my %items = map { $_ => 1 } (
    'APPLES',
    'SILVER',
);

my @groups = (
    [ 'cookies',         [ 'CHOCOLATE CHIP', 'PEANUT BUTTER' ] ],
    [ 'previous metals', [ 'SILVER', 'GOLD', 'PLATINUM' ]      ],
);

my $lover;
for my $group (@groups) {
    my ($group_name, $group_members) = @$group;
    if ( grep $items{$_}, @$group_members ) {
        print "This guy loves $group_name.\n";
        ++$lover;
    }
}

if (!$lover) {
    print "This guy loves nothing.\n";
}
[download]

EDIT: I should have made it clear that ordering is important and that 'this guy' is a simple man and can only love one thing. I know that this hints that I should be using an array of arrays instead of a hash of arrays, but the key-value relationship is something I would like to preserve if at all possible.

After reading your EDIT, I am confused as to what the requirements really are. What does "ordering is important" mean? Order of "what" exactly?

A hash has no intrinsic "order" to the keys - you should assume that hash keys will come out in any order when you access a hash via (keys %hash) or (keys %$ref_2_hash).

It would help at least me, if you could back up a bit.. Write some more text describing what data you have and the kind of "look-up" that you desire. It could be that excellent solutions are being offered to the "wrong problem".