i wouldn't even think of starving before they reach a size of 3 inch or larger you could seriously stunt or hurt the fish as they can be very stubborn and may not eat for weeks maybe even months at which time they become easy pray and are likely to contract disease
my advise is have a selection of foods ready for them and if they start getting to thin just cave and give them a good meal then start over. I have found the best way is to run warmer water (above 80) to get their metabolism up and mix it in slowly. feed pellet first every day, feeding live every other day and decreasing the live food by adding a day between live feeds every couple of weeks, they will start taking pellet eventually and its less of a shock then just completely waiting till they eat just the pellet. its best to give your fish options and a variety of foods not just pellet or live and/or freeze dried