RSA: Byzantine-Robust Stochastic Aggregation Methods for Distributed Learning from Heterogeneous Datasets

In this paper, we propose a class of robust stochastic subgradient methods for distributed learning from heterogeneous datasets at presence of an unknown number of Byzantine workers. The Byzantine workers, during the learning process, may send arbitrary incorrect messages to the master due to data corruptions, communication failures or malicious attacks, and consequently bias the learned model. The key to the proposed methods is a regularization term incorporated with the objective function so as to robustify the learning task and mitigate the negative effects of Byzantine attacks. The resultant subgradient-based algorithms are termed Byzantine-Robust Stochastic Aggregation methods, justifying our acronym RSA used henceforth. In contrast to most of the existing algorithms, RSA does not rely on the assumption that the data are independent and identically distributed (i.i.d.) on the workers, and hence fits for a wider class of applications. Theoretically, we show that: i) RSA converges to a near-optimal solution with the learning error dependent on the number of Byzantine workers; ii) the convergence rate of RSA under Byzantine attacks is the same as that of the stochastic gradient descent method, which is free of Byzantine attacks. Numerically, experiments on real dataset corroborate the competitive performance of RSA and a complexity reduction compared to the state-of-the-art alternatives.Comment: To appear in AAAI 201

Effect of Achyranthes bidentata Blume extract on carrageenan-induced chronic prostatitis in rats

Purpose: To investigate the effect of Achyranthes bidentata Blume. Extract (ABBE) on carrageenaninduced chronic prostatitis in rats.Methods: Experimental chronic non-bacterial prostatitis (CNP) was induced in rats by 1 % carrageenan (0.1 mL). Prostate index (PI) and prostate specific antigen (PSA) were determined after 3 weeks of adiministration. Relative inflammatory factors, viz, tumor necrosis factor-α (TNF-α), interleukin1β (IL-1β), cyclooxygenase-2 (COX-2), prostaglandin E2 (PEG2), transforming growth factor-β1 (TGF-β1) and connective tissue growth factor (CTGF) in the prostate tissues of all group rats were measured.Results: In CNP model, ABBE decreased PI and PSA compared with untreated control group (p < 0.01). Morphometric analysis showed a significant reduction in chronic inflammatory cell infiltrates and interstitial fibrosis compared to control group. Reduced values of TNF-α, IL-1β, COX-2, PEG2 were observed in ABBE-treated groups compared with model group respectively (p < 0.01). Moreover, the levels of TGF-β1 and CTGF in ABBE-treated groups were significantly lower, and in addition, there was alleviation of the inflammatory state of the prostate gland (p < 0.01).Conclusion: ABBE showed antichronic non-bacterial prostatitis effect by multiple ways in rats, thus indicating its potential suitability for the treatment of chronic prostatitis.Keywords: Achyranthes bidentata Blume., Chronic prostatitis, Inflammatory cel