Off-Policy Value-Based Reinforcement Learning for Large Language Models

Reinforcement learning (RL) approaches for Large Language Models (LLMs) frequently use on-policy algorithms, such as PPO or GRPO. However, policy lag from distributed training architectures and differences between the training and inference policies break this assumption, making the data off-policy by design. To rectify this, prior work has focused on making this off-policy data appear more on-policy, either via importance sampling (IS), or by more closely aligning the training and inference policies by explicitly modifying the inference engine. In this work, we embrace off-policyness and propose a novel off-policy RL algorithm that does not require these modifications: Optimal Advantage-based Policy Optimization with Lagged Inference policy (OAPL). We show that OAPL outperforms GRPO with importance sampling on competition math benchmarks, and can match the performance of a publicly available coding model, DeepCoder, on LiveCodeBench, while using 3x fewer generations during training. We further empirically demonstrate that models trained via OAPL have improved test time scaling under the Pass@k metric. OAPL allows for efficient, effective post-training even with lags of more than 400 gradient steps between the training and inference policies, 100x more off-policy than prior approaches.

Reinforcement learning algorithms for Large Language Models (LLMs) are largely distinguished by their variance reduction strategy. Group-relative methods like GRPO reduce gradient variance by sampling multiple rollouts per prompt, but provide only sequence-level credit. Training is also blocked by straggler rollouts, reducing throughput and increasing off-policyness. Learned value functions theoretically address both problems, providing token-level advantages without requiring large groups. However, additional infrastructure engineering challenges combined with the practical success of critic-free methods have made it difficult to justify their inclusion in RL pipelines. We propose two complementary strategies to improve the performance of value function RL: 1) Privileged Value Functions (PVF) which provide an elegant mechanism to inject additional task-relevant token-level signal without biasing the policy objective; 2) TETHER, a baseline that adaptively interpolates between group-relative and value baselines depending on the value function accuracy. Across several reasoning tasks, both strategies consistently improve over the standard value function baseline, and are competitive with or outperform mean-baseline GRPO.

Traditional on-policy Reinforcement Learning with Verifiable Rewards (RLVR) frameworks suffer from experience waste and reward homogeneity, which directly hinders learning efficiency on difficult samples during large language models post-training. In this paper, we introduce Batch Adaptation Policy Optimization (BAPO), an off-policy RLVR framework to improve the data efficiency in large language models post-training. It dynamically selects training batches by re-evaluating historically difficult samples and reusing high-quality ones, while holding a lower bound guarantee for policy improvement. Extensive experiments further demonstrate that BAPO achieves an average 12.5% improvement over GRPO across mathematics, planning, and visual reasoning tasks. Crucially, BAPO successfully resolves 40.7% of problems that base models consistently fail to solve.