PACE: Defying the Scaling Hypothesis of Exploration in Iterative Alignment for Mathematical Reasoning

Abstract: Iterative Direct Preference Optimization has emerged as the state-of-the-art paradigm for aligning LLMs on reasoning tasks. Standard implementations (DPO-R1) rely on Best-of-N sampling (e.g., $N \ge 8$) to mine golden trajectories from the distribution tail. In this paper, we challenge this scaling hypothesis and reveal a counter-intuitive phenomenon: in mathematical reasoning, aggressive exploration yields diminishing returns and even catastrophic policy collapse. We theoretically demonstrate that scaling $N$ amplifies verifier noise and induces detrimental distribution shifts. To resolve this, we introduce \textbf{PACE} (Proximal Alignment via Corrective Exploration), which replaces brute-force mining with a generation-based corrective strategy. Operating with a minimal budget ($2<N<3$), PACE synthesizes high-fidelity preference pairs from failed explorations. Empirical evaluations show that PACE outperforms DPO-R1 $(N=16)$ while using only about $1/5$ of the compute, demonstrating superior robustness against reward hacking and label noise.