On the Role of Batch Size in Stochastic Conditional Gradient Methods
This work provides theoretical insights and practical guidelines for optimizing batch size and stepsize in large-scale training, addressing a key efficiency problem for machine learning practitioners, though it is incremental as it builds on existing momentum-based algorithms.
The paper investigates how batch size affects stochastic conditional gradient methods under a μ-KL condition, revealing that increasing batch size initially improves accuracy but saturates or degrades performance beyond a critical threshold under a fixed token budget, with experiments on NanoGPT confirming these predictions.
We study the role of batch size in stochastic conditional gradient methods under a $μ$-Kurdyka-Åojasiewicz ($μ$-KL) condition. Focusing on momentum-based stochastic conditional gradient algorithms (e.g., Scion), we derive a new analysis that explicitly captures the interaction between stepsize, batch size, and stochastic noise. Our study reveals a regime-dependent behavior: increasing the batch size initially improves optimization accuracy but, beyond a critical threshold, the benefits saturate and can eventually degrade performance under a fixed token budget. Notably, the theory predicts the magnitude of the optimal stepsize and aligns well with empirical practices observed in large-scale training. Leveraging these insights, we derive principled guidelines for selecting the batch size and stepsize, and propose an adaptive strategy that increases batch size and sequence length during training while preserving convergence guarantees. Experiments on NanoGPT are consistent with the theoretical predictions and illustrate the emergence of the predicted scaling regimes. Overall, our results provide a theoretical framework for understanding batch size scaling in stochastic conditional gradient methods and offer guidance for designing efficient training schedules in large-scale optimization.