Comment: Entropy Learning for Dynamic Treatment Regimes
This is an incremental contribution aimed at improving evaluation methods for dynamic treatment regimes in fields like healthcare or policy-making.
The comment critiques an existing method for evaluating dynamic treatment regimes that uses inverse probability weighting, noting its inefficiency and high variance, and proposes an optimization-based alternative extending prior work to longitudinal settings.
I congratulate Profs. Binyan Jiang, Rui Song, Jialiang Li, and Donglin Zeng (JSLZ) for an exciting development in conducting inferences on optimal dynamic treatment regimes (DTRs) learned via empirical risk minimization using the entropy loss as a surrogate. JSLZ's approach leverages a rejection-and-importance-sampling estimate of the value of a given decision rule based on inverse probability weighting (IPW) and its interpretation as a weighted (or cost-sensitive) classification. Their use of smooth classification surrogates enables their careful approach to analyzing asymptotic distributions. However, even for evaluation purposes, the IPW estimate is problematic as it leads to weights that discard most of the data and are extremely variable on whatever remains. In this comment, I discuss an optimization-based alternative to evaluating DTRs, review several connections, and suggest directions forward. This extends the balanced policy evaluation approach of Kallus (2018a) to the longitudinal setting.