I must admit I did not understand even the basics of this posting. I Need to start way further behind this level of abstraction.
θ∗,ψ∗←argminθ,ψg(θ,ψ)
With no prior explanation and say, yep, now that you put it that way, it's true?
In the context of optimization, a star refers to the value of the variable that minimizes (or maximizes) a function you're interested in.
You will also see a hat over a variable (https://en.wikipedia.org/wiki/Hat_operator#Estimated_value) sometimes (from statistics) which is an estimate of some quantity from data (and that estimate may be obtained by minimizing a function - solving an optimization problem)
By the way, this is the first result when googling argmin: https://en.wikipedia.org/wiki/Arg_max
It takes a function g, and returns the values of it's arguments (theta and psi) that minimize the function g.