Future Policy Aware Preference Learning for Mathematical Reasoning

Abstract: Preference learning methods such as Direct Preference Optimization (DPO) have become standard for LLM post-training, yet they are often ineffective for mathematical reasoning. A key challenge is the large token overlap between preferred and dispreferred trajectories; lowering the probability of dispreferred trajectories also reduces the probability of shared useful tokens, leading to over-penalization and overall performance collapse. As a mitigation, existing algorithms include the probability of a trajectory under the current policy as a regularization term, which decreases the effect of the gradient when the probability is low. However, by the time this effect takes hold, useful tokens may have already been over-penalized as the model has begun to degrade. To address this, we propose Future Policy Aware (FPA) preference learning, which replaces the current policy with a future policy in the regularization term. This future policy is estimated via lightweight, logit-space extrapolation from a reference model toward the current model. FPA enables safer training by preemptively regularizing potentially problematic gradients. We apply FPA to DPO, RPO, and SimPER and evaluate them on the MATH and GSM8K benchmarks. FPA yields consistent performance gains, with the largest improvements observed with SimPER, achieving gains of up to 5.75%. We demonstrate that FPA provides proactive regularization while preserving the probability of shared, useful mathematical tokens, and enables longer, degradation-free training with negligible computational overhead. We will release our code publicly upon publication.