# A priori Estimates for Deep Residual Network in Continuous-time Reinforcement Learning

arXiv: https://arxiv.org/abs/2402.16899 · HTML: https://mlsanity.com/paper/2402.16899/

## 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 27 of its 50 references that are in the map.
- First posted on arXiv 24 Feb 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, 27 of 27)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Rainbow: Combining Improvements in Deep Reinforcement Learning](https://mlsanity.com/paper/1710.02298/) (2017)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers](https://mlsanity.com/paper/1811.04918/) (2018)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [A Theoretical Analysis of Deep Q-Learning](https://mlsanity.com/paper/1901.00137/) (2019)
- [Reinforcement learning based recommender systems: A survey](https://mlsanity.com/paper/2101.06286/) (2021)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering](https://mlsanity.com/paper/1807.04518/) (2018)
- [A Priori Estimates of the Population Risk for Two-layer Neural Networks](https://mlsanity.com/paper/1810.06397/) (2018)
- [Avoiding Overfitting: A Survey on Regularization Methods for Convolutional Neural Networks](https://mlsanity.com/paper/2201.03299/) (2022)
- [Reinforcement Learning for UAV Attitude Control](https://mlsanity.com/paper/1804.04154/) (2018)
- [Risk Bounds and Rademacher Complexity in Batch Reinforcement Learning](https://mlsanity.com/paper/2103.13883/) (2021)
- [Reinforcement Learning with General Value Function Approximation: Provably Efficient Approach via Bounded Eluder Dimension](https://mlsanity.com/paper/2005.10804/) (2020)
- [Reinforcement Learning for Quantitative Trading](https://mlsanity.com/paper/2109.13851/) (2021)
- [Approximation and Estimation for High-Dimensional Deep Learning Networks](https://mlsanity.com/paper/1809.03090/) (2018)
- [A Priori Estimates of the Population Risk for Residual Networks](https://mlsanity.com/paper/1903.02154/) (2019)
- [Optimizing for Interpretability in Deep Neural Networks with Tree Regularization](https://mlsanity.com/paper/1908.05254/) (2019)
- [An L2 Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximation](https://mlsanity.com/paper/2104.07794/) (2021)
- [Capacity Control of ReLU Neural Networks by Basis-path Norm](https://mlsanity.com/paper/1809.07122/) (2018)
- [Rate of Convergence and Error Bounds for LSTD(λ)](https://mlsanity.com/paper/1405.3229/) (2014)

## Abstract (arXiv)

Deep reinforcement learning excels in numerous large-scale practical applications. However, existing performance analyses ignores the unique characteristics of continuous-time control problems, is unable to directly estimate the generalization error of the Bellman optimal loss and require a boundedness assumption. Our work focuses on continuous-time control problems and proposes a method that is applicable to all such problems where the transition function satisfies semi-group and Lipschitz properties. Under this method, we can directly analyze the a priori generalization error of the Bellman optimal loss. The core of this method lies in two transformations of the loss function. To complete the transformation, we propose a decomposition method for the maximum operator. Additionally, this analysis method does not require a boundedness assumption. Finally, we obtain an a priori generalization error without the curse of dimensionality.