# Geometric Value Iteration: Dynamic Error-Aware KL Regularization for Reinforcement Learning

arXiv: https://arxiv.org/abs/2107.07659 · HTML: https://mlsanity.com/paper/2107.07659/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 16 Jul 2021.

## Builds on (most cited first, 17 of 17)

- [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)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (2019)
- [Understanding the impact of entropy on policy optimization](https://mlsanity.com/paper/1811.11214/) (2018)
- [Diagnosing Bottlenecks in Deep Q-learning Algorithms](https://mlsanity.com/paper/1902.10250/) (2019)
- [Munchausen Reinforcement Learning](https://mlsanity.com/paper/2007.14430/) (2020)
- [Increasing the Action Gap: New Operators for Reinforcement Learning](https://mlsanity.com/paper/1512.04860/) (2015)
- [Trust-PCL: An Off-Policy Trust Region Method for Continuous Control](https://mlsanity.com/paper/1707.01891/) (2017)
- [Momentum in Reinforcement Learning](https://mlsanity.com/paper/1910.09322/) (2019)
- [Deep Conservative Policy Iteration](https://mlsanity.com/paper/1906.09784/) (2019)

## Built on by (most cited first, 1 of 1)

- [Generalized Munchausen Reinforcement Learning using Tsallis KL Divergence](https://mlsanity.com/paper/2301.11476/) (2023)

## Abstract (arXiv)

The recent boom in the literature on entropy-regularized reinforcement learning (RL) approaches reveals that Kullback-Leibler (KL) regularization brings advantages to RL algorithms by canceling out errors under mild assumptions. However, existing analyses focus on fixed regularization with a constant weighting coefficient and do not consider cases where the coefficient is allowed to change dynamically. In this paper, we study the dynamic coefficient scheme and present the first asymptotic error bound. Based on the dynamic coefficient error bound, we propose an effective scheme to tune the coefficient according to the magnitude of error in favor of more robust learning. Complementing this development, we propose a novel algorithm, Geometric Value Iteration (GVI), that features a dynamic error-aware KL coefficient design with the aim of mitigating the impact of errors on performance. Our experiments demonstrate that GVI can effectively exploit the trade-off between learning speed and robustness over uniform averaging of a constant KL coefficient. The combination of GVI and deep networks shows stable learning behavior even in the absence of a target network, where algorithms with a constant KL coefficient would greatly oscillate or even fail to converge.