# Reinforcement Learning with Depreciating Assets

arXiv: https://arxiv.org/abs/2302.14176 · HTML: https://mlsanity.com/paper/2302.14176/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 44 references that are in the map.
- First posted on arXiv 27 Feb 2023.

## Builds on (most cited first, 6 of 6)

- [Environment-Independent Task Specifications via GLTL](https://mlsanity.com/paper/1704.04341/) (2017)
- [Discounting in LTL](https://mlsanity.com/paper/1406.4249/) (2014)
- [Qualitative Analysis of Concurrent Mean-payoff Games](https://mlsanity.com/paper/1409.5306/) (2014)
- [General limit value in zero-sum stochastic games](https://mlsanity.com/paper/1410.5231/) (2014)
- [A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic games](https://mlsanity.com/paper/1501.06525/) (2015)
- [Tauberian theorems for general iterations of operators: applications to zero-sum stochastic games](https://mlsanity.com/paper/1609.02175/) (2016)

## Built on by (most cited first, 2 of 2)

- [Multi-Level Strategic Classification: Incentivizing Improvement through Promotion and Relegation Dynamics](https://mlsanity.com/paper/2602.11439/) (2026)
- [Sequential Strategic Classification with Multi-Stage Selective Classifiers](https://mlsanity.com/paper/2605.04202/) (2026)

## Abstract (arXiv)

A basic assumption of traditional reinforcement learning is that the value of a reward does not change once it is received by an agent. The present work forgoes this assumption and considers the situation where the value of a reward decays proportionally to the time elapsed since it was obtained. Emphasizing the inflection point occurring at the time of payment, we use the term asset to refer to a reward that is currently in the possession of an agent. Adopting this language, we initiate the study of depreciating assets within the framework of infinite-horizon quantitative optimization. In particular, we propose a notion of asset depreciation, inspired by classical exponential discounting, where the value of an asset is scaled by a fixed discount factor at each time step after it is obtained by the agent. We formulate a Bellman-style equational characterization of optimality in this context and develop a model-free reinforcement learning approach to obtain optimal policies.