# Symmetric Behavior Regularized Policy Optimization

arXiv: https://arxiv.org/abs/2508.04225 · HTML: https://mlsanity.com/paper/2508.04225/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Offline RL algorithms, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 34 of its 51 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Placed in

- Offline RL and imitation learning from data / [Offline RL algorithms](https://mlsanity.com/offlinerl/offline-rl-algorithms/)

## Builds on (most cited first, 30 of 34)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Uncertainty-Based Offline Reinforcement Learning with Diversified Q-Ensemble](https://mlsanity.com/paper/2110.01548/) (2021)
- [DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections](https://mlsanity.com/paper/1906.04733/) (2019)
- [Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints](https://mlsanity.com/paper/2309.16240/) (2023)
- [Revisiting the Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2305.09836/) (2023)
- [OptiDICE: Offline Policy Optimization via Stationary Distribution Correction Estimation](https://mlsanity.com/paper/2106.10783/) (2021)
- [Aligning Language Models with Preferences through f-divergence Minimization](https://mlsanity.com/paper/2302.08215/) (2023)
- [Extreme Q-Learning: MaxEnt RL without Entropy](https://mlsanity.com/paper/2301.02328/) (2023)
- [Offline RL with No OOD Actions: In-Sample Learning via Implicit Value Regularization](https://mlsanity.com/paper/2303.15810/) (2023)
- [f-Divergence Minimization for Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/2307.15190/) (2023)
- [Reinforcement Learning via Fenchel-Rockafellar Duality](https://mlsanity.com/paper/2001.01866/) (2020)
- [Correcting the Mythos of KL-Regularization: Direct Alignment without Overoptimization via Chi-Squared Preference Optimization](https://mlsanity.com/paper/2407.13399/) (2024)
- [How Far I'll Go: Offline Goal-Conditioned Reinforcement Learning via f-Advantage Regression](https://mlsanity.com/paper/2206.03023/) (2022)
- [Behavior Proximal Policy Optimization](https://mlsanity.com/paper/2302.11312/) (2023)
- [Greedification Operators for Policy Optimization: Investigating Forward and Reverse KL Divergences](https://mlsanity.com/paper/2107.08285/) (2021)
- [Leverage the Average: an Analysis of KL Regularization in RL](https://mlsanity.com/paper/2003.14089/) (2020)
- [ODICE: Revealing the Mystery of Distribution Correction Estimation via Orthogonal-gradient Update](https://mlsanity.com/paper/2402.00348/) (2024)
- [f-PO: Generalizing Preference Optimization with f-divergence Minimization](https://mlsanity.com/paper/2410.21662/) (2024)
- [A general class of surrogate functions for stable and efficient reinforcement learning](https://mlsanity.com/paper/2108.05828/) (2021)
- [f-Policy Gradients: A General Framework for Goal Conditioned RL using f-Divergences](https://mlsanity.com/paper/2310.06794/) (2023)
- [Iteratively Refined Behavior Regularization for Offline Reinforcement Learning](https://mlsanity.com/paper/2306.05726/) (2023)

## Abstract (arXiv)

Behavior Regularized Policy Optimization (BRPO) leverages asymmetric divergence regularization to mitigate distribution shift in offline reinforcement learning. This paper is the first to study the open question of symmetric BRPO. Using didactic examples, we show that symmetric regularization can outperform asymmetric regularization in addressing one-sided bias, near-boundary policy updates, and projection geometry consistency. However, symmetric divergences do not fit BRPO naturally: they do not permit a closed-form solution when used as regularizers, and can lead to numerical instability when used as optimization objectives. We first introduce a universal BRPO framework using an infinite series of Pearson-Vajda divergences to represent any f-divergence, which includes both symmetric and asymmetric divergences. We use a finite-series approximation to obtain the following results for symmetric BRPO: (1) a closed-form optimal policy expression; (2) a numerically stable optimization surrogate; and (3) a tight upper bound on the approximation quality. On the D4RL benchmark and in didactic examples, we show that the proposed method achieves consistently strong results and is robust to the number of terms in the approximation.