优化器选择会影响模型公平性，RMSProp比SGD更易收敛到公平解。

We study whether and how the choice of optimization algorithm can impact group fairness in deep neural networks. Through stochastic differential equation analysis of optimization dynamics in an analytically tractable setup, we demonstrate that the choice of optimization algorithm indeed influences fairness outcomes, particularly under severe imbalance. Furthermore, we show that when comparing two categories of optimizers, adaptive methods and stochastic methods, RMSProp (from the adaptive category) has a higher likelihood of converging to fairer minima than SGD (from the stochastic category). Building on this insight, we derive two new theoretical guarantees showing that, under appropriate conditions, RMSProp exhibits fairer parameter updates and improved fairness in a single optimization step compared to SGD. We then validate these findings through extensive experiments on three publicly available datasets, namely CelebA, FairFace, and MS-COCO, across different tasks as facial expression recognition, gender classification, and multi-label classification, using various backbones. Considering multiple fairness definitions including equalized odds, equal opportunity, and demographic parity, adaptive optimizers like RMSProp and Adam consistently outperform SGD in terms of group fairness, while maintaining comparable predictive accuracy. Our results highlight the role of adaptive updates as a crucial yet overlooked mechanism for promoting fair outcomes. We release the source code at: https://github.com/Mkolahdoozi/Some-Optimizers-Are-More-Equal.