稀疏活动网络上随机最优化的分布式无导数学习方法
Distributed Derivative-free Learning Method for Stochastic Optimization over a Network with Sparse Activity
摘要：
本文研究了通信网络中节点偶发活动的分布式最优化问题。每个主动节点应用某种学习方法来控制其动作以最大化全局效用函数，该全局效用函数被定义为主动节点的局部效用函数之和。研究了效用函数受非加性随机过程扰动的随机最优化问题。我们考虑一个更具挑战性的情况下，学习方法必须只基于效用函数的标量近似，而不是其封闭形式的表达，使典型的梯度下降法不能应用。当网络受到一些随机和时变过程的影响，并且每个节点不能完全了解网络状态时，这种设置是非常现实的。我们提出了一个分布式优化算法，并证明了它几乎必然收敛到最优。在目标函数为强凹函数的条件下，得到了收敛速度.数值结果也证明了我们的主张。
英文摘要：
This paper addresses a distributed optimization problem in a communication network where nodes are active sporadically. Each active node applies some learning method to control its action to maximize the global utility function, which is defined as the sum of the local utility functions of active nodes. We deal with stochastic optimization problem with the setting that utility functions are disturbed by some non-additive stochastic process. We consider a more challenging situation where the learning method has to be performed only based on a scalar approximation of the utility function, rather than its closed-form expression, so that the typical gradient descent method cannot be applied. This setting is quite realistic when the network is affected by some stochastic and time-varying process, and that each node cannot have the full knowledge of the network states. We propose a distributed optimization algorithm and prove its almost surely convergence to the optimum. Convergence rate is also derived with an additional assumption that the objective function is strongly concave. Numerical results are also presented to justify our claim.
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