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Lexicographic Multi-Objective On-Policy Distillation
arXiv:2610.02359v1 Announce Type: cross Abstract: Reinforcement learning from verifiable rewards (RLVR) usually optimizes answer correctness, yet useful language-model behavior also requires high-qual
arXiv:2610.02359v1 Announce Type: cross Abstract: Reinforcement learning from verifiable rewards (RLVR) usually optimizes answer correctness, yet useful language-model behavior also requires high-quality reasoning and concise responses. Existing multi-reward post-training methods typically scalarize rewards or combine specialists without explicitly protecting a reward priority order. This is problematic when trade-offs are asymmetric: conciseness, for example, should not improve at the cost of correctness. We introduce Lexicographic Multi-Objective On-Policy Distillation (LMOPD), a multi-teacher method for integrating reward-specialized policies under explicit priorities. For each student rollout, LMOPD selects the specialist for the first objective whose gate detects a deficiency, then locally projects its centered log-policy correction to remove components that oppose higher-priority specialists. We evaluate 30B-A3B mixture-of-experts transformer models in two- and four-expert settings on three math benchmarks, measuring retained specialist gains. With two experts, LMOPD's point estimates fully retain the accuracy and reasoning-quality gains while acquiring 46.9% of the conciseness gain. With four experts, it retains approx90% of both the accuracy gain and reasoning-correctness gain, compared to only approx57% by the next best evaluated baseline. Matched four-expertablations show that lexicographic routing outperforms random routing and that projection further strengthens both top-priority capabilities. Across both scales, LMOPD preserves the highest-priority capabilities more effectively than the existing baselines we evaluate, demonstrating the value of explicit priorities for specialist integration.
Related
- Weak-to-Strong Generalization via Direct On-Policy Distillation
- When and Where to Trust the Teacher: Unifying On-Policy Distillation and GRPO through Entropy-Calibrated Credit Assignment
- SIPO: Unifying Reinforcement Learning with On-Policy Self-Distillation
- On-policy Distillation with Verifiable Reward
- SAF-OPD: Stable Advantage Fusion for On-Policy Distillation
Source: arXiv cs.AI | 2026-10-05