14. ProGO: Probabilistic Global Optimizer

Addressing the limitations of current global optimization algorithms, especially when tackling non-convex functions and when gradient information is computationally intensive or absent, we introduce a novel approach. Our proposed Probabilistic Global Optimizer (ProGO) is based on a sequence of multidimensional integrations that converge to global optima under specific regularity conditions. This gradient-free method benefits from a robust convergence framework built on the properties of emerging optima distributions. We've also created a latent slice sampler with a geometric convergence rate for sampling from these distributions to approximate global optima effectively. ProGO is designed as a versatile framework that scales to approximate global optima for continuous functions across any dimension. Our empirical tests on well-known non-convex functions demonstrate ProGO's superior performance over many established algorithms in terms of regret value and convergence speed.

Time series forecasting

Machine learning

Subsampling

Pareto efficiency

Autoregressive processes

Ensemble methods