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Sampling to Achieve the Goal: An Age-aware Remote Markov Decision Process

Aimin Li, Shaohua Wu, Gary C. F. Lee, Xiaomeng Cheng, Sumei Sun

TL;DR

The paper addresses the link between AoI and remote decision quality in a time-slotted remote MDP where observation delay is controllable via AoI, not fixed. It introduces an age-aware remote MDP that can be reduced to a standard, delay-free MDP with a constraint, enabling tractable optimization of joint sampling and control actions. The authors prove the existence of optimal stationary deterministic policies under unichain conditions and propose two practical solvers (Bisec-MRVI and FPBI) with FPBI offering faster convergence. A key finding is that minimizing AoI alone can yield suboptimal decision performance, illustrating the value of goal-oriented sampling that directly optimizes the remote decision-making objective; AoI thus functions effectively as side information to facilitate decisions.

Abstract

Age of Information (AoI) has been recognized as an important metric to measure the freshness of information. Central to this consensus is that minimizing AoI can enhance the freshness of information, thereby facilitating the accuracy of subsequent decision-making processes. However, to date the direct causal relationship that links AoI to the utility of the decision-making process is unexplored. To fill this gap, this paper provides a sampling-control co-design problem, referred to as an age-aware remote Markov Decision Process (MDP) problem, to explore this unexplored relationship. Our framework revisits the sampling problem in [1] with a refined focus: moving from AoI penalty minimization to directly optimizing goal-oriented remote decision-making process under random delay. We derive that the age-aware remote MDP problem can be reduced to a standard MDP problem without delays, and reveal that treating AoI solely as a metric for optimization is not optimal in achieving remote decision making. Instead, AoI can serve as important side information to facilitate remote decision making.

Sampling to Achieve the Goal: An Age-aware Remote Markov Decision Process

TL;DR

The paper addresses the link between AoI and remote decision quality in a time-slotted remote MDP where observation delay is controllable via AoI, not fixed. It introduces an age-aware remote MDP that can be reduced to a standard, delay-free MDP with a constraint, enabling tractable optimization of joint sampling and control actions. The authors prove the existence of optimal stationary deterministic policies under unichain conditions and propose two practical solvers (Bisec-MRVI and FPBI) with FPBI offering faster convergence. A key finding is that minimizing AoI alone can yield suboptimal decision performance, illustrating the value of goal-oriented sampling that directly optimizes the remote decision-making objective; AoI thus functions effectively as side information to facilitate decisions.

Abstract

Age of Information (AoI) has been recognized as an important metric to measure the freshness of information. Central to this consensus is that minimizing AoI can enhance the freshness of information, thereby facilitating the accuracy of subsequent decision-making processes. However, to date the direct causal relationship that links AoI to the utility of the decision-making process is unexplored. To fill this gap, this paper provides a sampling-control co-design problem, referred to as an age-aware remote Markov Decision Process (MDP) problem, to explore this unexplored relationship. Our framework revisits the sampling problem in [1] with a refined focus: moving from AoI penalty minimization to directly optimizing goal-oriented remote decision-making process under random delay. We derive that the age-aware remote MDP problem can be reduced to a standard MDP problem without delays, and reveal that treating AoI solely as a metric for optimization is not optimal in achieving remote decision making. Instead, AoI can serve as important side information to facilitate remote decision making.
Paper Structure (32 sections, 8 theorems, 61 equations, 4 figures, 1 table, 2 algorithms)

This paper contains 32 sections, 8 theorems, 61 equations, 4 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Optimal Sampling and Remote Decision Making Policy Under Random Delay
  4. Sufficient Statistics of History
  5. Simplification of Problem $\mathcal{P}2$
  6. Reformulate Problem $\mathcal{P}4$ as a Standard MDP
  7. Existence of Optimal Stationary Deterministic Policy
  8. Numerical Solutions
  9. Simulation Results
  10. Conclusion
  11. Proof of Lemma \ref{['l1']}
  12. Proof of Sufficient Statistics
  13. Determining $a_t^S$ is equivalent to Determining $Z_i$
  14. Proof of Lemma \ref{['l3']}
  15. Proof of Part (i)
  16. ...and 17 more sections

Key Result

Lemma 1

In our problem, during the interval $t\in [D_{i},D_{i+1})$, $\mathcal{G}_i=(X_{S_i},Y_i,A_{i-1})\in\mathcal{S}\times\mathcal{Y}\times\mathcal{A}$ is a sufficient statistics of $\mathcal{I}_t$. Besides, determining the optimal sampling actions $a_t^S$ under condition (eq4) is equivalent to determinin

Figures (4)

  • Figure 1: Evolution of the age $\Delta(t)$ over time.
  • Figure 2: Comparisons among standard MDP, DDMDP, SDMDP, and age-aware remote MDP.
  • Figure 3: Average age and average cost vs. $p$ with i.i.d random delay $Y_i$, where $\Pr(Y_i=1)=p$ and $\Pr(Y_i=10)=1-p$.
  • Figure 4: Bisec-MRVI vs. FPBI, where $p=0.5$.

Theorems & Definitions (12)

  • Definition 1
  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Lemma 4
  • Theorem 2
  • Lemma 5
  • proof
  • Corollary 1
  • proof
  • ...and 2 more