Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes

Value of Information in Feedback Control: Global Optimality

“…More specifically, Rabi and Baras [5] formulated the optimal event-triggered estimation of the scalar Wiener and Ornstein-Uhlenbeck processes as an optimal multiple stopping time problem by discarding the signaling effect, and showed that the optimal triggering policy is symmetric. Guo and Kostina [6], [7] contributed to this area by studying the optimal event-triggered estimation of the scalar Wiener, Ornstein-Uhlenbeck, and Lévy processes in the presence of signaling effect, and obtained a similar result as in [5]. Furthermore, Sun et al [8] studied the optimal event-triggered estimation of the scalar Wiener process with random communication delay by discarding the signaling effect, and showed that the optimal triggering policy is symmetric.…”

“…Remark 1: The optimization problem in ( 6) formulates the rate-regulation trade-off for multi-dimensional controlled Gauss-Markov processes under an information structure that includes observations from multiple sensors with measurement noise. Note that the objective function (7) penalizes the packet rate in the communication channel, and is appropriate for packet switching networks; while the objective function (8) penalizes the state deviation and control effort, and is appropriate for regulation tasks. Moreover, note that the set of globally optimal solutions cannot be empty because we have already proved in [24] that at least one Nash equilibrium exists in this problem.…”

Communication-Efficient Federated Learning via Optimal Client Sampling

“…As shown there, thresholding the increase in signal magnitude is an optimal sampling policy for estimating parameters of an OU process. An extension of these results to a larger class of continuous Markov processes with regularity conditions is reported in [21].…”

“…Optimal sampling of the OU process. Rate-constrained sampling of stochastic processes has been widely studied in literature, primarily in the context of communications and control [25,11,37,41,36,51,40,21]. In [25,11], this problem is studied for random i.i.d.…”

“…When a sampling frequency constraint limits the number of samples that could be collected by a server, the nodes should locally decide when to send an update. Guo et al [21] show that the optimal strategy in this case is to sample at time τ = inf{t ≥ 0 : |θ t − E[θ t |θ 0 ]| > γ}, and that the optimal decoding policy is given by θt = E[θ t |θ 0 ], t ∈ [0, τ ). In particular, for the OU process in (1), θt = e −λt θ 0 + (1 − e −λt )µ; note that λ and µ are unknown (more on this below).…”