# The Age of Incorrect Information: A New Performance Metric for Status Updates

## TL;DR

This paper introduces the Age of Incorrect Information (AoII), a new metric for status updates that emphasizes informative, correct, and fresh updates, and develops optimal policies for minimizing it under power constraints.

## Contribution

The paper proposes AoII as a novel metric for status updates, formulates its optimization as a CMDP, and provides a low-complexity algorithm for optimal transmission policies under power constraints.

## Key findings

- Always update policy minimizes average AoII, age, and error.
- Optimal policies under power constraints are mixtures of Lagrange policies.
- Simulation shows AoII outperforms AoI in maintaining informative updates.

## Abstract

In this paper, we introduce a new performance metric in the framework of status updates that we will refer to as the Age of Incorrect Information (AoII). This new metric deals with the shortcomings of both the Age of Information (AoI) and the conventional error penalty functions as it neatly extends the notion of fresh updates to that of fresh "informative" updates. The word informative in this context refers to updates that bring new and correct information to the monitor side. After properly motivating the new metric, and with the aim of minimizing its average, we formulate a Markov Decision Process (MDP) in a transmitter-receiver pair scenario where packets are sent over an unreliable channel. We show that a simple "always update" policy minimizes the aforementioned average penalty along with the average age and prediction error. We then tackle the general, and more realistic case, where the transmitter cannot surpass a specific power budget. The problem is formulated as a Constrained Markov Decision Process (CMDP) for which we provide a Lagrangian approach to solve. After characterizing the optimal transmission policy of the Lagrangian problem, we provide a rigorous mathematical proof to showcase that a mixture of two Lagrange policies is optimal for the CMDP in question. Equipped with this, we provide a low complexity algorithm that finds the AoII-optimal operating point of the system in the constrained scenario. Lastly, simulation results are laid out to showcase the performance of the proposed policy and highlight the differences with the AoI framework.