Optimal Policy Learning with Observational Data in Multi-Action
  Scenarios: Estimation, Risk Preference, and Potential Failures
Giovanni Cerulli
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.