CONCUR: Concordant Auxiliary Rewards for Multi-Task, Multi-Reward Reinforcement Learning

To improve task performance while encouraging desirable response properties, LLM post-training often combines a primary reward (e.g., correctness) with auxiliary rewards (e.g., brevity or efficiency). However, how these rewards are aggregated can critically affect training outcomes. We show that symmetric aggregation, which treats reward channels equally, can induce a failure where aggregate reward improves while primary-task performance degrades, even when individual rewards are meaningful. We investigate this aggregation-induced failure through a one-step multi-reward decision formulation, characterizing when it constitutes multi-reward hacking. We prove that, under symmetric aggregation, deterministic conditional-mean GRPO converges to auxiliary-favoring behavior when auxiliary rewards are more reliably obtained, regardless of initialization. We propose Trust-Anchored Gating (TAG), which first elects an anchor channel based on the policy drift induced by optimizing each channel alone, then gates auxiliary credit on anchor satisfaction. Unlike calibration-sensitive static reweighting, TAG structurally eliminates credit for auxiliary-only outcomes while preserving additional credit for joint success. In the same analytical setting, TAG provably reverses this selection, converging to the primary-favoring action from any initialization when the primary channel is anchored. Experiments across Qwen and Llama models on mathematics and program synthesis reveal substantial degradation under symmetric, constrained, and normalized aggregation, whereas TAG mitigates this failure. On Qwen3-4B with a brevity reward, TAG achieves 0.581 pass@4 versus 0.220 for additive aggregation, while shortening responses by 44% relative to correctness-only training.

Reinforcement learning (RL) is used to improve the reasoning abilities of LLMs, while training data span heterogeneous tasks. However, most RL post-training pipelines rely on fixed or manually designed task mixtures, even though task usefulness changes as training progresses. Online curriculum methods often define learnability by update magnitude, ignoring whether the update translates into reward gains, which can misallocate rollout budget toward tasks with large but ineffective updates. We propose PAC, a Progress-Augmented Advantage Curriculum for multi-task RL of LLMs that combines two task-level signals: advantage-derived learnability, which measures the magnitude of the policy update a task can induce, and recent reward gains, which show whether those updates have improved task performance. A Bayesian Thompson Sampling controller uses these signals to allocate rollouts across tasks during GRPO training. We evaluate PAC under two settings: a multi-level reasoning setting and a multi-domain reasoning setting. PAC improves sample efficiency and final performance: it reaches comparable validation scores with fewer rollout steps and achieves higher final averages than random sampling and advantage-based curriculum baselines in both settings. These results show that jointly tracking advantage signals and actual reward gains yields an effective online curriculum for LLM post-training.

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.