# GPG: Generalized Policy Gradient Theorem for Transformer-based Policies

arXiv: https://arxiv.org/abs/2512.10365 · HTML: https://mlsanity.com/paper/2512.10365/

## 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 29 of its 38 references that are in the map.
- First posted on arXiv 11 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, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [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)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [Search-o1: Agentic Search-Enhanced Large Reasoning Models](https://mlsanity.com/paper/2501.05366/) (2025)
- [A Survey of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2312.14925/) (2023)
- [WebWalker: Benchmarking LLMs in Web Traversal](https://mlsanity.com/paper/2501.07572/) (2025)
- [Agentic Reinforced Policy Optimization](https://mlsanity.com/paper/2507.19849/) (2025)
- [Tool-Star: Empowering LLM-Brained Multi-Tool Reasoner via Reinforcement Learning](https://mlsanity.com/paper/2505.16410/) (2025)
- [Agentic Entropy-Balanced Policy Optimization](https://mlsanity.com/paper/2510.14545/) (2025)
- [Controlling Large Language Model-based Agents for Large-Scale Decision-Making: An Actor-Critic Approach](https://mlsanity.com/paper/2311.13884/) (2023)
- [SQLBench: A Comprehensive Evaluation for Text-to-SQL Capabilities of Large Language Models](https://mlsanity.com/paper/2403.02951/) (2024)
- [PET-SQL: A Prompt-Enhanced Two-Round Refinement of Text-to-SQL with Cross-consistency](https://mlsanity.com/paper/2403.09732/) (2024)
- [DMQR-RAG: Diverse Multi-Query Rewriting for RAG](https://mlsanity.com/paper/2411.13154/) (2024)
- [DualRAG: A Dual-Process Approach to Integrate Reasoning and Retrieval for Multi-Hop Question Answering](https://mlsanity.com/paper/2504.18243/) (2025)
- [SheetAgent: Towards A Generalist Agent for Spreadsheet Reasoning and Manipulation via Large Language Models](https://mlsanity.com/paper/2403.03636/) (2024)
- [SQL-to-Schema Enhances Schema Linking in Text-to-SQL](https://mlsanity.com/paper/2405.09593/) (2024)
- [General Table Question Answering via Answer-Formula Joint Generation](https://mlsanity.com/paper/2503.12345/) (2025)

## Abstract (arXiv)

We present the Generalized Policy Gradient (GPG) Theorem, specifically designed for Transformer-based policies. Notably, we demonstrate that both standard Policy Gradient Theorem and GRPO emerge as special cases within our GPG framework. Furthermore, we explore its practical applications in training Large Language Models (LLMs), offering new insights into efficient policy optimization.