Regular Tree Search for Simulation Optimization

TL;DR

This paper introduces Regular Tree Search, a novel adaptive sampling algorithm for simulation optimization that recursively partitions the search space and converges globally under certain noise conditions.

Contribution

It proposes a new class of random search algorithms combining adaptive sampling with recursive partitioning, including a specific UCT-based strategy, with proven convergence guarantees.

Findings

Reliable global optimum identification in numerical experiments

Accurate estimation of objective values achieved

Convergence proven under sub-Gaussian noise assumptions

Abstract

Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which integrates adaptive sampling with recursive partitioning of the search space. The algorithm concentrates simulations on increasingly promising regions by iteratively refining a tree structure. A tree search strategy guides sampling decisions, while partitioning is triggered when the number of samples in a leaf node exceeds a threshold that depends on its depth. Furthermore, a specific tree search strategy, Upper Confidence Bounds applied to Trees (UCT), is employed in the Regular Tree Search. We prove global convergence under sub-Gaussian noise, based on assumptions involving the optimality gap, without requiring continuity of the objective function. Numerical experiments confirm that the algorithm reliably identifies the global optimum and provides accurate estimates of its objective value.