# Finite-Time Bounds for Average-Reward Fitted Q-Iteration

arXiv: https://arxiv.org/abs/2510.17391 · HTML: https://mlsanity.com/paper/2510.17391/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Offline RL algorithms, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 46 of its 96 references that are in the map.
- First posted on arXiv 20 Oct 2025.

## Placed in

- Offline RL and imitation learning from data / [Offline RL algorithms](https://mlsanity.com/offlinerl/offline-rl-algorithms/)

## Builds on (most cited first, 30 of 46)

- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Information-Theoretic Considerations in Batch Reinforcement Learning](https://mlsanity.com/paper/1905.00360/) (2019)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [A Theoretical Analysis of Deep Q-Learning](https://mlsanity.com/paper/1901.00137/) (2019)
- [Keep Doing What Worked: Behavioral Modelling Priors for Offline Reinforcement Learning](https://mlsanity.com/paper/2002.08396/) (2020)
- [Top-K Off-Policy Correction for a REINFORCE Recommender System](https://mlsanity.com/paper/1812.02353/) (2018)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [What are the Statistical Limits of Offline RL with Linear Function Approximation?](https://mlsanity.com/paper/2010.11895/) (2020)
- [Offline Reinforcement Learning with Realizability and Single-policy Concentrability](https://mlsanity.com/paper/2202.04634/) (2022)
- [Minimax-Optimal Off-Policy Evaluation with Linear Function Approximation](https://mlsanity.com/paper/2002.09516/) (2020)
- [Batch Value-function Approximation with Only Realizability](https://mlsanity.com/paper/2008.04990/) (2020)
- [Model-free Reinforcement Learning in Infinite-horizon Average-reward Markov Decision Processes](https://mlsanity.com/paper/1910.07072/) (2019)
- [Variance-reduced Q-learning is minimax optimal](https://mlsanity.com/paper/1906.04697/) (2019)
- [Accelerated Algorithms for Smooth Convex-Concave Minimax Problems with O(1/k2) Rate on Squared Gradient Norm](https://mlsanity.com/paper/2102.07922/) (2021)
- [Offline Reinforcement Learning: Fundamental Barriers for Value Function Approximation](https://mlsanity.com/paper/2111.10919/) (2021)
- [A First Order Method for Solving Convex Bi-Level Optimization Problems](https://mlsanity.com/paper/1702.03999/) (2017)
- [Variance Reduced Value Iteration and Faster Algorithms for Solving Markov Decision Processes](https://mlsanity.com/paper/1710.09988/) (2017)
- [Learning and Planning in Average-Reward Markov Decision Processes](https://mlsanity.com/paper/2006.16318/) (2020)
- [Learning Infinite-horizon Average-reward MDPs with Linear Function Approximation](https://mlsanity.com/paper/2007.11849/) (2020)
- [Regret Minimization for Reinforcement Learning by Evaluating the Optimal Bias Function](https://mlsanity.com/paper/1906.05110/) (2019)
- [Misspecified Linear Bandits](https://mlsanity.com/paper/1704.06880/) (2017)
- [Approximate Policy Iteration Schemes: A Comparison](https://mlsanity.com/paper/1405.2878/) (2014)
- [Primal-Dual π Learning: Sample Complexity and Sublinear Run Time for Ergodic Markov Decision Problems](https://mlsanity.com/paper/1710.06100/) (2017)
- [Towards Tight Bounds on the Sample Complexity of Average-reward MDPs](https://mlsanity.com/paper/2106.07046/) (2021)
- [Stochastic first-order methods for average-reward Markov decision processes](https://mlsanity.com/paper/2205.05800/) (2022)

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

- [Learning Policy from a Single Trajectory in Average-Reward Markov Decision Process](https://mlsanity.com/paper/2606.16729/) (2026)
- [Average-Reward Policy Identification from a Single Continuing Trajectory](https://mlsanity.com/paper/2610.20486/) (2026)

## Abstract (arXiv)

Although there is an extensive body of work characterizing the sample complexity of discounted-return offline RL with function approximations, prior work on the average-reward setting has received significantly less attention, and existing approaches rely on restrictive assumptions, such as ergodicity or linearity of the MDP. In this work, we establish the first sample complexity results for average-reward offline RL with function approximation for weakly communicating MDPs, a much milder assumption. To this end, we introduce Anchored Fitted Q-Iteration, which combines the standard Fitted Q-Iteration with an anchor mechanism. We show that the anchor, which can be interpreted as a form of weight decay, is crucial for enabling finite-time analysis in the average-reward setting. We also extend our finite-time analysis to the setup where the dataset is generated from a single-trajectory rather than IID transitions, again leveraging the anchor mechanism.