This paper revisits Deep Mutual Learning (DML), a simple yet effective computing paradigm. We propose using R\'{e}nyi divergence instead of the KL divergence, which is more flexible and tunable, to improve vanilla DML. This modification is able to consistently improve performance over vanilla DML with limited additional complexity. The convergence properties of the proposed paradigm are analyzed theoretically, and Stochastic Gradient Descent with a constant learning rate is shown to converge with $\mathcal{O}(1)$-bias in the worst case scenario for nonconvex optimization tasks. That is, learning will reach nearby local optima but continue searching within a bounded scope, which may help mitigate overfitting. Finally, our extensive empirical results demonstrate the advantage of combining DML and R\'{e}nyi divergence, leading to further improvement in model generalization.

翻译：本文重新审视了深度相互学习（DML），一种简单而有效的计算范式。我们提出使用比KL散度更灵活且可调的Rényi散度来改进原始DML。该修改能够以有限的额外复杂度持续提升原始DML的性能。从理论上分析了所提出范式的收敛性质，证明在非凸优化任务的最坏情形下，采用恒定学习率的随机梯度下降法以$\mathcal{O}(1)$偏差收敛。即学习过程将到达附近的局部最优解，但会在有界范围内持续搜索，这可能有助于缓解过拟合。最后，广泛的实验结果表明，结合DML与Rényi散度能进一步提升模型泛化能力。