Not sure if it's faster, but you could always try not using placeholders:

my $sql = sprintf q[
SELECT *
FROM my_table
WHERE 
   col_1 IN (%s) AND
   col_2 IN (%s)
], join(', ', @$set_1), join(', ', @$set_2);
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If you can't be sure that they are all integers, be sure to map then through $dbh->quote first.