Mobile health leverages personalized, contextually-tailored interventions optimized through bandit and reinforcement learning algorithms. Despite its promise, challenges like participant heterogeneity, nonstationarity, and nonlinearity in rewards hinder algorithm performance. We propose a robust contextual bandit algorithm, termed ``DML-TS-NNR'', that simultaneously addresses these challenges via (1) modeling the differential reward with user- and time-specific incidental parameters, (2) network cohesion penalties, and (3) debiased machine learning for flexible estimation of baseline rewards. We establish a high-probability regret bound that depends solely on the dimension of the differential reward model. This feature enables us to achieve robust regret bounds even when the baseline reward is highly complex. We demonstrate the superior performance of the DML-TS-NNR algorithm in a simulation and two off-policy evaluation studies.