cs.AIFeb 28, 2026
SaveK^2-Agent: Co-Evolving Know-What and Know-How for Hierarchical Mobile Device Control
Organizations: Department of Computer Science and Technology, Tsinghua University · Huawei Noah’s Ark Lab · Institute of Automation, Chinese Academy of Sciences
Abstract
Existing mobile device control agents often perform poorly when solving complex tasks requiring long-horizon planning and precise operations, typically due to a lack of relevant task experience or unfamiliarity with skill execution. We propose K2-Agent, a hierarchical framework that models human-like cognition by separating and co-evolving declarative (knowing what) and procedural (knowing how) knowledge for planning and execution. K2-Agent's high level reasoner is bootstrapped from a single demonstration per task and runs a Summarize-Reflect-Locate-Revise (SRLR) loop to distill and iteratively refine task-level declarative knowledge through self-evolution. The low-level executor is trained with our curriculum-guided Group Relative Policy Optimization (C-GRPO), which (i) constructs a balanced sample pool using decoupled reward signals and (ii) employs dynamic demonstration injection to guide the model in autonomously generating successful trajectories for training. On the challenging AndroidWorld benchmark, K2-Agent achieves a 76.1% success rate using only raw screenshots and open-source backbones. Furthermore, K2-Agent shows powerful dual generalization: its high-level declarative knowledge transfers across diverse base models, while its low-level procedural skills achieve competitive performance on unseen tasks in ScreenSpot-v2 and Android-in-the-Wild (AitW).
Figures & tables
Figure 1: K²-Agent’s co-evolutionary learning curve on AndroidWorld. The main curve shows the agent’s success rate steadily improving. Ablations (lower curves) confirm the contribution of key components, and subplots below illustrate the expanding mastery over new apps and tasks.
Figure 2: Overview of the K²-Agent . Top : The SRLR loop where declarative knowledge (knowing what) is iteratively improved using feedback. Bottom : The skill acquisition process where procedural knowledge (knowing how) is learned via C-GRPO, bootstrapped from a single demonstration.
Figure 3: An illustration of the SRLR self-evolution loop. (1) Summarize: An initial knowledge base is automatically distilled from a demonstration. (2) Reflect: The agent analyzes its execution trace to identify deviations. (3) Locate: The failure’s root cause is pinpointed. (4) Revise: Atomic operators repair the knowledge base for the next iteration.
Figure 4: Our C-GRPO framework, featuring its two main curriculum components: Error-Decoupled Replay Balancing (left) to construct balanced mini-batches, and Dynamic Demonstration Injection (center) to provide adaptive guidance for the GRPO update (right).
| Type | Agent | Base Model | Input | SR |
| Training free | M3A ( Rawles et al., 2024 ) | GPT-4 Turbo | Screenshot + A11y | 30.6 |
| AndroidGen ( Lai et al., 2025 ) | GPT-o | A11y Tree | 46.8 | |
| Agent S2 ( Agashe et al., 2025 ) | Claude-3.5-Sonnet | Screenshot | 54.3 | |
| MobileUse ( Li et al., 2025 ) | Qwen2.5-VL-72B | Screenshot | 62.9 | |
| DroidRun ( DroidRun, 2025 ) | Gemini-2.5-Pro | Screenshot + A11y | 63.0 | |
| FinalRun ( FinalRun, 2025 ) | GPT-5 | Screenshot + A11y | 76.7 |
Table 1: Comparison of K 2 -Agent and baselines on AndroidWorld. Our method reports the mean ± std over 3 independent runs.
| Agent | AitW-General (SR %) | AitW-WebShopping (SR %) |
| SoM ( Zheng et al., 2024 ) | 16.7 | 11.5 |
| AppAgent ( Zhang et al., 2025 ) | 17.7 | 8.3 |
| CogAgent ( Hong et al., 2024 ) | 25.0 | 38.5 |
| AutoUI ( Zhang and Zhang, 2023 ) | 22.9 | 25.0 |
| DigiRL ( Bai et al., 2024 ) | 71.9 | 67.2 |
| K 2 -Agent | 86.5 | 68.3 |
Table 2: Zero-shot transfer to AitW using the low-level executor trained on AndroidWorld.
| Mobile | Desktop | Web | |||||
| Agent Model | Text | Icon | Text | Icon | Text | Icon | Overall |
| Operator ( OpenAI, 2025 ) | 47.3 | 41.5 | 90.2 | 80.3 | 92.8 | 84.3 | 70.5 |
| Claude 3.7 Sonnet ( Anthropic, 2025a ) | - | - | - | - | - | - | 87.6 |
| UI-TARS-72B ( Qin et al., 2025 ) | 94.8 | 86.3 | 91.2 | 87.9 | 91.5 | 87.7 | 90.3 |
| JEDI-7B ( Xie et al., 2025 ) | 96.9 | 87.2 | 95.9 | 87.9 | 94.4 | 84.2 | 91.7 |
| GUI-Owl-32B ( Ye et al., 2025 ) | 98.6 | 90.0 | 97.9 | 87.8 | 94.4 | 86.7 | 93.2 |
Table 3: Zero-shot performance of the K²-Agent executor on the ScreenSpot-v2 benchmark.
Figure 5: Ablation and Component Analysis. (a) : The declarative knowledge from our SRLR loop provides a substantial performance boost across four different powerful VLM backbones. (b) : Training reward curves for the low-level executor comparing full C-GRPO (blue), C-GRPO without replay balancing (red), and C-GRPO without demonstration injection (green).
| Configuration | SR (%) |
| No Hierarchy | 35.3 |
| No Hierarchy + SRLR | 58.6 |
| SRLR + SFT-Low | 62.0 |
| SRLR + GRPO-Low | 68.9 |
| K²-Agent (Full) | 76.1 |
Table 4: Ablation study of K²-Agent components on AndroidWorld benchmark.
Figure 6: Parameter sensitivity of C-GRPO. (a) : Varying the conventional pool ratio . (b) : Effect of the injection temperature in the difficulty-gating function.
Appendix figures & tables13 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 7: Cognitive inspiration for the K²-Agent framework. The design maps the human distinction between declarative (“knowing what”) and procedural (“knowing how”) knowledge onto a hierarchical agent architecture.
Figure 8: Distribution of the induced declarative knowledge
Figure 9: An example of a single training data sample in JSON format.
| Component | Hyperparameter | Value |
| High-Level Planner ( ) | ||
| MAX_ITER | Max revision cycles per task | 10 |
| SUCCESS_THRESH | Consecutive successes to stop | 3 |
| Low-Level Executor ( ) | ||
| Base Learning Rate | Learning rate for policy | |
| Epoch Count | Number of training epochs | 2 |
Table 5: Comprehensive list of hyperparameters for K²-Agent.
| Application | Description | # Tasks | |
| Simple Calendar Pro | A calendar app for creating, deleting, and managing events and appointments. | 17 | |
| Settings | The Android system settings app for managing device settings such as Bluetooth, Wi-Fi, and brightness. | 15 | |
| Markor | A note-taking app for creating, editing, deleting, and managing notes and folders. | 14 | |
| Broccoli - Recipe App | A recipe management app for adding, deleting, and organizing recipes. | 13 | |
| Pro Expense | An expense tracking app for adding, deleting, and managing expenses. | 9 | |
| Simple SMS Messenger | An SMS app for sending, replying to, and resending text messages. | 7 | |
Table 6: Overview of the 20 applications and the number of associated tasks in the AndroidWorld ( Rawles et al., 2024 ) . The description for each app highlights its core functionality.
| Action | Description | Arguments |
| click | Performs a standard, short tap on a specific screen location. Used for activating buttons, selecting items, or placing cursor focus. | coordinate |
| long_press | Executes a sustained press at a given coordinate. Essential for tasks like selecting text, opening context menus, or revealing hidden options. | coordinate |
| swipe | Drags from a starting point to an ending point. Used for scrolling, navigating pages, or adjusting sliders. | coordinate, coordinate2 |
| type | Inputs a character sequence into the currently focused text field. This action directly injects text, bypassing the on-screen keyboard. | text |
| system_button | Triggers a system-level hardware button command, such as navigating back or returning to the home screen. | button |
| terminate | Ends the current task episode, reporting the final outcome. This signals to the high-level planner whether the goal was achieved. | status |
Table 7: The structured action space of K²-Agent. Each action is defined as a function call with specific arguments to control the mobile device.
Figure 10: Public leaderboard of AndroidWorld as of August 2025, showing K²-Agent ranked 1st among all methods using only raw screenshots.
| Task | K²-Agent | mobile-use | K²-Agent(Gemini) | UI-Venus-72B | DroidRun | K²-Agent(Gpt-4o) |
|---|---|---|---|---|---|---|
| AudioRecorderRecordAudio | ✓ | ✓ | ✓ | ✓ | ✓ | ✗ |
| AudioRecorder-FileName | ✓ | ✓ | ✓ | ✗ | ✓ | ✓ |
| BrowserDraw | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
| BrowserMaze | ✓ | ✓ | ✗ | ✗ | ✓ | ✗ |
| BrowserMultiply | ✓ | ✓ | ✓ | ✗ | ✓ | ✓ |
| CameraTakePhoto | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Table 8: Detailed performance comparison on all 116 tasks in AndroidWorld.
| Mobile | Desktop | Web | |||||
| Agent Model | Text | Icon | Text | Icon | Text | Icon | Overall |
| Operator ( OpenAI, 2025 ) | 47.3 | 41.5 | 90.2 | 80.3 | 92.8 | 84.3 | 70.5 |
| Claude 3.7 Sonnet ( Anthropic, 2025a ) | - | - | - | - | - | - | 87.6 |
| UI-TARS-1.5 ( Qin et al., 2025 ) | - | - | - | - | - | - | 94.2 |
| Seed-1.5-VL ( Guo et al., 2025 ) | - | - | - | - | - | - | 95.2 |
| SeeClick ( Cheng et al., 2024 ) | 78.4 | 50.7 | 70.1 | 29.3 | 55.2 | 32.5 | 55.1 |
Table 9: Zero-shot performance of the K²-Agent executor on the ScreenSpot-v2 benchmark, compared to other state-of-the-art GUI grounding models. Our executor demonstrates competitive performance, highlighting the strong generalization of its learned procedural skills.
Figure 11: Successful execution of the complex, multi-app task MarkorCreateNoteAndSms .
Figure 12: A representative failure case from the RetroCreatePlaylist task.
Figure 13: Declarative knowledge generalization on Android-in-the-Wild (AitW).
Figure 14: Zero-shot procedural skill transfer to the ScreenSpot-v2 benchmark.
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