# ISOPO: Proximal policy gradients without pi-old

arXiv: https://arxiv.org/abs/2512.23353 · HTML: https://mlsanity.com/paper/2512.23353/

## Key facts

- Cited by 1 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 15 of its 19 references that are in the map.
- First posted on arXiv 29 Dec 2025.

## 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, 15 of 15)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [Do Not Let Low-Probability Tokens Over-Dominate in RL for LLMs](https://mlsanity.com/paper/2505.12929/) (2025)
- [On-Policy RL with Optimal Reward Baseline](https://mlsanity.com/paper/2505.23585/) (2025)

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

- [PROMA: Projected Microbatch Accumulation for Reference-Free Proximal Policy Updates](https://mlsanity.com/paper/2601.10498/) (2026)

## Abstract (arXiv)

This note introduces Isometric Policy Optimization (ISOPO), an efficient method to approximate the natural policy gradient in a single gradient step. In comparison, existing proximal policy methods such as GRPO or CISPO use multiple gradient steps with variants of importance ratio clipping to approximate a natural gradient step relative to a reference policy. In its simplest form, ISOPO normalizes the log-probability gradient of each sequence in the Fisher metric before contracting with the advantages. Another variant of ISOPO transforms the microbatch advantages based on the neural tangent kernel in each layer. ISOPO applies this transformation layer-wise in a single backward pass and can be implemented with negligible computational overhead compared to vanilla REINFORCE.