UniXGrad: A Universal, Adaptive Algorithm with Optimal Guarantees for Constrained Optimization
This provides a universal solution for constrained optimization problems, though it is incremental as it builds on existing methods like Mirror-Prox.
The authors tackled the problem of stochastic constrained convex optimization by proposing UniXGrad, an adaptive accelerated algorithm that achieves optimal rates for smooth/non-smooth problems with deterministic or stochastic oracles without prior knowledge of problem parameters.
We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth problems with either deterministic/stochastic first-order oracles. This is done without any prior knowledge of the smoothness nor the noise properties of the problem. To the best of our knowledge, this is the first adaptive, unified algorithm that achieves the optimal rates in the constrained setting. We demonstrate the practical performance of our framework through extensive numerical experiments.