# Measurable Monte Carlo Search Error Bounds

arXiv: https://arxiv.org/abs/2106.04715 · HTML: https://mlsanity.com/paper/2106.04715/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 8 Jun 2021.

## Builds on (most cited first, 3 of 3)

- [Combining Neural Networks and Tree Search for Task and Motion Planning in Challenging Environments](https://mlsanity.com/paper/1703.07887/) (2017)
- [LeTS-Drive: Driving in a Crowd by Learning from Tree Search](https://mlsanity.com/paper/1905.12197/) (2019)
- [A central limit theorem for temporally non-homogenous Markov chains with applications to dynamic programming](https://mlsanity.com/paper/1505.00749/) (2015)

## Built on by (most cited first, 1 of 1)

- [Interpretable Local Tree Surrogate Policies](https://mlsanity.com/paper/2109.08180/) (2021)

## Abstract (arXiv)

Monte Carlo planners can often return sub-optimal actions, even if they are guaranteed to converge in the limit of infinite samples. Known asymptotic regret bounds do not provide any way to measure confidence of a recommended action at the conclusion of search. In this work, we prove bounds on the sub-optimality of Monte Carlo estimates for non-stationary bandits and Markov decision processes. These bounds can be directly computed at the conclusion of the search and do not require knowledge of the true action-value. The presented bound holds for general Monte Carlo solvers meeting mild convergence conditions. We empirically test the tightness of the bounds through experiments on a multi-armed bandit and a discrete Markov decision process for both a simple solver and Monte Carlo tree search.