  There have been many works that focus on the sampling set design for a static
graph signal, but few for time-varying graph signals (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 achieve a minimal tracking error for
the long-term. 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. By
introducing a new tool for analyzing the convexity or concavity of composite
functions, we prove that the truncated problem is convex. Finally, we
demonstrate the performance of the proposed approach through numerical
experiments.
