Group Relative Policy Optimization

Reinforcement learning (RL) trains small language model agents to answer multi-hop questions by retrieving evidence over multiple turns, but reported gains typically rely on thousands of on-policy rollouts per update. We study RL for such agents on commodity GPUs, where each update samples only a few rollouts per question. Most sampled trajectories then retrieve none of the required evidence, so the outcome reward gives the policy little to learn from and small agents settle for answering without retrieval, a failure we call retrieval collapse. DAVID-GRPO addresses this with two mechanisms: (1) expert trajectory seeding places a handful of off-policy expert trajectories into the GRPO groups of the early updates, and (2) evidence-guided continuation rewards evidence coverage and resumes the most promising partial trajectory. The evidence for each training question is constructed from the corpus link graph, without annotated evidence. On six multi-hop QA benchmarks, DAVID-GRPO trained on four RTX 3090 GPUs with 144 rollouts per step brings Qwen2.5-1.5B to 22.6 average EM against 11.9 for the best baseline under the same budget, is comparable to Tree-GRPO trained with 20 times more rollouts, and, unlike the baselines that stop after at most one search, learns to retrieve across turns. The implementation is available at: https://github.com/AsadalJung/David-GRPO

Automated Theorem Proving (ATP) is a fundamental AI challenge, requiring machine-verifiable proofs in formal languages like Lean to evaluate reasoning. Reinforcement Learning (RL), especially Group Relative Policy Optimization (GRPO), is a mainstream approach. However, GRPO faces two critical issues in ATP: its relative advantage estimation may conflict with binary verifier feedback under composite rewards, and its static sampling strategy discards batches without valid proofs, causing data waste. Repeated training on mastered problems also wastes computation. To address this, we propose Group Dual-dynamic and Equal-right Advantage Policy Optimization (GDEPO), incorporating three core mechanisms: 1) dynamic additional sampling, resampling ineffective batches until a valid proof is found; 2) equal-right advantage, decoupling the advantage function's sign (correctness) from its magnitude (auxiliary rewards) to ensure stable policy updates while increasing effective computation; and 3) dynamic additional iterations, applying extra gradient steps to initially failed but eventually successful samples to accelerate learning. Experiments on MinF2F-test, MathOlympiadBench, and PutnamBench confirm GDEPO's effectiveness, with ablation studies validating its synergistic components. The method enhances data utilization and optimization efficiency, offering a novel training paradigm for ATP.

Group Relative Policy Optimization (GRPO) enables stable and preference-oriented updates via group-wise comparisons for post-training video generation. However, GRPO directly optimizes reward-induced advantages. Under sustained optimization, the reward score can lose fidelity as a proxy for true video quality, consistent with the phenomenon described by Goodhart's Law. This leads to two recurring issues: (i) shortcut-driven optimization under composite objectives and (ii) reward saturation within prompt groups. To address these issues, we introduce TaRoS, a Target-Robust Reward Signaling framework for Video generation GRPO. TaRoS leverages component level performance assessment together with intra-group sparsity to organize multi-aspect rewards towards optimization objectives. In addition, it adaptively downweights components that exhibit saturation, thereby preserving effective optimization directions and mitigating redundancy. This maintains meaningful optimization directions and preserves within-group ranking separation, thereby preventing reward hacking and leading to more reliable policy updates. Extensive experiments show consistent improvements in visual fidelity, motion coherence, and text-video alignment over strong baselines.

Group Relative Policy Optimization (GRPO) trains language models without a value critic using rewards centered within sampled response groups. We study how importance weighting, clipping, and length normalization affect its stochastic updates and propose Trajectory-level Importance-Corrected GRPO (TIC-GRPO), combining an upper importance-ratio cap with a full-trajectory likelihood ratio. Under common maximum-length normalization, a trajectory change of measure gives a score second moment proportional to the response horizon. We propagate this estimate through the actual empirical baseline and all inner updates. With separately optimized constant steps, the sampling term in TIC's stationarity bound has a linear horizon coefficient, versus order three halves for token-level GRPO$_2$. Matching upper and lower bounds separate the capped methods' worst-case response-level variances by a factor $T$. The bounds track prompt count, response-group size, vocabulary size, reward scale, and score regularity; per-response-normalized GRPO also retains a length-covariance term. Experiments at two Qwen3 scales on four reasoning and coding benchmarks evaluate both mechanisms in sampled-token-normalized training.

Although GRPO substantially enhances flow matching models in human preference alignment of image generation, methods such as FlowGRPO and DanceGRPO still exhibit inefficiency due to the necessity of sampling and optimizing over all denoising steps specified by the Markov Decision Process (MDP). In this paper, we propose $\textbf{MixGRPO}$, a novel framework that leverages the flexibility of mixed sampling strategies through the integration of stochastic differential equations (SDE) and ordinary differential equations (ODE). This streamlines the optimization process within the MDP to improve efficiency and boost performance. Specifically, MixGRPO introduces a sliding window mechanism, using SDE sampling and GRPO-guided optimization only within the window, while applying ODE sampling outside. This design confines sampling randomness to the time-steps within the window, thereby reducing the optimization overhead, and allowing for more focused gradient updates to accelerate convergence. Additionally, as time-steps beyond the sliding window are not involved in optimization, higher-order solvers are supported for faster sampling. So we present a faster variant, termed $\textbf{MixGRPO-Flash}$, which further improves training efficiency while achieving comparable performance. MixGRPO exhibits substantial gains across multiple dimensions of human preference alignment, outperforming DanceGRPO in both effectiveness and efficiency, with nearly 50% lower training time. Notably, MixGRPO-Flash further reduces training time by 71%.