Stabilizing Reinforcement Learning for Honesty Alignment in Language Models on Deductive Reasoning

Reinforcement learning with verifiable rewards (RLVR) has recently emerged as a promising framework for aligning language models with complex reasoning objectives. However, most existing methods optimize only for final task outcomes, leaving models vulnerable to collapse when negative rewards dominate early training. This challenge is especially pronounced in honesty alignment, where models must not only solve answerable queries but also identify when conclusions cannot be drawn from the given premises. Deductive reasoning provides an ideal testbed because it isolates reasoning capability from reliance on external factual knowledge. To investigate honesty alignment, we curate two multi-step deductive reasoning datasets from graph structures, one for linear algebra and one for logical inference, and introduce unanswerable cases by randomly perturbing an edge in half of the instances. We find that GRPO, with or without supervised fine tuning initialization, struggles on these tasks. Through extensive experiments across three models, we evaluate stabilization strategies and show that curriculum learning provides some benefit but requires carefully designed in distribution datasets with controllable difficulty. To address these limitations, we propose Anchor, a reinforcement learning method that injects ground truth trajectories into rollouts, preventing early training collapse. Our results demonstrate that this method stabilizes learning and significantly improves the overall reasoning performance, underscoring the importance of training dynamics for enabling reliable deductive reasoning in aligned language models.