One Step, One Lead: Mitigating Higher-Order Interference in Multi-Domain Reinforcement Learning via Cross-Step Control
Zihan Lin, Xiaohan Wang, Jie Cao, Jiajun Chai, Guojun Yin, Wei Lin, Ran He
Abstract
Reinforcement learning (RL) across multiple domains can broaden the reasoning capabilities of large language models (LLMs), yet joint training often degrades individual-domain performance and can destabilize optimization. Existing work typically diagnoses such interference from a single-step view using first-order gradient alignment or curvature-based proxies. We show that this view can miss a critical form of sequential interference: same-point domain gradients may remain nearly orthogonal even when consecutive realized updates partially reverse one another in output space. We further show that consecutive token log-probability footprints recover this interaction directly from adjacent checkpoints as a local second-order interaction in output space, without explicitly reconstructing same-step curvature. Building on this insight, we propose OSOL, which designates a focus domain at each iteration, uses the preceding checkpoint footprint to rank token-level rebound risk, and applies a drift-ranked, adaptively scaled correction within the standard GRPO update. Our analysis shows that this correction suppresses the targeted cross-step output backtracking component. Controlled studies further show that cross-step backtracking is more strongly associated with subsequent task damage than same-point gradient diagnostics, while the preceding footprint ranks future rebound risk more accurately than Hessian-based proxies. On Qwen3-30B-A3B, OSOL reaches a domain-macro average of 0.4822, improving by 5.7% over the strongest compared baseline, without explicit higher-order differentiation.