Differentially Private Stochastic Gradient Descent for Outcome Weighted Learning

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The development of individualized treatment rules in precision medicine seeks to optimize clinical outcomes for patients with varying responses to treatment. This paper focuses on outcome weighted learning, a method for estimating optimal treatment rules that take into account patient-specific characteristics within a weighted classification framework. We introduce a differentially private stochastic gradient descent algorithm within the framework of outcome weighted learning. This approach involves adding Gaussian noise to the gradient at each iteration, thereby ensuring the privacy of sensitive medical data while effectively managing large-scale datasets common in clinical practice. Unlike traditional differential privacy methods, which primarily focus on input-output type data, our approach integrates input-action-reward type data. This incorporation guarantees that both privacy and utility are preserved, with utility measured by the excess value function of the estimated individualized treatment rule. In our analysis, we establish convergence rates for the excess value function under logistic loss function, hinge loss function, and smoothed hinge loss function constructed via the Moreau envelope. These results provide rigorous utility guarantees for differentially private outcome weighted learning in precision medicine. Furthermore, empirical experiments support these theoretical findings and highlight the practical value of smoothing techniques in privacy-preserving learning for precision medicine.