# Regularized Q-learning through Robust Averaging

arXiv: https://arxiv.org/abs/2405.02201 · HTML: https://mlsanity.com/paper/2405.02201/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 3 May 2024.

## 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, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Randomized Ensembled Double Q-Learning: Learning Fast Without a Model](https://mlsanity.com/paper/2101.05982/) (2021)
- [Maxmin Q-learning: Controlling the Estimation Bias of Q-learning](https://mlsanity.com/paper/2002.06487/) (2020)
- [Averaged-DQN: Variance Reduction and Stabilization for Deep Reinforcement Learning](https://mlsanity.com/paper/1611.01929/) (2016)
- [Finite-Time Analysis of Asynchronous Stochastic Approximation and Q-Learning](https://mlsanity.com/paper/2002.00260/) (2020)
- [Variance-reduced Q-learning is minimax optimal](https://mlsanity.com/paper/1906.04697/) (2019)
- [Munchausen Reinforcement Learning](https://mlsanity.com/paper/2007.14430/) (2020)
- [Explicit Mean-Square Error Bounds for Monte-Carlo and Linear Stochastic Approximation](https://mlsanity.com/paper/2002.02584/) (2020)
- [Regularized Q-learning](https://mlsanity.com/paper/2202.05404/) (2022)
- [The Mean-Squared Error of Double Q-Learning](https://mlsanity.com/paper/2007.05034/) (2020)
- [Mean-Covariance Robust Risk Measurement](https://mlsanity.com/paper/2112.09959/) (2021)
- [Fastest Convergence for Q-learning](https://mlsanity.com/paper/1707.03770/) (2017)
- [Convex Q Learning in a Stochastic Environment: Extended Version](https://mlsanity.com/paper/2309.05105/) (2023)
- [Convex Q-Learning, Part 1: Deterministic Optimal Control](https://mlsanity.com/paper/2008.03559/) (2020)
- [Sufficient Exploration for Convex Q-learning](https://mlsanity.com/paper/2210.09409/) (2022)

## Abstract (arXiv)

We propose a new Q-learning variant, called 2RA Q-learning, that addresses some weaknesses of existing Q-learning methods in a principled manner. One such weakness is an underlying estimation bias which cannot be controlled and often results in poor performance. We propose a distributionally robust estimator for the maximum expected value term, which allows us to precisely control the level of estimation bias introduced. The distributionally robust estimator admits a closed-form solution such that the proposed algorithm has a computational cost per iteration comparable to Watkins' Q-learning. For the tabular case, we show that 2RA Q-learning converges to the optimal policy and analyze its asymptotic mean-squared error. Lastly, we conduct numerical experiments for various settings, which corroborate our theoretical findings and indicate that 2RA Q-learning often performs better than existing methods.