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arXiv · 2312.09350

The Gittins index is optimal for dynamic allocation with conditionally independent filtrations

Christopher Wang
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Abstract

The dynamic allocation problem, also known as the `multi-armed bandit' problem, simulates a situation in which an agent is faced with a tradeoff between actions that yield an immediate reward and actions whose benefits can only be perceived in the future. In this paper, we show that the non-Markovian, discrete-time problem can be solved by following a Gittins index strategy, without the assumption that the rewards processes are independent. Instead, we require the underlying multi-parameter filtration to satisfy a conditional independence property. We provide three representations of the maximal attainable value under an optimal strategy. Furthermore, we discuss the relationship between index-type strategies and the `synchronization' paradigm from operations research.

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Christopher Wang. 2023-12-14. The Gittins index is optimal for dynamic allocation with conditionally independent filtrations. https://arxiv.org/abs/2312.09350

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