# Local Guidance, Global Impact: Gaussian-Reshaped Trust Region Unlocks Behavior Transitions

arXiv: https://arxiv.org/abs/2606.03382 · HTML: https://mlsanity.com/paper/2606.03382/

## 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 61 of its 78 references that are in the map.
- First posted on arXiv 2 Jun 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 61)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Solving Rubik's Cube with a Robot Hand](https://mlsanity.com/paper/1910.07113/) (2019)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Leveraging Procedural Generation to Benchmark Reinforcement Learning](https://mlsanity.com/paper/1912.01588/) (2019)
- [Efficient Online Reinforcement Learning with Offline Data](https://mlsanity.com/paper/2302.02948/) (2023)
- [Towards Continual Reinforcement Learning: A Review and Perspectives](https://mlsanity.com/paper/2012.13490/) (2020)
- [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)
- [Residual Policy Learning](https://mlsanity.com/paper/1812.06298/) (2018)
- [What Matters In On-Policy Reinforcement Learning? A Large-Scale Empirical Study](https://mlsanity.com/paper/2006.05990/) (2020)
- [Bigger, Better, Faster: Human-level Atari with human-level efficiency](https://mlsanity.com/paper/2305.19452/) (2023)
- [SimpleTIR: End-to-End Reinforcement Learning for Multi-Turn Tool-Integrated Reasoning](https://mlsanity.com/paper/2509.02479/) (2025)
- [Phasic Policy Gradient](https://mlsanity.com/paper/2009.04416/) (2020)
- [Loss of Plasticity in Continual Deep Reinforcement Learning](https://mlsanity.com/paper/2303.07507/) (2023)
- [Continual World: A Robotic Benchmark For Continual Reinforcement Learning](https://mlsanity.com/paper/2105.10919/) (2021)
- [A Definition of Continual Reinforcement Learning](https://mlsanity.com/paper/2307.11046/) (2023)

## Abstract (arXiv)

While Proximal Policy Optimization (PPO) demonstrates strong performance in stationary settings, we show that its standard optimization paradigm struggles in continual and non-stationary environments. The failure does not stem from insufficient model capacity or overly restrictive clipping. Instead, PPO performs persistent, directionally inefficient local updates, which indicates a lack of geometry-aware guidance for accumulating meaningful behavioral change and ultimately hindering transitions toward new behavior patterns. Although divergence-based regularization introduces partial geometric awareness, its monotonically increasing penalties implicitly discourage large policy deviations, even when such shifts are necessary for effective adaptation. To address this limitation, we propose Gaussian Trust Region Policy Optimization (GTR), which reshapes the trust region using a Gaussian kernel. The resulting constraint is bounded and non-monotonic, providing strong local stability while progressively relaxing under sustained high-advantage updates. To further improve robustness, we introduce a Mixture Gaussian Anchor that adapts to recent policy trajectories, reducing variance induced by stale references. GTR is architecture-agnostic and achieves strong performance across games, simulated robotic control, open-world exploration, and language model post-training. These results demonstrate that geometry-aware trust-region design can be a promising direction for robust reinforcement learning in complex non-stationary environments. Our code is available at https://anonymous.4open.science/r/GTR_demo/README.md.