# Non-Asymptotic Best Policy Identification Guarantees in Online Reinforcement Learning

arXiv: https://arxiv.org/abs/2607.17201 · HTML: https://mlsanity.com/paper/2607.17201/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 9 of its 35 references that are in the map.
- First posted on arXiv 19 Jul 2026.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 9 of 9)

- [Thresholding Bandit for Dose-ranging: The Impact of Monotonicity](https://mlsanity.com/paper/1711.04454/) (2017)
- [Adaptive Exploration for Multi-Reward Multi-Policy Evaluation](https://mlsanity.com/paper/2502.02516/) (2025)
- [The regret lower bound for communicating Markov Decision Processes](https://mlsanity.com/paper/2501.13013/) (2025)
- [Pure Exploration with Feedback Graphs](https://mlsanity.com/paper/2503.07824/) (2025)
- [Policy Testing in Markov Decision Processes](https://mlsanity.com/paper/2505.15342/) (2025)
- [Asymptotically Optimal Sequential Testing with Markovian Data](https://mlsanity.com/paper/2602.17587/) (2026)
- [Pure Exploration with Infinite Answers](https://mlsanity.com/paper/2505.22473/) (2025)
- [Non-Asymptotic Analysis of (Sticky) Track-and-Stop](https://mlsanity.com/paper/2505.22475/) (2025)
- [Optimal Best Arm Identification under Differential Privacy](https://mlsanity.com/paper/2510.17348/) (2025)

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

- [Average-Reward Policy Identification from a Single Continuing Trajectory](https://mlsanity.com/paper/2610.20486/) (2026)

## Abstract (arXiv)

In this work we study the Best Policy Identification (BPI) problem in online, tabular Reinforcement Learning. This is an active sequential hypothesis testing problem in which the learner's objective is to identify an optimal policy in a Markov Decision Process (MDP) with high confidence, while minimizing the expected sample complexity to do so. We consider an online setting with deterministic rewards, where the agent must strategically navigate through the MDP in order to effectively explore. Previous works in the literature have provided asymptotically optimal methods for BPI, such as the Navigate and Stop (NaS) algorithm and its variants, however existing analysis remains asymptotic. In this work, we fill that gap by providing the first non-asymptotic sample complexity guarantees for NaS, showing that its sample complexity depends not only on the characteristic time, but also on the connectivity of the underlying MDP, the curvature of the optimal characteristic time, and other instance-dependent quantities. We identify these additional attributes and make explicit their contributions to the overall sample complexity.