# CORE: Code-based Inverse Self-Training Framework with Graph Expansion for Virtual Agents

arXiv: https://arxiv.org/abs/2601.02201 · HTML: https://mlsanity.com/paper/2601.02201/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Embodied and 3D vision-language models, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 36 of its 44 references that are in the map.
- First posted on arXiv 5 Jan 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)
- Synthetic data and self-improvement for LLMs / [Self-evolving LLM agents](https://mlsanity.com/synth/self-evolving-llm-agents/)

## Builds on (most cited first, 30 of 36)

- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [OSWorld: Benchmarking Multimodal Agents for Open-Ended Tasks in Real Computer Environments](https://mlsanity.com/paper/2404.07972/) (2024)
- [A Survey on Multimodal Large Language Models](https://mlsanity.com/paper/2306.13549/) (2023)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [Behavioral Cloning from Observation](https://mlsanity.com/paper/1805.01954/) (2018)
- [AndroidWorld: A Dynamic Benchmarking Environment for Autonomous Agents](https://mlsanity.com/paper/2405.14573/) (2024)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Navigating the Digital World as Humans Do: Universal Visual Grounding for GUI Agents](https://mlsanity.com/paper/2410.05243/) (2024)
- [OS-ATLAS: A Foundation Action Model for Generalist GUI Agents](https://mlsanity.com/paper/2410.23218/) (2024)
- [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://mlsanity.com/paper/2207.01780/) (2022)
- [MM-LLMs: Recent Advances in MultiModal Large Language Models](https://mlsanity.com/paper/2401.13601/) (2024)
- [Aguvis: Unified Pure Vision Agents for Autonomous GUI Interaction](https://mlsanity.com/paper/2412.04454/) (2024)
- [GUI-R1 : A Generalist R1-Style Vision-Language Action Model For GUI Agents](https://mlsanity.com/paper/2504.10458/) (2025)
- [ShowUI: One Vision-Language-Action Model for GUI Visual Agent](https://mlsanity.com/paper/2411.17465/) (2024)
- [DigiRL: Training In-The-Wild Device-Control Agents with Autonomous Reinforcement Learning](https://mlsanity.com/paper/2406.11896/) (2024)
- [Trial and Error: Exploration-Based Trajectory Optimization for LLM Agents](https://mlsanity.com/paper/2403.02502/) (2024)
- [Mobile-Agent-E: Self-Evolving Mobile Assistant for Complex Tasks](https://mlsanity.com/paper/2501.11733/) (2025)
- [WebCanvas: Benchmarking Web Agents in Online Environments](https://mlsanity.com/paper/2406.12373/) (2024)
- [RoboCat: A Self-Improving Generalist Agent for Robotic Manipulation](https://mlsanity.com/paper/2306.11706/) (2023)
- [Fine-tuning Multimodal LLMs to Follow Zero-shot Demonstrative Instructions](https://mlsanity.com/paper/2308.04152/) (2023)
- [Self-play with Execution Feedback: Improving Instruction-following Capabilities of Large Language Models](https://mlsanity.com/paper/2406.13542/) (2024)
- [Large Language Models Can Self-Improve At Web Agent Tasks](https://mlsanity.com/paper/2405.20309/) (2024)
- [CRAB: Cross-environment Agent Benchmark for Multimodal Language Model Agents](https://mlsanity.com/paper/2407.01511/) (2024)
- [ScribeAgent: Towards Specialized Web Agents Using Production-Scale Workflow Data](https://mlsanity.com/paper/2411.15004/) (2024)
- [Comprehensive Overview of Reward Engineering and Shaping in Advancing Reinforcement Learning Applications](https://mlsanity.com/paper/2408.10215/) (2024)
- [BAGEL: Bootstrapping Agents by Guiding Exploration with Language](https://mlsanity.com/paper/2403.08140/) (2024)

## Abstract (arXiv)

The development of Multimodal Virtual Agents has made significant progress through the integration of Multimodal Large Language Models. However, mainstream training paradigms face key challenges: Behavior Cloning is simple and effective through imitation but suffers from low behavioral diversity, while Reinforcement Learning is capable of discovering novel strategies through exploration but heavily relies on manually designed reward functions. To address the conflict between these two methods, we present CORE, a Code-based Inverse Self-Training Framework with Graph Expansion that bridges imitation and exploration, offering a novel training framework that promotes behavioral diversity while eliminating the reliance on manually reward design. Specifically, we introduce Semantic Code Abstraction to automatically infers reward functions from expert demonstrations without manual design. The inferred reward function, referred to as the Label Function, is executable code that verifies one key step within a task. Building on this, we propose Strategy Graph Expansion to enhance in-domain behavioral diversity, which constructs a multi-path graph called Strategy Graph that captures diverse valid solutions beyond expert demonstrations. Furthermore, we introduce Trajectory-Guided Extrapolation, which enriches out-of-domain behavioral diversity by utilizing both successful and failed trajectories to expand the task space. Experiments on Web and Android platforms demonstrate that CORE significantly improves both overall performance and generalization, highlighting its potential as a robust and generalizable training paradigm for building powerful virtual agents.