data_dict = {} # maybe a dictionary is not the best choice
for j in parameters: # j = (alpha, beta, gamma) and cycle through
for k in number_of_experiments: # lots of experiments (10^4)
file = open('storage.pkl', 'ab')
data = experiment() # experiment returns some numerical value
# experiment takes ~ 1 seconds, but increase
# as parameters scale
data_dict.setdefault(j, []).append(data)
pickle.dump(data_dict, file)
file.close()