# Sampling for Data Freshness Optimization: Non-linear Age Functions

arXiv: https://arxiv.org/abs/1812.07241 · HTML: https://mlsanity.com/paper/1812.07241/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2018.

## Built on by (most cited first, 10 of 10)

- [An Online Learning Approach to Optimizing Time-Varying Costs of AoI](https://mlsanity.com/paper/2105.13383/) (2021)
- [Timely Communications for Remote Inference](https://mlsanity.com/paper/2404.16281/) (2024)
- [The Age of Correlated Features in Supervised Learning based Forecasting](https://mlsanity.com/paper/2103.00092/) (2021)
- [How Does Data Freshness Affect Real-time Supervised Learning?](https://mlsanity.com/paper/2208.06948/) (2022)
- [Online Learning of Whittle Indices for Restless Bandits with Non-Stationary Transition Kernels](https://mlsanity.com/paper/2506.18186/) (2025)
- [Multimodal Remote Inference](https://mlsanity.com/paper/2508.07555/) (2025)
- [The Best Time for an Update: Risk-Sensitive Minimization of Age-Based Metrics](https://mlsanity.com/paper/2401.10265/) (2024)
- [Asynchronous Fractional Multi-Agent Deep Reinforcement Learning for Age-Minimal Mobile Edge Computing](https://mlsanity.com/paper/2409.16832/) (2024)
- [Policy Gradient Algorithms for Age-of-Information Cost Minimization](https://mlsanity.com/paper/2512.11990/) (2025)
- [Beyond Freshness and Semantics: A Coupon-Collector Framework for Effective Status Updates](https://mlsanity.com/paper/2603.26998/) (2026)

## Abstract (arXiv)

In this paper, we study how to take samples at a data source for improving the freshness of received data samples at a remote receiver. We use non-linear functions of the age of information to measure data freshness, and provide a survey of non-linear age functions and their applications. The sampler design problem is studied to optimize these data freshness metrics, even when there is a sampling rate constraint. This sampling problem is formulated as a constrained Markov decision process (MDP) with a possibly uncountable state space. We present a complete characterization of the optimal solution to this MDP: The optimal sampling policy is a deterministic or randomized threshold policy, where the threshold and the randomization probabilities are characterized based on the optimal objective value of the MDP and the sampling rate constraint. The optimal sampling policy can be computed by bisection search, and the curse of dimensionality is circumvented. These age optimality results hold for (i) general data freshness metrics represented by monotonic functions of the age of information, (ii) general service time distributions of the queueing server, (iii) both continuoustime and discrete-time sampling problems, and (iv) sampling problems both with and without the sampling rate constraint. Numerical results suggest that the optimal sampling policies can be much better than zero-wait sampling and the classic uniform sampling.