In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Q: Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the underlying factors driving their empirical success in min-max problems such as GANs remain unclear. In this paper, we aim at bridging  this gap from both theoretical and empirical perspectives. First, we analyze a variant of Optimistic Stochastic Gradient (OSG) proposed in~\citep{daskalakis2017training} for solving a class of non-convex non-concave min-max problem and establish $O(\epsilon^{-4})$ complexity for finding $\epsilon$-first-order stationary point, in which the algorithm only requires invoking one stochastic first-order oracle while enjoying state-of-the-art iteration complexity achieved by stochastic extragradient method by~\citep{iusem2017extragradient}. Then we propose an adaptive variant of OSG named Optimistic Adagrad (OAdagrad) and reveal an \emph{improved} adaptive complexity $\widetilde{O}\left(\epsilon^{-\frac{2}{1-\alpha}}\right)$~\footnote{Here $\widetilde{O}(\cdot)$ compresses a logarithmic factor of $\epsilon$. }, where $\alpha$ characterizes the growth rate of the cumulative stochastic gradient and $0\leq \alpha\leq 1/2$. To the best of our knowledge, this is the first work for establishing adaptive complexity in non-convex non-concave min-max optimization. Empirically, our experiments show that indeed adaptive gradient algorithms outperform their non-adaptive counterparts in GAN training. Moreover, this observation can be explained by the slow growth rate of the cumulative stochastic gradient, as observed empirically.

A: This paper provides novel analysis of adaptive gradient algorithms for solving non-convex non-concave min-max problems as GANs, and explains the reason why adaptive gradient methods outperform its non-adaptive counterparts by empirical studies.
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Q: Noise injection is a fundamental tool for data augmentation, and yet there is no widely accepted procedure to incorporate it with learning frameworks. This study analyzes the effects of adding or applying different noise models of varying magnitudes to Convolutional Neural Network (CNN) architectures. Noise models that are distributed with different density functions are given common magnitude levels via Structural Similarity (SSIM) metric in order to create an appropriate ground for comparison. The basic results are conforming with the most of the common notions in machine learning, and also introduces some novel heuristics and recommendations on noise injection. The new approaches will provide better understanding on optimal learning procedures for image classification.

A: Ideal methodology to inject noise to input data during CNN training
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Q: Solving long-horizon sequential decision making tasks in environments with sparse rewards is a longstanding problem in reinforcement learning (RL) research. Hierarchical Reinforcement Learning (HRL) has held the promise to enhance the capabilities of RL agents via operation on different levels of temporal abstraction. Despite the success of recent works in dealing with inherent nonstationarity and sample complexity, it remains difficult to generalize to unseen environments and to transfer different layers of the policy to other agents. In this paper, we propose a novel HRL architecture, Hierarchical Decompositional Reinforcement Learning (HiDe), which allows decomposition of the hierarchical layers into independent subtasks, yet allows for joint training of all layers in end-to-end manner. The main insight is to combine a control policy on a lower level with an image-based planning policy on a higher level. We evaluate our method on various complex continuous control tasks for navigation, demonstrating that generalization across environments and transfer of higher level policies can be achieved. See videos https://sites.google.com/view/hide-rl

A:
Learning Functionally Decomposed Hierarchies for Continuous Navigation Tasks
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