# Statistical Guarantees for Lifelong Reinforcement Learning using PAC-Bayes Theory

arXiv: https://arxiv.org/abs/2411.00401 · HTML: https://mlsanity.com/paper/2411.00401/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 37 of its 54 references that are in the map.
- First posted on arXiv 1 Nov 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, 30 of 37)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Target-driven Visual Navigation in Indoor Scenes using Deep Reinforcement Learning](https://mlsanity.com/paper/1609.05143/) (2016)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Towards Continual Reinforcement Learning: A Review and Perspectives](https://mlsanity.com/paper/2012.13490/) (2020)
- [A Definition of Continual Reinforcement Learning](https://mlsanity.com/paper/2307.11046/) (2023)
- [Meta-Learning by Adjusting Priors Based on Extended PAC-Bayes Theory](https://mlsanity.com/paper/1711.01244/) (2017)
- [A general sample complexity analysis of vanilla policy gradient](https://mlsanity.com/paper/2107.11433/) (2021)
- [learn2learn: A Library for Meta-Learning Research](https://mlsanity.com/paper/2008.12284/) (2020)
- [On the role of data in PAC-Bayes bounds](https://mlsanity.com/paper/2006.10929/) (2020)
- [A Provably Efficient Model-Free Posterior Sampling Method for Episodic Reinforcement Learning](https://mlsanity.com/paper/2208.10904/) (2022)
- [Data-dependent Initializations of Convolutional Neural Networks](https://mlsanity.com/paper/1511.06856/) (2015)
- [Robust and Efficient Transfer Learning with Hidden-Parameter Markov Decision Processes](https://mlsanity.com/paper/1706.06544/) (2017)
- [Lifelong Policy Gradient Learning of Factored Policies for Faster Training Without Forgetting](https://mlsanity.com/paper/2007.07011/) (2020)
- [Regret Minimization Experience Replay in Off-Policy Reinforcement Learning](https://mlsanity.com/paper/2105.07253/) (2021)
- [Lipschitz Lifelong Reinforcement Learning](https://mlsanity.com/paper/2001.05411/) (2020)
- [PAC-Bayes Control: Learning Policies that Provably Generalize to Novel Environments](https://mlsanity.com/paper/1806.04225/) (2018)
- [Efficient Frameworks for Generalized Low-Rank Matrix Bandit Problems](https://mlsanity.com/paper/2401.07298/) (2024)
- [Prediction and Control in Continual Reinforcement Learning](https://mlsanity.com/paper/2312.11669/) (2023)
- [Lifelong Learning with a Changing Action Set](https://mlsanity.com/paper/1906.01770/) (2019)
- [The Effectiveness of World Models for Continual Reinforcement Learning](https://mlsanity.com/paper/2211.15944/) (2022)
- [Probably Approximately Correct Vision-Based Planning using Motion Primitives](https://mlsanity.com/paper/2002.12852/) (2020)
- [Statistical Guarantees for Variational Autoencoders using PAC-Bayesian Theory](https://mlsanity.com/paper/2310.04935/) (2023)

## Built on by (most cited first, 7 of 7)

- [The Computational Limits of State-Space Models and Mamba via the Lens of Circuit Complexity](https://mlsanity.com/paper/2412.06148/) (2024)
- [Breaking the Frozen Subspace: Importance Sampling for Low-Rank Optimization in LLM Pretraining](https://mlsanity.com/paper/2502.05790/) (2025)
- [Scaling Law Phenomena Across Regression Paradigms: Multiple and Kernel Approaches](https://mlsanity.com/paper/2503.01314/) (2025)
- [Unlocking the Potential of Text-to-Image Diffusion with PAC-Bayesian Theory](https://mlsanity.com/paper/2411.17472/) (2024)
- [CoVE: Compressed Vocabulary Expansion Makes Better LLM-based Recommender Systems](https://mlsanity.com/paper/2506.19993/) (2025)
- [Time and Memory Trade-off of KV-Cache Compression in Tensor Transformer Decoding](https://mlsanity.com/paper/2503.11108/) (2025)
- [PAC-Bayesian Reinforcement Learning Trains Generalizable Policies](https://mlsanity.com/paper/2510.10544/) (2025)

## Abstract (arXiv)

Lifelong reinforcement learning (RL) has been developed as a paradigm for extending single-task RL to more realistic, dynamic settings. In lifelong RL, the "life" of an RL agent is modeled as a stream of tasks drawn from a task distribution. We propose EPIC (Empirical PAC-Bayes that Improves Continuously), a novel algorithm designed for lifelong RL using PAC-Bayes theory. EPIC learns a shared policy distribution, referred to as the world policy, which enables rapid adaptation to new tasks while retaining valuable knowledge from previous experiences. Our theoretical analysis establishes a relationship between the algorithm's generalization performance and the number of prior tasks preserved in memory. We also derive the sample complexity of EPIC in terms of RL regret. Extensive experiments on a variety of environments demonstrate that EPIC significantly outperforms existing methods in lifelong RL, offering both theoretical guarantees and practical efficacy through the use of the world policy.