# A Central Limit Theorem, Loss Aversion and Multi-Armed Bandits

arXiv: https://arxiv.org/abs/2106.05472 · HTML: https://mlsanity.com/paper/2106.05472/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 49 references that are in the map.
- First posted on arXiv 10 Jun 2021.

## Builds on (most cited first, 1 of 1)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)

## Built on by (most cited first, 1 of 1)

- [Research on Optimal Control Problem Based on Reinforcement Learning under Knightian Uncertainty](https://mlsanity.com/paper/2506.13207/) (2025)

## Abstract (arXiv)

This paper studies a multi-armed bandit problem where the decision-maker is loss averse, in particular she is risk averse in the domain of gains and risk loving in the domain of losses. The focus is on large horizons. Consequences of loss aversion for asymptotic (large horizon) properties are derived in a number of analytical results. The analysis is based on a new central limit theorem for a set of measures under which conditional variances can vary in a largely unstructured history-dependent way subject only to the restriction that they lie in a fixed interval.