[论文解读] Structural Monotonicity in Transmission Scheduling for Remote State Estimation with Hidden Channel Mode

Hampei Sasahara|arXiv (Cornell University)|Jan 27, 2026

Age of Information Optimization被引用 0

一句话总结

该论文发展状态空间折叠以在具有隐藏信道模态的远程状态估计的 POMDP 中恢复基于 TP2 的单调性，并证明最优停止策略的阈值结构。

ABSTRACT

This study treats transmission scheduling for remote state estimation over unreliable channels with a hidden mode. A local Kalman estimator selects scheduling actions, such as power allocation and resource usage, and communicates with a remote estimator based on acknowledgement feedback, balancing estimation performance and communication cost. The resulting problem is naturally formulated as a partially observable Markov decision process (POMDP). In settings with observable channel modes, it is well known that monotonicity of the value function can be established via investigating order-preserving property of transition kernels. In contrast, under partial observability, the transition kernels generally lack this property, which prevents the direct application of standard monotonicity arguments. To overcome this difficulty, we introduce a novel technique, referred to as state-space folding, which induces transformed transition kernels recovering order preservation on the folded space. This transformation enables a rigorous monotonicity analysis in the partially observable setting. As a representative implication, we focus on an associated optimal stopping formulation and show that the resulting optimal scheduling policy admits a threshold structure.

研究动机与目标

• Motivate transmission scheduling for remote state estimation over unreliable channels with hidden modes.
• Formulate the problem as a POMDP with holding time and hidden channel state.
• Establish structural monotonicity via state-space folding to recover order preservation.
• Show that the optimal stopping policy has a threshold structure.

提出的方法

• Model the system as a discrete-time linear plant with Kalman-based local estimation.
• Introduce state-space folding to transform the holding-time kernel into a TP2-compatible form.
• Prove TP2 properties for the folded kernels and derive monotonicity of the belief update.
• Prove that the value function is increasing in holding time and belief, yielding a threshold policy in stopping problems.

实验结果

研究问题

• RQ1 Can structural monotonicity be established for POMDPs with hidden channel modes in remote state estimation?
• RQ2 Does state-space folding restore order preservation and enable monotone analysis under partial observability?
• RQ3 Is there a threshold structure for optimal stopping policies in this setting?

主要发现

• A state-space folding technique restores TP2 properties for the folded transition kernels.
• The value function is increasing in both holding time and the belief of the unfavorable channel mode.
• In the optimal stopping setting, the optimal policy is characterized by a threshold on the belief that is monotone with respect to holding time.
• The threshold b_th(tau) decreases as holding time increases.