Identifying Optimal Sequential Decisions

TL;DR

This paper explores the conditions under which optimal sequential decision strategies can be identified from data, emphasizing the importance of conditional strategies over atomic ones and providing a graphical criterion for their identifiability.

Contribution

It introduces a graphical criterion for identifying optimal conditional strategies in sequential decision problems, extending previous work on atomic interventions.

Findings

Conditional strategies are often necessary for optimality.

Identifiability of strategies is more restrictive for conditional interventions.

A simple graphical criterion can determine strategy identifiability.

Abstract

We consider conditions that allow us to find an optimal strategy for sequential decisions from a given data situation. For the case where all interventions are unconditional (atomic), identifiability has been discussed by Pearl & Robins (1995). We argue here that an optimal strategy must be conditional, i.e. take the information available at each decision point into account. We show that the identification of an optimal sequential decision strategy is more restrictive, in the sense that conditional interventions might not always be identified when atomic interventions are. We further demonstrate that a simple graphical criterion for the identifiability of an optimal strategy can be given.