Sampling Policy Design for Tracking Time-varying Graph Signals with Adaptive Budget Allocation

There have been many works that focus on the sampling policy design for static graph signals (GS), but few for time-varying GS. In this paper, we concentrate on how to select vertices to sample and how to allocate the sampling budget for a time-varying GS to reduce tracking error. In the Kalman Filter (KF) framework, the problem of sampling policy design and budget allocation is formulated as an infinite horizon sequential decision process, in which the optimal sampling policy is obtained by Dynamic Programming (DP). Since the optimal policy is intractable, an approximate algorithm is proposed by truncating the infinite horizon to two stages. By introducing a new tool for analyzing the convexity or concavity of composite functions, we prove that the truncated problem is convex so that it can be solved by standard tools. Finally, we demonstrate the performance of the proposed approach through numerical experiments.