Noticed one day when I was pulling up a hill that my headlights were pulsing a little bit. Waiting for the day when they just go out...wonder how much this will cost me?

I have a 2013 Chevrolet Impala LT. I purchased this vehicle used with approximately 32,029 miles in September 2013. I am currently at 50,205 miles and when I accelerate my headlights and interior lights pulse. Only when I accelerate does the lights pulse. The more gas I give it the faster the lights pulse. Took it to the shop but they could not tell me what was wrong with it. Does anyone have a clue what this could be.