When Do Larger Batches Help Scale LLM Reinforcement Learning?

Larger batches reduce the variance of stochastic gradients per update and are therefore often expected to accelerate training. Yet whether this statistical benefit translates into lower wall-clock time-to-target remains unclear, because each update consumes more samples and may take longer to execute. We study this tradeoff in reinforcement learning for large language models. We separate its algorithmic and systems effects by comparing learning and execution along their natural axes. At the algorithmic level, we compare configurations at equal cumulative sample counts while retuning batch-dependent hyperparameters. Over a bounded range of batch sizes, this procedure yields an approximately batch-size-invariant family whose members follow similar sample-indexed learning trajectories. At the systems level, we exploit the computational asymmetry between rollout generation and training: autoregressive generation is often memory-bandwidth-bound at low concurrency, whereas training work scales approximately with the number of processed tokens. Combining these two views yields a direct decision rule: a larger-batch configuration reduces time-to-target only when its throughput gain exceeds its samples-to-target penalty. Experiments with GRPO and PPO support both sides of this decomposition. At the algorithmic level, square-root learning-rate scaling with Adam produces approximately batch-size-invariant learning curves over a bounded range of batch sizes. At the systems level, larger batches improve generation throughput by up to 2.29x on fixed hardware. In GRPO, combining higher throughput with learning-rate retuning reduces time-to-target by up to 29%, whereas increasing the batch without retuning is slower despite its higher throughput.

Deriving Scaling Laws for OpenEuroLLM Models: Learning Rate, Batch Size and Loss

We study the scaling behavior of learning rate and batch size in pretraining dense large language models on English-prevalent corpora. Beyond scaling jointly optimal learning rates and batch sizes, we investigate their marginal evolution with model capacity and data scale and develop a model that captures these relationships. As we employ a Warmup-Stable-Decay learning rate schedule, we further investigate the gains from learning rate annealing over a broad range of hyperparameters settings, models and data budgets, and whether the optimal learning rate and batch size transfer between the stable and decay phases. Finally, we characterize the dependence of loss on model capacity and dataset size, evaluating recently proposed scaling forms that explicitly model their interaction. We find these approaches particularly effective at capturing both undertraining and overtraining regimes across our experiments. This study establishes a first baseline and scaling procedure for the development of future OpenEuroLLM models. We open-source the complete collection of pretraining runs used in this study.

How to Allocate Your Tokens? Scaling Laws with Training Steps and Batch Size

We propose a scaling law that takes into account model size and training data while explicitly splitting the latter into training steps and batch size (called three-term law). Fitting the proposed law on a large set of training runs, we find that it correctly recovers the scaling of the optimal batch size. Moreover, because it makes use of training runs with suboptimal batch size, our proposed law can be robustly fit with a significantly smaller amount of training runs. We further show that the three-term law can be used to derive scaling laws for suboptimal batch sizes, and that it matches previous empirical findings related to the critical batch size.

Beyond a Single Explanation of the Adam--SGD Gap

Prior work has identified several factors that can contribute to the performance gap between Adam and SGD, spanning data aspects, architecture design, and optimization properties. Yet these explanations are often studied in isolation, leaving their relative importance unclear. In this work, we revisit these hypotheses through a controlled empirical study across vision, language, genomics, and graph tasks, spanning modern and classical architectures, and carefully designed training setups. Our results suggest that no single factor consistently explains the Adam--SGD gap. For instance, the Adam advantage can (1) persist under a uniform vocabulary distribution yet nearly disappear under a heavy-tailed one; (2) reverse in favor of SGD in softmax-attention models; and (3) become larger under soft architectural modifications, e.g., when ReLU is replaced by a GeLU nonlinearity. This suggests that the gap arises from nontrivial data and architecture interactions, rather than from a single common factor. Yet, we observe a pattern across our settings: a \emph{crossover batch size} at which the relative advantage shifts from SGD to Adam as the batch size scales. These empirical results are captured by our theoretical gap model, which predicts this batch-size-dependent crossover. Our perspective helps reconcile several existing hypotheses while offering practical insights across domains.