We propose a new method for estimating the minimizer $\boldsymbol{x}^*$ and the minimum value $f^*$ of a smooth and strongly convex regression function $f$ from the observations contaminated by random noise. Our estimator $\boldsymbol{z}_n$ of the minimizer $\boldsymbol{x}^*$ is based on a version of the projected gradient descent with the gradient estimated by a regularized local polynomial algorithm. Next, we propose a two-stage procedure for estimation of the minimum value $f^*$ of regression function $f$. At the first stage, we construct an accurate enough estimator of $\boldsymbol{x}^*$, which can be, for example, $\boldsymbol{z}_n$. At the second stage, we estimate the function value at the point obtained in the first stage using a rate optimal nonparametric procedure. We derive non-asymptotic upper bounds for the quadratic risk and optimization error of $\boldsymbol{z}_n$, and for the risk of estimating $f^*$. We establish minimax lower bounds showing that, under certain choice of parameters, the proposed algorithms achieve the minimax optimal rates of convergence on the class of smooth and strongly convex functions.
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传统的数据湖泊通过启用时间旅行，运行SQL查询，使用酸性交易摄入数据以及可视化PBABYTE尺度数据集在云存储中，为分析工作负载提供了关键的数据基础架构。它们使组织能够分解数据孤岛，解锁数据驱动的决策，提高运营效率并降低成本。但是，随着深度学习接管常见的分析工作流程，传统数据湖泊对诸如自然语言处理（NLP），音频处理，计算机视觉和涉及非尾巴数据集的应用程序的有用程度降低。本文介绍了Deep Lake，这是一个开源湖泊，用于在Activeloop开发的深度学习应用程序。 Deep Lake保持了一项关键区别的香草数据湖的好处：它以张量的形式存储复杂数据，例如图像，视频，注释以及表格数据，并将数据迅速流式传输到网络上（a ）张量查询语言，（b）浏览器可视化引擎或（c）不牺牲GPU利用率的深度学习框架。可以从Pytorch，Tensorflow，Jax，与许多MLOPS工具集成在一起的数据集。
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