Mining or Synthesis? Rethinking Exploration Efficiency in Iterative Alignment of Mathematical Reasoning

Iterative Direct Preference Optimization (DPO) has emerged as a widely used paradigm for aligning Large Language Models on reasoning tasks. Existing approaches typically rely on Best-of-N sampling (N\geq8) to mine positive trajectories from the distribution tail. In this work, we show that in mathematical reasoning, increasing N yields diminishing returns while increasing verifier-induced false-positive risk and the distribution shift required for policy updates. To address this, we introduce PACE (Proximal Alignment via Corrective Exploration), a generation-based corrective framework that replaces exhaustive mining with low-budget exploration (2\leq N\leq3). Rather than searching for increasingly rare positive samples, PACE synthesizes high-fidelity preference pairs from failed explorations through corrective hindsight refinement and verification-guided filtering. Empirically, PACE matches or exceeds the performance of DPO-R1 (N=16) while using about 1/5 of the compute, and remains robust under 20% label corruption, where high-N baselines exhibit substantially higher noise exploitation.