We introduce Mutual Reinforcement Learning, a framework for concurrent RL post-training in which heterogeneous LLM policies exchange typed experience while keeping separate parameters, objectives, and tokenizers. The framework combines a Shared Experience Exchange (SEE), Multi-Worker Resource Allocation (MWRA), and a Tokenizer Heterogeneity Layer (THL) that retokenizes text and aligns token-level traces across incompatible vocabularies. This substrate makes the experience-sharing design question operational across model families. We instantiate three controlled probes on top of GRPO: data-level rollout sharing via Peer Rollout Pooling (PRP), value-level advantage sharing via Cross-Policy GRPO Advantage Sharing (XGRPO), and outcome-level success transfer via Success-Gated Transfer (SGT). A contextual-bandit analysis characterizes their structural positions on a stability-support trade-off: PRP pays density-ratio variance and THL residual costs, XGRPO preserves on-policy actor support while changing scalar baselines, and SGT supplies a rescue-set score direction toward verified peer successes. In the evaluated regime, outcome-level sharing occupies the favorable point of this trade-off.
Group Relative Policy Optimization (GRPO) has been a key driver of recent progress in reinforcement learning with verifiable rewards (RLVR) for large language models, but it is typically trained in a low-staleness, near-on-policy regime that incurs substantial system overhead. We ask a simple question: How off-policy can GRPO be? We show that GRPO-style algorithms can tolerate substantially larger rollout staleness than previously assumed, and propose Mu-GRPO, an RL training framework that organizes training into a small number (e.g., four) of large sequential generation-optimization stages. This design induces high rollout staleness while greatly reducing rollout-optimization switching overhead. To stabilize learning under stale data, Mu-GRPO combines relaxed clipping, which preserves useful stale-rollout gradients, with negative-advantage veto, which removes destabilizing post-trigger suffix updates in negative-advantage responses. Across five language models and multiple math reasoning benchmarks, Mu-GRPO matches or exceeds the performance of standard GRPO while achieving around 2x speedup in wall-clock training time, establishing a substantially improved performance-efficiency trade-off for LLM reinforcement learning.
Reinforcement Learning with Verifiable Rewards (RLVR) for language-model reasoning can fail at both extremes of task difficulty: easy prompts often produce all-correct, low-diversity rollout groups with little gradient signal, while hard prompts can produce all-incorrect groups with no positive reward. We introduce ExTra (Exploratory Trajectory Optimization), a GRPO-compatible framework that extracts exploration signals from the model's own rollouts. ExTra combines two mechanisms: (i) a novelty reward that adds embedding-based diversity bonuses after GRPO normalization, rewarding diverse correct solutions; and (ii) entropy-guided prefix regeneration, which scores partial trajectories using entropy signals and continues exploration from promising intermediate steps. Across six mathematical reasoning benchmarks, ExTra improves Qwen3-1.7B over GRPO by about +5 points on pass@1 and +7 points on pass@16, showing that trajectory-level exploration signals can improve both single-sample accuracy and inference-time coverage.
Reinforcement Learning from Human Feedback (RLHF) is the standard approach for aligning large language models with human preferences, but its quality is limited by static, task-agnostic reward models. This mismatch leads to sparse learning signals and suboptimal alignment. We introduce MeRLa (Meta-Learned Reward Shaping), a principled framework that meta-learns a task-aware shaping function Φ(x,y;φ) across auxiliary tasks before RLHF training. The learned shaping produces a composite reward that preserves policy optimality while providing task-specific learning signals. Our meta-objective combines task discrimination, entropy regularization, and potential-based conservation for stable convergence. We provide theoretical guarantees for policy invariance, analyze representation drift sensitivity, and formally address incentive misalignment from entropy maximization. Experiments on LLaMA-3-8B across four benchmarks show consistent improvements over PPO, DPO, GRPO, and DAPO, achieving a 90.8% length-controlled win rate on AlpacaEval 2.0 and a score of 9.14 on MT-Bench, with 41% less training instability. MeRLa retains its benefits when combined with process-based and rubric-based enhanced rewards.