[dekhn]

Boost circuits are common for driving LEDs, for example a joule thief would be perfect for running this on fewer batteries.

[kragen]

true, but it's challenging to get a boost converter, even a very simple one like a joule thief, into the space of this earring; i think it's too small for a millihenry. using a larger number of smaller batteries might be a better option

[crote]

True, but that's still going to consume more energy - not to mention the boost circuit probably taking up more space than the additional battery.

[dekhn]

It looks like you can get reasonable SMD boost chips and pack them and their entire support infra in <10mm https://hhtronik.com/product/uboost/ which is about the same as two batteries as used in this project.