  Cross-Domain Sequential Recommendation (CDSR) aims to predict future
interactions based on user's historical sequential interactions from multiple
domains. Generally, a key challenge of CDSR is how to mine precise cross-domain
user preference based on the intra-sequence and inter-sequence item
interactions. Existing works first learn single-domain user preference only
with intra-sequence item interactions, and then build a transferring module to
obtain cross-domain user preference. However, such a pipeline and implicit
solution can be severely limited by the bottleneck of the designed transferring
module, and ignores to consider inter-sequence item relationships. In this
paper, we propose C^2DSR to tackle the above problems to capture precise user
preferences. The main idea is to simultaneously leverage the intra- and inter-
sequence item relationships, and jointly learn the single- and cross- domain
user preferences. Specifically, we first utilize a graph neural network to mine
inter-sequence item collaborative relationship, and then exploit sequential
attentive encoder to capture intra-sequence item sequential relationship. Based
on them, we devise two different sequential training objectives to obtain user
single-domain and cross-domain representations. Furthermore, we present a novel
contrastive cross-domain infomax objective to enhance the correlation between
single- and cross- domain user representations by maximizing their mutual
information. To validate the effectiveness of C^2DSR, we first re-split four
e-comerce datasets, and then conduct extensive experiments to demonstrate the
effectiveness of our approach C^2DSR.
