Best strategy for bulk inserts where some violate unique constraint?

I'm using Pyscopg2 to insert multiple rows at once, using a dictionary as
shown at the bottom of this page:
https://wiki.postgresql.org/wiki/Psycopg2_Tutorial

I notice that even if just one entry violates a table unique constraint (an
IntegrityError in psycopg2 parlance), the entire contents of the dictionary
do not get inserted into the table.

Is there any way to tell postgres: it's ok to reject individual entries
that may violate table unique constraints, but at the same time allow those
which do not?

It's too expensive for me to do the inserts one at a time where I could
just catch the psycopg2.IntegrityError.