Vision-language models are increasingly deployed as computer-use agents (CUAs) that operate desktops and browsers. Top-performing CUAs are framework-based systems that decompose planning and execution, while end-to-end screenshot-to-action policies are easier to deploy but lag behind on benchmarks such as OSWorld-Verified. GUI datasets like OSWorld pose two bottlenecks: they expose only a few hundred interactive, verifiable tasks and environments, and expert trajectories must be gathered by interacting with these environments, making such data hard to scale. We therefore ask how reinforcement learning from verifiable rewards (RLVR) can best exploit a small pool of exist expert trajectories to train end-to-end policies. Na"ively mixing these off-policy traces into on-policy RLVR is brittle: even after format conversion, expert trajectories exhibit structural mismatch and distribution shift from the learner. We propose BEPA (Bi-Level Expert-to-Policy Assimilation), which turns static expert traces into policy-aligned guidance via self-rolled reachable trajectories under the base policy (LEVEL-1) and a per-task, dynamically updated cache used in RLVR (LEVEL-2). On OSWorld-Verified, BEPA improves UITARS1.5-7B success from 22.87% to 32.13% and raises a held-out split from 5.74% to 10.30%, with consistent gains on MMBench-GUI and Online-Mind2Web. Our code and data are available at an anonymous repository: https://anonymous.4open.science/r/ACL_BEPA.

Federated domain-specific instruction tuning (FedDIT) for large language models (LLMs) aims to enhance performance in specialized domains using distributed private and limited data, yet identifying key performance drivers and optimal augmentation strategies remains challenging. We empirically establish that cross-client domain coverage, rather than data heterogeneity, is the pivotal factor. We then introduce FedDCA, an algorithm that explicitly maximizes this coverage through diversity-oriented client center selection and retrieval-based augmentation, constructing diverse, non-redundant cross-client instruction sets. Extensive experiments across multiple domains demonstrate FedDCA’s superiority over eleven baselines, achieving performance gains of up to 29.19% and domain coverage improvements of 4.82%-21.36%. FedDCA maintains its effectiveness in diverse and challenging scenarios, including data selection, held-out settings where task-specific public data is scarce and various data heterogeneity, with manageable privacy risks. This work clarifies critical FedDIT dynamics and presents FedDCA as an effective, privacy-preserving, and scalable solution for advancing domain-specific LLM tuning.