Moreover, our robust coreset can be efficiently maintained in fullydynamic environment. To the best of our knowledge, this is the first robust and fully-dynamic coreset construction method for these optimization problems.

In this section, we present some additional experiments. Section A.1, we conduct experiments using different number of parties (as opposed to three parties Section A.3, we test our methods in VKMC with different number of centers; and finally in Section A.4, we conduct experiments on another dataset ( KC House Dataset [35]). In this section, we test our algorithms using different number of parties. Empirical setup Most of the experimental setups are the same as those in Section 6, except that now we use 5 parties instead of 3 parties. Empirical results Figure 4 and 5 summarize our results for VRLR and VKMC respectively.

In this big data era, we often confront large-scale data in many machine learning tasks. A common approach for dealing with large-scale data is to build a small summary, {\em e.g.,} coreset, that can efficiently represent the original input. However, real-world datasets usually contain outliers and most existing coreset construction methods are not resilient against outliers (in particular, the outliers can be located arbitrarily in the space by an adversarial attacker). In this paper, we propose a novel robust coreset method for the {\em continuous-and-bounded learning} problem (with outliers) which includes a broad range of popular optimization objectives in machine learning, like logistic regression and $ k $-means clustering. Moreover, our robust coreset can be efficiently maintained in fully-dynamic environment. To the best of our knowledge, this is the first robust and fully-dynamic coreset construction method for these optimization problems. We also conduct the experiments to evaluate the effectiveness of our robust coreset in practice.