SHE2: Stochastic Hamiltonian Exploration and Exploitation for Derivative-Free Optimization

Abstract

Derivative-free optimization (DFO) using trust region methods is frequently used for machine learning applications, such as (hyper-)parameter optimization without the derivatives of objective functions known. Inspired by the recent work in continuous-time minimizers, our work models the common trust region methods with the exploration-exploitation using a dynamical system coupling a pair of dynamical processes. While the first exploration process searches the minimum of the blackbox function through minimizing a time-evolving surrogation function, another exploitation process updates the surrogation function time-to-time using the points traversed by the exploration process. The efficiency of derivative-free optimization thus depends on ways the two processes couple. In this paper, we propose a novel dynamical system, namely ---Stochastic Hamiltonian Exploration and Exploitation, that surrogates the subregions of blackbox function using a time-evolving quadratic function, then explores and tracks the minimum of the quadratic functions using a fast-converging Hamiltonian system. The \ algorithm is later provided as a discrete-time numerical approximation to the system. To further accelerate optimization, we present \ that parallelizes multiple \ threads for concurrent exploration and exploitation. Experiment results based on a wide range of machine learning applications show that \ outperform a boarder range of derivative-free optimization algorithms with faster convergence speed under the same settings.

Tasks

Reproductions