With Large Language Model (LLM) pre-training and fine-tuning shifting its focus from data volume to data quality, quality data selection has emerged as a critical research topic. Existing online data selection methods for LLM training are typically "batch-constrained", limiting optimization to local utility within random batches. To overcome this, we propose GAIA (Global Adaptive Instruction tuning via GAussian processes), a framework that formulates data valuation as a global estimation process. GAIA employs Gaussian Process regression to model continuous utility manifolds across the semantic space, utilizing an adaptive strategy fusion mechanism to dynamically prioritize high-utility samples. By casting the strategy-posterior update as an instance of the classical fixed-share Hedge framework for tracking the best expert, we inherit a dynamic-regret guarantee that characterizes GAIA's robustness under non-stationary quality scores during training. Empirical evaluations on three datasets demonstrate that GAIA significantly outperforms state-of-the-art baselines like \greats, establishing our method as a scalable and robust solution for efficient instruction tuning.

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