Quantum Speedups for Sampling and Non-convex Optimization with Stochastic Oracles

We present quantum speedups for sampling from distributions of the form $π\propto e^{-f}$ on $\mathbb{R}^d$. We consider two stochastic oracle models: a stochastic gradient oracle, where $f=\frac{1}{n}\sum_{i=1}^n f_i $ and component gradients $\{\nabla f_i\}_{i \in [n]}$ are available, and a stocha