# Offline Estimation of Controlled Markov Chains: Minimaxity and Sample Complexity

arXiv: https://arxiv.org/abs/2211.07092 · HTML: https://mlsanity.com/paper/2211.07092/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 71 references that are in the map.
- First posted on arXiv 14 Nov 2022.

## Builds on (most cited first, 17 of 17)

- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [MOPO: Model-based Offline Policy Optimization](https://mlsanity.com/paper/2005.13239/) (2020)
- [MOReL : Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2005.05951/) (2020)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [Reinforcement Learning in Healthcare: A Survey](https://mlsanity.com/paper/1908.08796/) (2019)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Pessimistic Q-Learning for Offline Reinforcement Learning: Towards Optimal Sample Complexity](https://mlsanity.com/paper/2202.13890/) (2022)
- [Settling the Sample Complexity of Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2204.05275/) (2022)
- [Active Learning for Nonlinear System Identification with Guarantees](https://mlsanity.com/paper/2006.10277/) (2020)
- [Towards Instance-Optimal Offline Reinforcement Learning with Pessimism](https://mlsanity.com/paper/2110.08695/) (2021)
- [Algorithms for multi-armed bandit problems](https://mlsanity.com/paper/1402.6028/) (2014)
- [Queueing Network Controls via Deep Reinforcement Learning](https://mlsanity.com/paper/2008.01644/) (2020)
- [The Importance of Non-Markovianity in Maximum State Entropy Exploration](https://mlsanity.com/paper/2202.03060/) (2022)
- [Probabilistic Machine Learning for Healthcare](https://mlsanity.com/paper/2009.11087/) (2020)
- [Settling the Horizon-Dependence of Sample Complexity in Reinforcement Learning](https://mlsanity.com/paper/2111.00633/) (2021)
- [Multi-Agent Reinforcement Learning: A Report on Challenges and Approaches](https://mlsanity.com/paper/1807.09427/) (2018)
- [Active Learning for Linear Parameter-Varying System Identification](https://mlsanity.com/paper/2005.00711/) (2020)

## Built on by (most cited first, 5 of 5)

- [CLT and Edgeworth Expansion for m-out-of-n Bootstrap Estimators of The Studentized Median](https://mlsanity.com/paper/2505.11725/) (2025)
- [Near-Optimal Clustering in Mixture of Markov Chains](https://mlsanity.com/paper/2506.01324/) (2025)
- [Central Limit Theorems for Transition Probabilities of Controlled Markov Chains](https://mlsanity.com/paper/2508.01517/) (2025)
- [Adaptive Estimation and Optimal Control in Offline Contextual MDPs without Stationarity](https://mlsanity.com/paper/2605.03393/) (2026)
- [Model-based Bootstrap of Controlled Markov Chains](https://mlsanity.com/paper/2605.12410/) (2026)

## Abstract (arXiv)

In this work, we study a natural nonparametric estimator of the transition probability matrices of a finite controlled Markov chain. We consider an offline setting with a fixed dataset, collected using a so-called logging policy. We develop sample complexity bounds for the estimator and establish conditions for minimaxity. Our statistical bounds depend on the logging policy through its mixing properties. We show that achieving a particular statistical risk bound involves a subtle and interesting trade-off between the strength of the mixing properties and the number of samples. We demonstrate the validity of our results under various examples, such as ergodic Markov chains, weakly ergodic inhomogeneous Markov chains, and controlled Markov chains with non-stationary Markov, episodic, and greedy controls. Lastly, we use these sample complexity bounds to establish concomitant ones for offline evaluation of stationary Markov control policies.