# Unbiased Multilevel Monte Carlo: Stochastic Optimization, Steady-state Simulation, Quantiles, and Other Applications

arXiv: https://arxiv.org/abs/1904.09929 · HTML: https://mlsanity.com/paper/1904.09929/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2019.

## Built on by (most cited first, 18 of 18)

- [A Finite Sample Complexity Bound for Distributionally Robust Q-learning](https://mlsanity.com/paper/2302.13203/) (2023)
- [Stochastic Bias-Reduced Gradient Methods](https://mlsanity.com/paper/2106.09481/) (2021)
- [Model-Free Robust Average-Reward Reinforcement Learning](https://mlsanity.com/paper/2305.10504/) (2023)
- [Distributionally Robust Optimization via Ball Oracle Acceleration](https://mlsanity.com/paper/2203.13225/) (2022)
- [Model-Free Robust Reinforcement Learning with Sample Complexity Analysis](https://mlsanity.com/paper/2406.17096/) (2024)
- [Finite-Sample Analysis of Policy Evaluation for Robust Average Reward Reinforcement Learning](https://mlsanity.com/paper/2502.16816/) (2025)
- [Constructing unbiased gradient estimators with finite variance for conditional stochastic optimization](https://mlsanity.com/paper/2206.01991/) (2022)
- [Multi-level Monte-Carlo Gradient Methods for Stochastic Optimization with Biased Oracles](https://mlsanity.com/paper/2408.11084/) (2024)
- [Bayesian Risk-Averse Q-Learning with Streaming Observations](https://mlsanity.com/paper/2305.11300/) (2023)
- [Sequential Decision-Making under Uncertainty: A Robust MDPs review](https://mlsanity.com/paper/2404.00940/) (2024)
- [Prediction-Enhanced Monte Carlo: A Machine Learning View on Control Variate](https://mlsanity.com/paper/2412.11257/) (2024)
- [Planning and Learning in Average Risk-aware MDPs](https://mlsanity.com/paper/2503.17629/) (2025)
- [Pessimism Principle Can Be Effective: Towards a Framework for Zero-Shot Transfer Reinforcement Learning](https://mlsanity.com/paper/2505.18447/) (2025)
- [Unbiased least squares regression via averaged stochastic gradient descent](https://mlsanity.com/paper/2406.18623/) (2024)
- [Multilevel and Sequential Monte Carlo for Training-Free Diffusion Guidance](https://mlsanity.com/paper/2601.21104/) (2026)
- [Quantum speedup of non-linear Monte Carlo problems](https://mlsanity.com/paper/2502.05094/) (2025)
- [Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control](https://mlsanity.com/paper/2506.19294/) (2025)
- [Benchmarking Stochastic Approximation Algorithms for Fairness-Constrained Training of Deep Neural Networks](https://mlsanity.com/paper/2507.04033/) (2025)

## Abstract (arXiv)

We present general principles for the design and analysis of unbiased Monte Carlo estimators in a wide range of settings. Our estimators posses finite work-normalized variance under mild regularity conditions. We apply our estimators to various settings of interest, including unbiased optimization in Sample Average Approximations, unbiased steady-state simulation of regenerative processes, quantile estimation and nested simulation problems.