaptive step size with an adjustable batch size. An increase in batch size and a decrease in step size are well-known techniques to tighten the area of convergence of SGD and decrease its variance. A range of studies by R. Byrd and J. Nocedal introduced various testing techniques to assess the quality of mini-batch gradient approximations and choose the appropriate batch sizes at every step. Methods that utilized exact tests were observed to converge within $O(LR^2/\varepsilon)$ iterations. Conversely, inexact test implementations sometimes resulted in non-convergence and erratic performance. To address these challenges, AdaBatchGrad incorporates both adaptive batch and step sizes, enhancing the method's robustness and stability. For exact tests, our approach converges in $O(LR^2/\varepsilon)$ iterations, analogous to standard gradient descent. For inexact tests, it achieves convergence in $O(\max\lbrace LR^2/\varepsilon, \sigma^2 R^2/\varepsilon^2 \rbrace )$ iterations. This makes AdaBatchGrad markedly more robust and computationally efficient relative to prevailing methods. To substantiate the efficacy of our method, we experimentally show, how the introduction of adaptive step size and adaptive batch size gradually improves the performance of regular SGD. The results imply that AdaBatchGrad surpasses alternative methods, especially when applied to inexact tests.

In Quest of Ground Truth: Learning Confident Models and Estimating Uncertainty in the Presence of Annotator Noise

The performance of the Deep Learning (DL) models depends on the quality of labels. In some areas, the involvement of human annotators may lead to noise in the data. When these corrupted labels are blindly regarded as the ground truth (GT), DL models suffer from performance deficiency. This paper presents a method that aims to learn a confident model in the presence of noisy labels. This is done in conjunction with estimating the uncertainty of multiple annotators. We robustly estimate the predictions given only the noisy labels by adding entropy or information-based regularizer to the classifier network. We conduct our experiments on a noisy version of MNIST, CIFAR-10, and FMNIST datasets. Our empirical results demonstrate the robustness of our method as it outperforms or performs comparably to other state-of-the-art (SOTA) methods. In addition, we evaluated the proposed method on the curated dataset, where the noise type and level of various annotators depend on the input image style. We show that our approach performs well and is adept at learning annotators' confusion. Moreover, we demonstrate how our model is more confident in predicting GT than other baselines. Finally, we assess our approach for segmentation problem and showcase its effectiveness with experiments.