Obtaining Lower Query Complexities Through Lightweight Zeroth-Order Proximal Gradient Algorithms.

Zeroth-order (ZO) optimization is one key technique for machine learning problems where gradient calculation is expensive or impossible. Several variance, reduced ZO proximal algorithms have been proposed to speed up ZO optimization for nonsmooth problems, and all of them opted for the coordinated ZO estimator against the random ZO estimator when approximating the true gradient, since the former is more accurate. While the random ZO estimator introduces a larger error and makes convergence analysis more challenging compared to coordinated ZO estimator, it requires only O(1) computation, which is significantly less than O(d) computation of the coordinated ZO estimator, with d being dimension of the problem space. To take advantage of the computationally efficient nature of the random ZO estimator, we first propose a ZO objective decrease (ZOOD) property that can incorporate two different types of errors in the upper bound of convergence rate. Next, we propose two generic reduction frameworks for ZO optimization, which can automatically derive the convergence results for convex and nonconvex problems, respectively, as long as the convergence rate for the inner solver satisfies the ZOOD property. With the application of two reduction frameworks on our proposed ZOR-ProxSVRG and ZOR-ProxSAGA, two variance-reduced ZO proximal algorithms with fully random ZO estimators, we improve the state-of-the-art function query complexities from Omindn1/2ε2,dε3 to O˜n+dε2 under d>n12 for nonconvex problems, and from Odε2 to O˜nlog1ε+dε for convex problems. Finally, we conduct experiments to verify the superiority of our proposed methods.

Circ_LRP6 facilitates osteosarcoma progression via the miR-122-5p/miR-204-5p/HMGB1 axis.

Circ_LRP6 is participated in the occurrence and development of numerous tumors. Nevertheless, its roles and mechanism in osteosarcoma (OS) is unknown. This study aims to illustrate this point. With the use of qRT-PCR, the level of circ_LRP6, miR-122-5p, miR-204-5p and HMGB1 was identified. To observe cell proliferation, migration and invasion, we adopted CCK-8 and Transwell assays in the present study. Besides, to prove the existing interaction, bioinformatics analysis and dual luciferase reporting assays were employed. The influence of circ_LRP6 on osteosarcoma in vivo was evaluated by subcutaneous tumor formation model in nude mice. In osteosarcoma tissues, circ_LRP6 and HMGB1 are strongly denoted, whereas miR-122-5p and miR-204-5p are under-expressed. Circ_LRP6 knockdown could significantly hinder the proliferation, migration and invasion of osteosarcoma cells. Circ_LRP6 hindered the proliferation of osteosarcoma in vivo. Bioinformatics predicted that miR-122-5p and miR-204-5p functioned as direct targets of circ_LRP6, and HMGB1 were possible target genes of miR-122-5p and miR-204-5p. The findings indicated that the low level of miR-122-5p and miR-204-5p and the overexpression of HMGB1 could partially restore and reduce the inhibitory impact of circ_LRP6 on the proliferation, migration and invasion of osteosarcoma cells. Circ_LRP6 affects osteosarcoma progression via the miR-122-5p/miR-204-5p/HMGB1 axis, and is shown to be a molecular biomarker.