I want to use Cognitive Services to translate some text, and we can train our custom models, I want to know is there any possible to host models on local server?
It sounds like you want to deploy your custom trained model of Azure Cognitive Service on an on-promise datacenter. As I known, Azure Stack supports Azure capabilities available on-premises, but its features do not include Azure Cognitive Services by now, as refer to Azure Stack key capabilities. Meanwhile, the model of Custom Translator is not public, just used on cloud, and can not be exported as a general format like ONNX. So may you need to contact with Azure offical sales to ask for your needs and how to buy.