Loss functions and sample mining strategies are essential components in deep metric learning algorithms. However, the existing loss function or mining strategy often necessitates the incorporation of additional hyperparameters, notably the threshold, which defines whether the sample pair is informative. The threshold provides a stable numerical standard for determining whether to retain the pairs. It is a vital parameter to reduce the redundant sample pairs participating in training. Nonetheless, finding the optimal threshold can be a time-consuming endeavor, often requiring extensive grid searches. Because the threshold cannot be dynamically adjusted in the training stage, we should conduct plenty of repeated experiments to determine the threshold. Therefore, we introduce a novel approach for adjusting the thresholds associated with both the loss function and the sample mining strategy. We design a static Asymmetric Sample Mining Strategy (ASMS) and its dynamic version, the Adaptive Tolerance ASMS (AT-ASMS), tailored for sample mining methods. ASMS utilizes differentiated thresholds to address the problems (too few positive pairs and too many redundant negative pairs) caused by only applying a single threshold to filter samples. The AT-ASMS can adaptively regulate the ratio of positive and negative pairs during training according to the ratio of the currently mined positive and negative pairs. This meta-learning-based threshold generation algorithm utilizes a single-step gradient descent to obtain new thresholds. We combine these two threshold adjustment algorithms to form the Dual Dynamic Threshold Adjustment Strategy (DDTAS). Experimental results show that our algorithm achieves competitive performance on the CUB200, Cars196, and SOP datasets. Our codes are available at https://github.com/NUST-Machine-Intelligence-Laboratory/DDTAS .