Reproduce “Local Bayesian optimization via maximizing probability of descent” on OpenResearch

About this paper

Quan Nguyen, Kaiwen Wu, Jacob R. Gardner, Roman Garnett

A new local Bayesian optimization method, Most-Probable Descent (MPD), directly optimizes for the probability of descending the objective function in high-dimensional, expensive black-box settings. The approach demonstrates superior or competitive sample efficiency against established baselines on synthetic and real-world optimization problems by deriving a theoretically sound most probable descent direction and an efficient acquisition function.

Key insights

• The negative expected gradient is not always the direction that maximizes the probability of descending the objective function; these directions can be nearly orthogonal.
• Gradient uncertainty alone is insufficient for guiding optimization; different probabilistic beliefs about the gradient can lead to vastly different descent probabilities even with identical uncertainty.
• A principled, coupled approach that simultaneously considers expected gradient and its uncertainty in both learning and moving phases leads to more efficient local Bayesian optimization.

Summary by alphaXiv.