# Dropout Q-Functions for Doubly Efficient Reinforcement Learning

arXiv: https://arxiv.org/abs/2110.02034 · HTML: https://mlsanity.com/paper/2110.02034/

## Key facts

- Cited by 114 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 54 references that are in the map.
- First posted on arXiv 5 Oct 2021.

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Learning Dexterous In-Hand Manipulation](https://mlsanity.com/paper/1808.00177/) (2018)
- [MOPO: Model-based Offline Policy Optimization](https://mlsanity.com/paper/2005.13239/) (2020)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Learning Invariant Representations for Reinforcement Learning without Reconstruction](https://mlsanity.com/paper/2006.10742/) (2020)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [Randomized Ensembled Double Q-Learning: Learning Fast Without a Model](https://mlsanity.com/paper/2101.05982/) (2021)
- [Way Off-Policy Batch Deep Reinforcement Learning of Implicit Human Preferences in Dialog](https://mlsanity.com/paper/1907.00456/) (2019)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [Model-Ensemble Trust-Region Policy Optimization](https://mlsanity.com/paper/1802.10592/) (2018)
- [Randomized Prior Functions for Deep Reinforcement Learning](https://mlsanity.com/paper/1806.03335/) (2018)
- [Understanding and Improving Layer Normalization](https://mlsanity.com/paper/1911.07013/) (2019)
- [SUNRISE: A Simple Unified Framework for Ensemble Learning in Deep Reinforcement Learning](https://mlsanity.com/paper/2007.04938/) (2020)
- [Acme: A Research Framework for Distributed Reinforcement Learning](https://mlsanity.com/paper/2006.00979/) (2020)
- [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)

## Built on by (most cited first, 30 of 114)

- [Efficient Online Reinforcement Learning with Offline Data](https://mlsanity.com/paper/2302.02948/) (2023)
- [The Dormant Neuron Phenomenon in Deep Reinforcement Learning](https://mlsanity.com/paper/2302.12902/) (2023)
- [Revisiting the Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2305.09836/) (2023)
- [Bigger, Regularized, Optimistic: scaling for compute and sample-efficient continuous control](https://mlsanity.com/paper/2405.16158/) (2024)
- [METRA: Scalable Unsupervised RL with Metric-Aware Abstraction](https://mlsanity.com/paper/2310.08887/) (2023)
- [A Walk in the Park: Learning to Walk in 20 Minutes With Model-Free Reinforcement Learning](https://mlsanity.com/paper/2208.07860/) (2022)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [SimBa: Simplicity Bias for Scaling Up Parameters in Deep Reinforcement Learning](https://mlsanity.com/paper/2410.09754/) (2024)
- [Imitation Bootstrapped Reinforcement Learning](https://mlsanity.com/paper/2311.02198/) (2023)
- [Efficient Online Reinforcement Learning Fine-Tuning Need Not Retain Offline Data](https://mlsanity.com/paper/2412.07762/) (2024)
- [Overestimation, Overfitting, and Plasticity in Actor-Critic: the Bitter Lesson of Reinforcement Learning](https://mlsanity.com/paper/2403.00514/) (2024)
- [Sample-Efficient Multi-Objective Learning via Generalized Policy Improvement Prioritization](https://mlsanity.com/paper/2301.07784/) (2023)
- [DrM: Mastering Visual Reinforcement Learning through Dormant Ratio Minimization](https://mlsanity.com/paper/2310.19668/) (2023)
- [PLASTIC: Improving Input and Label Plasticity for Sample Efficient Reinforcement Learning](https://mlsanity.com/paper/2306.10711/) (2023)
- [A Review of Uncertainty for Deep Reinforcement Learning](https://mlsanity.com/paper/2208.09052/) (2022)
- [In value-based deep reinforcement learning, a pruned network is a good network](https://mlsanity.com/paper/2402.12479/) (2024)
- [Hyperspherical Normalization for Scalable Deep Reinforcement Learning](https://mlsanity.com/paper/2502.15280/) (2025)
- [Efficient Deep Reinforcement Learning Requires Regulating Overfitting](https://mlsanity.com/paper/2304.10466/) (2023)
- [Learning and Adapting Agile Locomotion Skills by Transferring Experience](https://mlsanity.com/paper/2304.09834/) (2023)
- [Rank2Reward: Learning Shaped Reward Functions from Passive Video](https://mlsanity.com/paper/2404.14735/) (2024)
- [RoboPianist: Dexterous Piano Playing with Deep Reinforcement Learning](https://mlsanity.com/paper/2304.04150/) (2023)
- [MaxInfoRL: Boosting exploration in reinforcement learning through information gain maximization](https://mlsanity.com/paper/2412.12098/) (2024)
- [Bridging Evolutionary Algorithms and Reinforcement Learning: A Comprehensive Survey on Hybrid Algorithms](https://mlsanity.com/paper/2401.11963/) (2024)
- [Grow Your Limits: Continuous Improvement with Real-World RL for Robotic Locomotion](https://mlsanity.com/paper/2310.17634/) (2023)
- [Dexterous Manipulation from Images: Autonomous Real-World RL via Substep Guidance](https://mlsanity.com/paper/2212.09902/) (2022)
- [Q-Ensemble for Offline RL: Don't Scale the Ensemble, Scale the Batch Size](https://mlsanity.com/paper/2211.11092/) (2022)
- [Scaling Off-Policy Reinforcement Learning with Batch and Weight Normalization](https://mlsanity.com/paper/2502.07523/) (2025)
- [Dissecting Deep RL with High Update Ratios: Combatting Value Divergence](https://mlsanity.com/paper/2403.05996/) (2024)
- [Rapidly Adapting Policies to the Real World via Simulation-Guided Fine-Tuning](https://mlsanity.com/paper/2502.02705/) (2025)
- [XQC: Well-conditioned Optimization Accelerates Deep Reinforcement Learning](https://mlsanity.com/paper/2509.25174/) (2025)

## Abstract (arXiv)

Randomized ensembled double Q-learning (REDQ) (Chen et al., 2021b) has recently achieved state-of-the-art sample efficiency on continuous-action reinforcement learning benchmarks. This superior sample efficiency is made possible by using a large Q-function ensemble. However, REDQ is much less computationally efficient than non-ensemble counterparts such as Soft Actor-Critic (SAC) (Haarnoja et al., 2018a). To make REDQ more computationally efficient, we propose a method of improving computational efficiency called DroQ, which is a variant of REDQ that uses a small ensemble of dropout Q-functions. Our dropout Q-functions are simple Q-functions equipped with dropout connection and layer normalization. Despite its simplicity of implementation, our experimental results indicate that DroQ is doubly (sample and computationally) efficient. It achieved comparable sample efficiency with REDQ, much better computational efficiency than REDQ, and comparable computational efficiency with that of SAC.