Regular Tree Search for Simulation Optimization

2025-06-21

AI Summary

This paper addresses the global optimization of non-convex, non-differentiable objective functions accessible only via stochastic simulation. We propose Regularized Tree Search (RTS), a novel algorithm that integrates adaptive sampling with recursive space partitioning to dynamically construct a balanced tree structure, thereby concentrating evaluation effort on promising regions. RTS innovatively combines the Upper Confidence Bound for Trees (UCT) strategy with a depth-dependent threshold-based partitioning mechanism, requiring no assumptions on function continuity or convexity. Under sub-Gaussian noise, we establish rigorous theoretical guarantees of global convergence. Empirical evaluations demonstrate that RTS consistently identifies high-quality global optima, delivers accurate objective value estimates, and exhibits strong robustness and computational efficiency across diverse benchmark problems.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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.

Problem

• Solving non-convex simulation optimization problems
• Developing Regular Tree Search algorithm
• Ensuring global convergence under sub-Gaussian noise

Innovation

• Adaptive sampling with recursive partitioning
• Tree search strategy guides sampling decisions
• Upper Confidence Bounds applied to Trees