论文标题
更快的异步非凸块块坐标下降具有本地选择的步骤
Faster Asynchronous Nonconvex Block Coordinate Descent with Locally Chosen Stepsizes
论文作者
论文摘要
分布式的非convex优化问题是学习和自治方面的许多应用，并且这些问题通常在代理商的计算和通信中面临异步。当这些操作中的延迟是有限的时，它们被称为部分异步。在本文中，我们为部分异步的块坐标下降提供了一个不协调的步骤选择规则，该规则仅需要本地信息才能实现，并且它导致一类非convex问题的速度比现有的步骤规则更快，这需要某种形式的全局信息。我们考虑的问题满足了误差绑定条件，而我们提出的步骤规则只要求每个代理知道（i）一定类型的Lipschitz在目标梯度的块中常数，以及（ii）IT与其邻居之间所经历的沟通延迟。该公式需要比现有方法更少的信息，通常允许代理使用更大的步骤，并减轻散乱者的影响，同时仍然保证融合到固定点。仿真结果提供了比较，并验证了我们开发的步骤规则所获得的更快的收敛性。
Distributed nonconvex optimization problems underlie many applications in learning and autonomy, and such problems commonly face asynchrony in agents' computations and communications. When delays in these operations are bounded, they are called partially asynchronous. In this paper, we present an uncoordinated stepsize selection rule for partially asynchronous block coordinate descent that only requires local information to implement, and it leads to faster convergence for a class of nonconvex problems than existing stepsize rules, which require global information in some form. The problems we consider satisfy the error bound condition, and the stepsize rule we present only requires each agent to know (i) a certain type of Lipschitz constant of its block of the gradient of the objective and (ii) the communication delays experienced between it and its neighbors. This formulation requires less information to be available to each agent than existing approaches, typically allows for agents to use much larger stepsizes, and alleviates the impact of stragglers while still guaranteeing convergence to a stationary point. Simulation results provide comparisons and validate the faster convergence attained by the stepsize rule we develop.
