# Understanding and Stabilizing Deep Q-Learning via Controlled Bootstrapping and Regulated Value Dynamics

arXiv: https://arxiv.org/abs/2608.16182 · HTML: https://mlsanity.com/paper/2608.16182/

## 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 32 of its 39 references that are in the map.
- First posted on arXiv 17 Aug 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, 30 of 32)

- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [CURL: Contrastive Unsupervised Representations for Reinforcement Learning](https://mlsanity.com/paper/2004.04136/) (2020)
- [Image Augmentation Is All You Need: Regularizing Deep Reinforcement Learning from Pixels](https://mlsanity.com/paper/2004.13649/) (2020)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Leveraging Procedural Generation to Benchmark Reinforcement Learning](https://mlsanity.com/paper/1912.01588/) (2019)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Transformers are Sample-Efficient World Models](https://mlsanity.com/paper/2209.00588/) (2022)
- [Data-Efficient Reinforcement Learning with Self-Predictive Representations](https://mlsanity.com/paper/2007.05929/) (2020)
- [Diffusion for World Modeling: Visual Details Matter in Atari](https://mlsanity.com/paper/2405.12399/) (2024)
- [Randomized Ensembled Double Q-Learning: Learning Fast Without a Model](https://mlsanity.com/paper/2101.05982/) (2021)
- [The Primacy Bias in Deep Reinforcement Learning](https://mlsanity.com/paper/2205.07802/) (2022)
- [The Dormant Neuron Phenomenon in Deep Reinforcement Learning](https://mlsanity.com/paper/2302.12902/) (2023)
- [Understanding plasticity in neural networks](https://mlsanity.com/paper/2303.01486/) (2023)
- [Controlling Overestimation Bias with Truncated Mixture of Continuous Distributional Quantile Critics](https://mlsanity.com/paper/2005.04269/) (2020)
- [SUNRISE: A Simple Unified Framework for Ensemble Learning in Deep Reinforcement Learning](https://mlsanity.com/paper/2007.04938/) (2020)
- [Bigger, Better, Faster: Human-level Atari with human-level efficiency](https://mlsanity.com/paper/2305.19452/) (2023)
- [When to use parametric models in reinforcement learning?](https://mlsanity.com/paper/1906.05243/) (2019)
- [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)
- [STORM: Efficient Stochastic Transformer based World Models for Reinforcement Learning](https://mlsanity.com/paper/2310.09615/) (2023)
- [Revisiting Rainbow: Promoting more Insightful and Inclusive Deep Reinforcement Learning Research](https://mlsanity.com/paper/2011.14826/) (2020)
- [Spectral Normalisation for Deep Reinforcement Learning: an Optimisation Perspective](https://mlsanity.com/paper/2105.05246/) (2021)
- [Overestimation, Overfitting, and Plasticity in Actor-Critic: the Bitter Lesson of Reinforcement Learning](https://mlsanity.com/paper/2403.00514/) (2024)
- [Stable Gradients for Stable Learning at Scale in Deep Reinforcement Learning](https://mlsanity.com/paper/2506.15544/) (2025)
- [SPQR: Controlling Q-ensemble Independence with Spiked Random Model for Reinforcement Learning](https://mlsanity.com/paper/2401.03137/) (2024)
- [Learning to Play Atari in a World of Tokens](https://mlsanity.com/paper/2406.01361/) (2024)

## Abstract (arXiv)

Deep Q-learning (DQL) has achieved remarkable empirical success in reinforcement learning, yet its training process remains notoriously unstable. Existing studies often attribute instability to isolated factors such as overestimation bias or representation learning issues, lacking a unified understanding of how different sources of instability interact during recursive value estimation. In this work, we provide a systematic analysis of instability in deep Q-learning from three complementary perspectives: operator-level bias in Bellman bootstrapping, estimator-level sensitivity of greedy action selection to regression noise, and parameter-dynamics imbalance under aggressive data reuse. We identify a reward-triggered self-reinforcing trap and characteristic parameter spike dynamics, then derive stabilization principles for controlled bootstrapping, ensemble quantile estimation, and spike-based parameter regulation. Experiments on Atari-100K and Procgen demonstrate competitive performance and improved training stability.