When to spend privacy: optimal allocation in private learning

The paper presents a framework for optimally allocating a fixed privacy budget across iterations of Differentially Private Stochastic Gradient Descent. By modeling the Gaussian noise-variance schedule as an open-loop control problem under a zero-Concentrated Differential Privacy constraint, the authors derive an exact-budget simplex formulation and introduce the Privacy‑Budget Adjoint Mirror Descent (PB‑AMD) algorithm. The method guarantees budget exhaustiveness, stability, and stationarity, and yields a square‑root allocation law that empirically outperforms existing allocation rules and reduces optimization time compared to projected gradient descent.

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