# Sample-Optimal Parametric Q-Learning Using Linearly Additive Features

arXiv: https://arxiv.org/abs/1902.04779 · HTML: https://mlsanity.com/paper/1902.04779/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2019.

## Built on by (most cited first, 2 of 2)

- [Offline Reinforcement Learning in Large State Spaces: Algorithms and Guarantees](https://mlsanity.com/paper/2510.04088/) (2025)
- [End-to-End Efficient RL for Linear Bellman Complete MDPs with Deterministic Transitions](https://mlsanity.com/paper/2603.23461/) (2026)

## Abstract (arXiv)

Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process's probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal policy using a sample size proportional to the feature dimension K and invariant with respect to the size of the state space. To further improve its sample efficiency, we exploit the monotonicity property and intrinsic noise structure of the Bellman operator, provided the existence of anchor state-actions that imply implicit non-negativity in the feature space. We augment the algorithm using techniques of variance reduction, monotonicity preservation, and confidence bounds. It is proved to find a policy which is ε-optimal from any initial state with high probability using widetildeO(K/ε2(1-γ)3) sample transitions for arbitrarily large-scale MDP with a discount factor γ∈(0,1). A matching information-theoretical lower bound is proved, confirming the sample optimality of the proposed method with respect to all parameters (up to polylog factors).