Python Multithread and PostgreSQL

I had to use connection pool.

import psycopg2 
import random
from concurrent.futures import ThreadPoolExecutor, as_completed
from psycopg2.pool import ThreadedConnectionPool

def write_sim_to_db(all_ids2):
    if all_ids1[i] != all_ids2:
        conn = tcp.getconn()
        c = conn.cursor()
        c.execute("""SELECT count(*) FROM similarity WHERE prod_id1 = %s AND prod_id2 = %s""", (all_ids1[i], all_ids2,))
        count = c.fetchone()
        if count[0] == 0:
            sim_sum = random.random()
            c.execute("""INSERT INTO similarity(prod_id1, prod_id2, sim_sum) 
                    VALUES(%s, %s, %s)""", (all_ids1[i], all_ids2, sim_sum,))
            conn.commit()
        tcp.putconn(conn)

DSN = "postgresql://user:pass@localhost/db"
tcp = ThreadedConnectionPool(1, 10, DSN)

all_ids1 = list(n for n in range(1000))
all_ids2_list = list(n for n in range(1000))

for i in range(len(all_ids1)):
    with ThreadPoolExecutor(max_workers=2) as pool:
        results = [pool.submit(write_sim_to_db, i) for i in all_ids2_list]

This is the sane approach to speed it up. It will be much faster and simpler than your code.

tuple_list = []
for p1 in range(3):
    for p2 in range(3):
        if p1 == p2: continue
        tuple_list.append((p1,p2,random.random()))

insert = """
    insert into similarity (prod_id1, prod_id2, sim_sum)
    select prod_id1, prod_id2, i.sim_sum
    from
        (values
            {}
        ) i (prod_id1, prod_id2, sim_sum)
        left join
        similarity s using (prod_id1, prod_id2)
    where s is null
""".format(',\n            '.join(['%s'] * len(tuple_list)))

print cur.mogrify(insert, tuple_list)
cur.execute(insert, tuple_list)

Output:

insert into similarity (prod_id1, prod_id2, sim_sum)
select prod_id1, prod_id2, i.sim_sum
from
    (values
        (0, 1, 0.7316830646236253),
        (0, 2, 0.36642199082207805),
        (1, 0, 0.9830936499726003),
        (1, 2, 0.1401200246162232),
        (2, 0, 0.9921581283868096),
        (2, 1, 0.47250175432277497)
    ) i (prod_id1, prod_id2, sim_sum)
    left join
    similarity s using (prod_id1, prod_id2)
where s is null

BTW there is no need for Python at all. It can all be done in a plain SQL query.