Online mirror descent

Imagine you want to walk down a path through a forest, but you're not sure which way to go. So, you make a guess and start walking. As you walk, you notice the trees and other things around you. Based on that information, you adjust your path a little bit. You do this again and again until you reach your destination.

Online mirror descent is kind of like that. It's a way of making decisions based on feedback you get as you go along. In this case, instead of walking through a forest, you're making decisions about something online, like what product to recommend to a customer or what ad to show someone.

The way online mirror descent works is by keeping track of something called a "loss function". This is just a fancy way of saying "how well are you doing?" For example, if you're trying to recommend a product to a customer, the loss function might be how many times they actually buy the product you suggest. If they buy it a lot, your loss function will be low (because you're doing well). If they don't buy it at all, your loss function will be high (because you're not doing well).

Now, online mirror descent looks at your loss function and tries to adjust your decisions based on it. It does this by imagining there's a mirror in front of you and asking "what decision would I make if I had to look at myself in this mirror?" Basically, it's trying to find the decision that will make you look as good as possible (i.e. have the lowest loss function).

So, using online mirror descent, you make a guess for your first decision based on the information you have, and then adjust it based on the feedback you get (i.e. the loss function). You do this again and again until you've made all your decisions. And hopefully, you end up with the best possible outcome (i.e. the lowest possible loss function).