# Regular Tree Search for Simulation Optimization

arXiv: https://arxiv.org/abs/2506.17696 · HTML: https://mlsanity.com/paper/2506.17696/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 21 Jun 2025.

## Builds on (most cited first, 11 of 11)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Learning Search Space Partition for Black-box Optimization using Monte Carlo Tree Search](https://mlsanity.com/paper/2007.00708/) (2020)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Review on Ranking and Selection: A New Perspective](https://mlsanity.com/paper/2008.00249/) (2020)
- [Simulation optimization: A review of algorithms and applications](https://mlsanity.com/paper/1706.08591/) (2017)
- [On the Convergence of CART under Sufficient Impurity Decrease Condition](https://mlsanity.com/paper/2310.17114/) (2023)
- [Review of Large-Scale Simulation Optimization](https://mlsanity.com/paper/2403.15669/) (2024)
- [Adaptive Split Balancing for Optimal Random Forest](https://mlsanity.com/paper/2402.11228/) (2024)
- [An Upper Confidence Bound Approach to Estimating the Maximum Mean](https://mlsanity.com/paper/2408.04179/) (2024)
- [Derivative-Free Optimization via Finite Difference Approximation: An Experimental Study](https://mlsanity.com/paper/2411.00112/) (2024)

## Abstract (arXiv)

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.