A0250
Title: Fisher consistency of surrogate losses for optimal dynamic treatment regimes
Authors: Nilanjana Laha - Texas A\&M University (United States) [presenting]
Nilson Chapagain - Texas A\&M University (United States)
Aaron Sonabend - Google Research (United States)
Abstract: Patients with chronic diseases often receive treatments over multiple stages. The aim is to learn the optimal dynamic treatment regime (DTR) from longitudinal data, where the number of stages and treatment options per stage are arbitrary. This reduces to a sequential, weighted multiclass classification problem. This is addressed by solving the classification problem across all stages using Fisher consistent surrogate losses. While special cases (e.g., binary treatments) admit such surrogates, a general theory remains undeveloped. Necessary and sufficient conditions are established for DTR Fisher consistency within the class of non-negative, stagewise separable surrogate losses, offering the first such result in the DTR literature. It is further shown that many convex surrogates, including smooth, permutation-equivariant, and relative-margin-based ones, are inconsistent in this setting. To overcome this, SDSS (simultaneous direct search with surrogates) is proposed, which leverages smooth, non-concave surrogates to learn optimal DTRs. A gradient-based algorithm is introduced for SDSS, and a sharp regret bound is derived under a small optimization error.
