Model-based Bootstrap of Controlled Markov Chains

2026-07-08 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

This paper introduces a novel model-based bootstrap method for transition kernels in finite Controlled Markov Chains (CMCs), specifically addressing challenges in offline reinforcement learning (RL) with nonstationary or history-dependent control policies. The method establishes distributional consistency for the bootstrap transition estimator in both single long-chain and episodic offline RL regimes, leveraging a new bootstrap law of large numbers and a martingale central limit theorem. It extends this consistency to downstream tasks like Offline Policy Evaluation (OPE) and Optimal Policy Recovery (OPR) by verifying Hadamard differentiability of Bellman operators, providing asymptotically valid confidence intervals for value and Q-functions. Experimental results on the RiverSwim problem (S=6 states, A=2 actions, γ=0.95) with B=1000 bootstrap replicates and N_reps=1000 Monte Carlo replications demonstrate that the proposed percentile CIs achieve near-nominal coverage (e.g., 95% coverage between 0.92–0.97) at sample sizes n ≥ 500 and episode lengths T ∈ {50,100}, significantly outperforming existing episodic bootstrap and plug-in CLT baselines which show poor calibration.

Key takeaway

For Machine Learning Engineers developing offline reinforcement learning systems, you should consider implementing the model-based bootstrap for more reliable uncertainty quantification. This approach provides asymptotically valid confidence intervals for value and Q-functions, even with nonstationary or history-dependent behavior policies. Specifically, prioritize using percentile CIs, as they demonstrated superior coverage on the RiverSwim problem, especially with sample sizes n ≥ 500 and episode lengths T ≥ 50. This can lead to more trustworthy policy evaluation and recovery.

Key insights

A model-based bootstrap provides robust confidence intervals for offline RL in nonstationary Controlled Markov Chains.

Principles

• Bootstrap consistency extends to nonstationary CMCs.
• Hadamard differentiability validates bootstrap for Bellman operators.
• Percentile CIs offer superior coverage in finite samples.

Method

The method generates bootstrap datasets from an empirical transition kernel and behavior policy, then computes bootstrap transition estimators. These are used to derive confidence intervals for OPE and OPR targets via Bellman equations.

In practice

• Use model-based bootstrap for robust offline RL uncertainty.
• Prioritize percentile CIs over pivot CIs for better coverage.
• Consider n ≥ 500 and T ≥ 50 for reliable CIs.

Topics

• Reinforcement Learning
• Offline RL
• Bootstrap Methods
• Controlled Markov Chains
• Confidence Intervals
• Policy Evaluation
• Optimal Policy Recovery

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

Related on AIssential

• Regularized Offline Policy Optimization with Posterior Hybrid Bayesian Belief — PhyB addresses offline RL uncertainty by approximating Bayesian expectations with a convex combination of dynamics models.
• ASymPO: Asymmetric-Scale Policy Optimization for Asynchronous LLM Post-Training Without Behavior Information — ASymPO stabilizes asynchronous LLM post-training by normalizing token loss with current policy probabilities, eliminating the need for behavior information.
• Provable Offline Reinforcement Learning for Structured Cyclic MDPs — CycleFQI offers a modular, theoretically robust offline RL solution for cyclic MDPs with heterogeneous stages.
• Q-MMR: Off-Policy Evaluation via Recursive Reweighting and Moment Matching — Q-MMR offers a dimension-free, finite-sample guarantee for off-policy evaluation using learned data weights.
• On-Policy Approximate Control Methods — Function approximation extends Sarsa and n-step Sarsa to large-scale reinforcement learning control problems.
• WOMBET: World Model-based Experience Transfer for Robust and Sample-efficient Reinforcement Learning — WOMBET unifies uncertainty-aware model-based data generation with adaptive online fine-tuning for efficient RL experience transfer.

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.