Recent years have seen a surge of interest in the algorithmic estimation of stochastic entropy production (EP) from the trajectory data via machine learning. A crucial element of such algorithms is the identification of a loss function whose minimization guarantees the accurate EP estimation. In this study, we show that there exists a host of loss functions, namely those implementing a variational representation of the $\alpha$-divergence, which can be used for the EP estimation. Among these loss functions, the one corresponding to $\alpha = -0.5$ exhibits the most robust performance against strong nonequilibrium driving or slow dynamics, which adversely affects the existing method based on the Kullback-Leibler divergence ($\alpha = 0$). To corroborate our findings, we present an exactly solvable simplification of the EP estimation problem, whose loss function landscape and stochastic properties demonstrate the optimality of $\alpha = -0.5$.

翻译：近年来，通过机器学习从轨迹数据中算法估计随机熵产生（EP）引起了广泛关注。此类算法的关键要素是识别一个损失函数，其最小化能保证准确的EP估计。在本研究中，我们证明存在一系列损失函数，即实现$\alpha$-散度变分表示的函数，可用于EP估计。在这些损失函数中，对应于$\alpha = -0.5$的函数在强非平衡驱动或慢动力学条件下表现出最鲁棒的性能，而这些条件会负面影响基于Kullback-Leibler散度（$\alpha = 0$）的现有方法。为验证我们的发现，我们提出了EP估计问题的一个精确可解简化模型，其损失函数景观与随机性质证明了$\alpha = -0.5$的最优性。