Distributed Adaptive Greedy Quasi-Newton Methods with Explicit Non-asymptotic Convergence Bounds

Though quasi-Newton methods have been extensively studied in the literature, they either suffer from local convergence or use a series of line searches for global convergence which is not acceptable in the distributed setting. In this work, we first propose a line search free greedy quasi-Newton (GQN) method with adaptive steps and establish explicit non-asymptotic bounds for both the global convergence rate and local superlinear rate. Our novel idea lies in the design of multiple greedy quasi-Newton updates, which involves computing Hessian-vector products, to control the Hessian approximation error, and a simple mechanism to adjust stepsizes to ensure the objective function improvement per iterate. Then, we extend it to the master-worker framework and propose a distributed adaptive GQN method whose communication cost is comparable with that of first-order methods, yet it retains the superb convergence property of its centralized counterpart. Finally, we demonstrate the advantages of our methods via numerical experiments

Feasibility and effect of para-right bundle branch pacing in patients with atrial fibrillation and complete atrioventricular block

Background: Chronic right ventricular apex (RVA) pacing can induce negative clinical effects. The aim of the present study was to compare RVA pacing with para-right bundle branch (para-RBB) pacing in terms of electrocardiogram (ECG) and echocardiographic (ECHO) features. Methods: Forty-one consecutive persistent atrial fibrillation patients with an indication for permanent pacing treatment due to complete atrioventricular block were randomly assigned to receive a screw-in lead either in the RVA (n = 22) or at the para-RBB (n = 19). Para-RBB pacing leads were located according to the RBB potential recorded by electrophysiology catheter. ECG was recorded before and after implantation. All patients underwent the pacemaker pro­gramming at 1 day, 6 months, 12 months and 24 months after implantation. ECHO examina­tion was performed during follow-up at 6, 12 and 24 months after implantation to assess the heart function and synchronism. Results: There was no significant difference in pacing lead parameters between para-RBB pacing group and RVA pacing group. Compared with RVA pacing group, the para-RBB pacing group obtained a narrower QRS complex, more synchronic ventricular systole, and less nega­tive effect on heart function (p < 0.05). Conclusions: Para-RBB pacing has potential clinical benefits and may be a physiological pacing site.