# View of Multiplicative Weights in contexts of combinatorial optimization, low-regret/online optimization, and entropy-regularized gradient descent?

I understand these are three places where multiplicative weights shows up (i.e. $w_{t+1} = w_{t}e^{- \text{loss}(w_{t})}$ or variations. And I understand a bit about these interpretations. But what ties them all together? In particular, multiplicative weights has been around a long time and appeared in combinatorial optimization contexts that I understand much less well than the low-regret interpretation. I kind of understand the connection between convex optimization and low-regret learning, but I don't understand why entropy appears as the proximal gradient regularization term. Is there an information-theoretic interpretation of all this? And does it clarify anything?