# From Imitation to Discrimination: Toward A Generalized Curriculum Advantage Mechanism Enhancing Cross-Domain Reasoning Tasks

arXiv: https://arxiv.org/abs/2512.02580 · HTML: https://mlsanity.com/paper/2512.02580/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 50 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 29 of 29)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [OS-ATLAS: A Foundation Action Model for Generalist GUI Agents](https://mlsanity.com/paper/2410.23218/) (2024)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [ScreenSpot-Pro: GUI Grounding for Professional High-Resolution Computer Use](https://mlsanity.com/paper/2504.07981/) (2025)
- [GUI-R1 : A Generalist R1-Style Vision-Language Action Model For GUI Agents](https://mlsanity.com/paper/2504.10458/) (2025)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [On the Effects of Data Scale on UI Control Agents](https://mlsanity.com/paper/2406.03679/) (2024)
- [GUIOdyssey: A Comprehensive Dataset for Cross-App GUI Navigation on Mobile Devices](https://mlsanity.com/paper/2406.08451/) (2024)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [OmniACT: A Dataset and Benchmark for Enabling Multimodal Generalist Autonomous Agents for Desktop and Web](https://mlsanity.com/paper/2402.17553/) (2024)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [Back to Basics: Revisiting REINFORCE Style Optimization for Learning from Human Feedback in LLMs](https://mlsanity.com/paper/2402.14740/) (2024)
- [Efficient Reinforcement Finetuning via Adaptive Curriculum Learning](https://mlsanity.com/paper/2504.05520/) (2025)
- [Curriculum Reinforcement Learning from Easy to Hard Tasks Improves LLM Reasoning](https://mlsanity.com/paper/2506.06632/) (2025)
- [Beyond Examples: High-level Automated Reasoning Paradigm in In-Context Learning via MCTS](https://mlsanity.com/paper/2411.18478/) (2024)
- [SPEED-RL: Faster Training of Reasoning Models via Online Curriculum Learning](https://mlsanity.com/paper/2506.09016/) (2025)
- [Strategic Data Ordering: Enhancing Large Language Model Performance through Curriculum Learning](https://mlsanity.com/paper/2405.07490/) (2024)
- [TemplateRL: Structured Template-Guided Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2505.15692/) (2025)
- [Let's Be Self-generated via Step by Step: A Curriculum Learning Approach to Automated Reasoning with Large Language Models](https://mlsanity.com/paper/2410.21728/) (2024)
- [Harnessing Negative Signals: Reinforcement Distillation from Teacher Data for LLM Reasoning](https://mlsanity.com/paper/2505.24850/) (2025)

## Abstract (arXiv)

Reinforcement learning has emerged as a paradigm for post-training large language models, boosting their reasoning capabilities. Such approaches compute an advantage value for each sample, reflecting better or worse performance than expected, thereby yielding both positive and negative signals for training. However, the indiscriminate mixing of the two signals in existing methods, especially from the early stages, may lead to ambiguous guidance and limited gains. To address this issue, we propose **CAPO** (**C**urriculum **A**dvantage **P**olicy **O**ptimization), an adaptive curriculum mechanism based on advantage signals. The proposed mechanism bootstraps imitation learning with positive-only advantage samples to establish robust foundations, and subsequently introduces negative signals to cultivate discriminative capabilities, thereby improving generalization across complex scenarios. Compatible with diverse optimization methods including GRPO, PPO, RLOO, and Reinforce++, our method consistently achieves stable and significant improvements in mathematical reasoning tasks, and further generalizes effectively to multimodal Graphical User Interface (GUI) reasoning scenarios, establishing itself as a versatile and robust optimization framework.