We propose a nonparametric additive model for estimating interpretable value functions in reinforcement learning. Learning effective adaptive clinical interventions that rely on digital phenotyping features is a major for concern medical practitioners. With respect to spine surgery, different post-operative recovery recommendations concerning patient mobilization can lead to significant variation in patient recovery. While reinforcement learning has achieved widespread success in domains such as games, recent methods heavily rely on black-box methods, such neural networks. Unfortunately, these methods hinder the ability of examining the contribution each feature makes in producing the final suggested decision. While such interpretations are easily provided in classical algorithms such as Least Squares Policy Iteration, basic linearity assumptions prevent learning higher-order flexible interactions between features. In this paper, we present a novel method that offers a flexible technique for estimating action-value functions without making explicit parametric assumptions regarding their additive functional form. This nonparametric estimation strategy relies on incorporating local kernel regression and basis expansion to obtain a sparse, additive representation of the action-value function. Under this approach, we are able to locally approximate the action-value function and retrieve the nonlinear, independent contribution of select features as well as joint feature pairs. We validate the proposed approach with a simulation study, and, in an application to spine disease, uncover recovery recommendations that are inline with related clinical knowledge.

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