MADA-RL: Multi-Agent Debate-Aware Reinforcement Learning for Parameter-Efficient Reasoning in Compact Models

Martino M. L. Pulici, Cuong Xuan Chu, Evgeny Kharlamov, Zifeng Ding, Volker Tresp, Yunpu Ma

Large language models achieve strong reasoning performance, but often at prohibitive training cost - a challenge that is especially acute for compact models ($\leq 4 \, \mathrm{B}$ parameters) trained under limited budgets. We introduce MADA-RL, a post-training framework that specializes compact models into generator and critic roles and trains them with a debate-aware learning signal, fine-tuning only a small subset of parameters via LoRA adapters. Our central contribution is a counterfactual critic advantage: a dynamic, role-conditioned baseline that redefines the critic's advantage as its reward minus the generator ensemble's per-instance accuracy. This explicitly optimizes critics to improve over generator consensus rather than to merely reproduce a correct answer, yielding more targeted credit assignment than static mean-reward normalization. At deployment, the specialized agents are composed in a lightweight multi-round protocol. Across five mathematical reasoning benchmarks, MADA-RL raises the accuracy of the DeepSeek-R1-Distill-Qwen-1.5B model from $39.9 \, \%$ to $41.9 \, \%$ ($+2.0$ points, $p < 0.001$) using $16$ times fewer trainable parameters than fully fine-tuned baselines, placing it on the accuracy-trainable-parameter Pareto front. It approaches, but does not surpass, the strongest baselines (DeepScaleR, STILL-3), which are trained on substantially larger datasets; we analyse this gap and the associated inference-time cost directly. A controlled study isolates the source of MADA-RL's gains: the counterfactual advantage produces the highest critic improvement rate of any model evaluated, indicating that trained critics learn to correct generator errors rather than to imitate them.