A Note on Inflation Parameter for Adaptive Parallel Subgradient Projection Algorithms-An Optimal Design in Case of Single Projection

摘要

The adaptive parallel subgradient projection algorithm (Yamada et. al., 2002) is based on a metric projection onto a certain closed half-space, which is constructed by the so-called inflation parameter. To improve the speed of convergence and the accuracy of estimation simultaneously, the parameter should be designed from the following aspects: (i) large enough to contain an estimandum, system to be estimated, with high probability, (ii) small enough to well-approximate the estimandum. It is of great interest to find a strategic design of the inflation parameter. In this paper, we present an optimal design of the inflation parameter in the sense of minimizing the squared distance to the estimandum, focusing on the case of single projection as a first step. The resulting formula suggests that excess estimation error as well as noise should be taken into account for the designing. By following the analysis, we propose an adaptive control technique of inflation parameter based on statistics of residual estimation error and noise process. Numerical examples verify that the proposed technique successfully improves the accuracy of estimation.