Dynamic Sampling that Adapts: Iterative DPO for Self-Aware Mathematical Reasoning
This addresses the need for adaptive data selection in online training for mathematical reasoning models, representing a novel method rather than an incremental improvement.
The paper tackles the problem of static data selection methods that lack adaptability during continuous training for mathematical reasoning tasks, introducing SAI-DPO which dynamically selects training data based on real-time model feedback. The result is an average performance boost of up to 21.3 percentage points across benchmarks, with specific gains of 10 and 15 points on AIME24 and AMC23.
In the realm of data selection for reasoning tasks, existing approaches predominantly rely on externally predefined static metrics such as difficulty and diversity, which are often designed for supervised fine-tuning (SFT) and lack adaptability to continuous training processes. A critical limitation of these methods is their inability to dynamically align with the evolving capabilities of models during online training, a gap that becomes increasingly pronounced with the rise of dynamic training paradigms and online reinforcement learning (RL) frameworks (e.g., R1 models). To address this, we introduce SAI-DPO, an algorithm that dynamically selects training data by continuously assessing a model's stage-specific reasoning abilities across different training phases. By integrating real-time model performance feedback, SAI-DPO adaptively adapts data selection to the evolving strengths and weaknesses of the model, thus enhancing both data utilization efficiency and final task performance. Extensive experiments on three state-of-the-art models and eight mathematical reasoning benchmarks, including challenging competition-level datasets (e.g., AIME24 and AMC23), demonstrate that SAI-DPO achieves an average performance boost of up to 21.3 percentage points, with particularly notable improvements of 10 and 15 points on AIME24 and AMC23, respectively. These results highlight the superiority of dynamic, model-adaptive data selection over static, externally defined strategies in advancing reasoning.