Private Zeroth-Order Nonsmooth Nonconvex Optimization

Published: 16 Jan 2024, Last Modified: 19 Apr 2024ICLR 2024 posterEveryoneRevisionsBibTeX
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Keywords: optimization, differential privacy, non-convex, non-smooth
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Abstract: We introduce a new zeroth-order algorithm for private stochastic optimization on nonconvex and nonsmooth objectives. Given a dataset of size $M$, our algorithm ensures $(\alpha,\alpha\rho^2/2)$-Renyi differential privacy and finds a $(\delta,\epsilon)$-stationary point so long as $M=\tilde\Omega(\frac{d}{\delta\epsilon^3} + \frac{d^{3/2}}{\rho\delta\epsilon^2})$. This matches the optimal complexity found in its non-private zeroth-order analog. Notably, although the objective is not smooth, we have privacy ``for free'' when $\rho \ge \sqrt{d}\epsilon$.
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Primary Area: optimization
Submission Number: 6503