[Paper Review] When to pull data from sensors for minimum Distance-based Age of incorrect Information metric

Saad Kriouile, Mohamad Assaad|arXiv (Cornell University)|Feb 6, 2022

Age of Information Optimization4 citations

TL;DR

This paper proposes a Whittle's index-based scheduling policy to minimize the Distance-based Age of Incorrect Information (AoII) in multi-sensor monitoring systems, where sensors follow a Markovian process and the scheduler estimates AoII without full state knowledge. The key contribution is a novel Whittle index expression that accounts for state distance, outperforming AoI-based policies in reducing information mismatch and freshness penalties.

ABSTRACT

The age of Information (AoI) has been introduced to capture the notion of freshness in real-time monitoring applications. However, this metric falls short in many scenarios, especially when quantifying the mismatch between the current and the estimated states. To circumvent this issue, in this paper, we adopt the age of incorrect information metric (AoII) that considers the quantified mismatch between the source and the knowledge at the destination while tracking the impact of freshness. We consider for that a problem where a central entity pulls the information from remote sources that evolve according to a Markovian Process. It selects at each time slot which sources should send their updates. As the scheduler does not know the actual state of the remote sources, it estimates at each time the value of AoII based on the Markovian sources' parameters. Its goal is to keep the time average of the AoII function as small as possible. For that purpose, We develop a scheduling scheme based on Whittle's index policy. To that extent, we use the Lagrangian Relaxation Approach and establish that the dual problem has an optimal threshold policy. Building on that, we compute the expressions of Whittle's indices. Finally, we provide some numerical results to highlight the performance of our derived policy compared to the classical AoI metric.

Motivation & Objective

• To address the limitation of traditional Age of Information (AoI) in capturing content mismatch between sensor states and monitor estimates.
• To model and minimize a distance-based Age of Incorrect Information (AoII) metric that quantifies the severity of estimation errors.
• To design a scheduling policy for a central monitor selecting sensors under partial observability, using estimated AoII instead of true state.
• To derive Whittle's indices for the AoII metric that incorporate state transition distances and Markov parameters.
• To evaluate the performance of the proposed policy against AoI-based and baseline scheduling schemes.

Proposed method

• Formulates the scheduling problem as a Partially Observable Markov Decision Process (POMDP) due to lack of full state knowledge at the scheduler.
• Uses Lagrangian relaxation to transform the constrained optimization into a dual problem with an optimal threshold policy.
• Derives closed-form expressions for Whittle's indices that depend on the Markov source parameters (transition probability $p_i$, distance $d_i$) and channel reliability $\rho_i$.
• Applies the Whittle index policy to select the $M$ sensors with the highest indices at each time slot for data pull.
• Employs a state-space model where AoII evolves based on successful/failed transmissions and state transitions, with state values defined as cumulative distances.
• Uses empirical averaging to compute the time-averaged AoII for performance evaluation under different policies.

Experimental results

Research questions

• RQ1 How can the Age of Incorrect Information (AoII) metric be extended to account for the magnitude of state differences in Markovian processes?
• RQ2 What is the optimal scheduling policy for minimizing time-averaged distance-based AoII when the scheduler has only partial knowledge of sensor states?
• RQ3 How do the Whittle indices for the distance-aware AoII metric depend on the Markov parameters and transmission reliability?
• RQ4 How does the proposed policy compare to AoI-based scheduling and baseline policies in terms of minimizing information mismatch?
• RQ5 Can the Whittle index framework be adapted to handle non-binary, distance-sensitive state errors in sensor monitoring systems?

Key findings

• The proposed Whittle's index policy (WIP-AoII) achieves significantly lower average empirical AoII than the AoI-based policy (WIP-AoI), especially when state distance matters.
• In a scenario with identical channel reliability ($\rho_1 = \rho_2 = 0.5$) but different source dynamics ($p_1 = 0.1$, $p_2 = 0.9$), WIP-AoII outperforms WIP-AoI by prioritizing sensors with higher mismatch sensitivity.
• When comparing against a weighted baseline (WWIP-AoI), the proposed policy with $w_i(n)$-based indices shows superior performance, proving the importance of the derived index expression.
• The derived Whittle index expression for AoII is $W_i(b_i^n) = d_i p_i w_i(n)$, where $w_i(n)$ captures the cubic dependence on the age state $n$ and channel reliability $\rho_i$.
• Numerical results confirm that ignoring state distance in scheduling leads to suboptimal performance, even when channel conditions are identical.
• The policy is optimal in the many-users regime and provides a low-complexity, scalable solution for IoT and real-time monitoring systems.