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Functionally constrained stochastic optimization problems, where neither theobjective function nor the constraint functions are analytically available,arise frequently in machine learning applications. In this work, assuming weonly have access to the noisy evaluations of the objective and constraintfunctions, we propose and analyze stochastic zeroth-order algorithms forsolving the above class of stochastic optimization problem. When the domain ofthe functions is $\mathbb{R}^n$, assuming there are $m$ constraint functions,we establish oracle complexities of order $\mathcal{O}((m+1)n/\epsilon^2)$ and$\mathcal{O}((m+1)n/\epsilon^3)$ respectively in the convex and nonconvexsetting, where $\epsilon$ represents the accuracy of the solutions required inappropriately defined metrics. The established oracle complexities are, to ourknowledge, the first such results in the literature for functionallyconstrained stochastic zeroth-order optimization problems. We demonstrate theapplicability of our algorithms by illustrating its superior performance on theproblem of hyperparameter tuning for sampling algorithms and neural networktraining.

Stochastic Zeroth-order Functional Constrained Optimization: Oracle Complexity and Applications