Amazon Personalize builds a recommendation model taking into account users, items and events. However, items are assumed as available, and this might not be the case for certain scenarios.
If items need to reflect a time window like availability in time (from date, to date), then you should be able to offer only valid items according to that restriction.
For instance, this would be the case for live shows: you should only recommend live shows that will happen in the future, either based on similarity or community behaviour. Live shows that already happened are part of the training, but are not valid products to recommend.
How can you model this availability restriction in Amazon Personalize?
There are a variety of business requirements that you may need to handle, that are not built in to the core of Amazon Personalize, and this is one of those. For these business requirements you need to build the logic into your wrapper around Amazon Personalize.
Edit: Personalize now allows you to filter recommendations on item metadata which looks like it would be sufficient for this use case. See the writeup here: https://aws.amazon.com/blogs/machine-learning/enhancing-recommendation-filters-by-filtering-on-item-metadata-with-amazon-personalize/