Optimal Policy Learning with Observational Data in Multi-Action Scenarios: Estimation, Risk Preference, and Potential Failures
<|reference_start|>Optimal Policy Learning with Observational Data in Multi-Action Scenarios: Estimation, Risk Preference, and Potential Failures: This paper deals with optimal policy learning (OPL) with observational data, i.e. data-driven optimal decision-making, in multi-action (or multi-arm) settings, where a finite set of decision options is available. It is organized in three parts, where I discuss respectively: estimation, risk preference, and potential failures. The first part provides a brief review of the key approaches to estimating the reward (or value) function and optimal policy within this context of analysis. Here, I delineate the identification assumptions and statistical properties related to offline optimal policy learning estimators. In the second part, I delve into the analysis of decision risk. This analysis reveals that the optimal choice can be influenced by the decision maker's attitude towards risks, specifically in terms of the trade-off between reward conditional mean and conditional variance. Here, I present an application of the proposed model to real data, illustrating that the average regret of a policy with multi-valued treatment is contingent on the decision-maker's attitude towards risk. The third part of the paper discusses the limitations of optimal data-driven decision-making by highlighting conditions under which decision-making can falter. This aspect is linked to the failure of the two fundamental assumptions essential for identifying the optimal choice: (i) overlapping, and (ii) unconfoundedness. Some conclusions end the paper.<|reference_end|>
@article{cerulli2024optimal,
    title={Optimal Policy Learning with Observational Data in Multi-Action
  Scenarios: Estimation, Risk Preference, and Potential Failures},
    author={Giovanni Cerulli},
    journal={arXiv preprint arXiv:2403.20250},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.20250},
    primaryClass={stat.ML cs.AI cs.LG}
}