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I work in data science, I reach many of the conclusions that a psychologist might, by means of aggregating a lot of data and backtracking on it. I have no formal training and all my opinions are based on conclusions we tested & drew from our work that translated into nearly no bad business decisions and constant growth.
Machine learning is not general intelligence. As such, although I believe that the comparison is not ill-willed, it's as far from the truth as it can be. ML is really a bunch of optimization problems that, when put together, form a coherent system that draws conclusions such as "is this a picture of an elephant?". Just as the brain does, there's a multitude of inputs and a central system that decides, mostly based on past experience what to do with said inputs.
I expect the brain also takes probabilities into account. So that it might choose an action if the worst possible option is also extremely unlikely.
In popular culture, it's called "least resistance path", it's also a trait that I see nearly all intelligent life forms exhibit.
What I find through my work is that, although bias is frowned upon, it's also a beautiful thing. Personally, I'm a contrarian and I like to believe the good ol' "people are stupid", but in reality, they really aren't. All the experiences you go throguh train your brain in exactly the same manner you speak of. The problem occurs when the multitude of paths isn't known at the start, that is to say, you're unexperienced.
Bias is not necessarily helpful min-maxing that happens in the background.
By the way, don't confuse this with what learning is. Min-maxing as you call it is a higher-level process that is what we can observe from the brain forming connections.
The problem with minimax algorithms is that they do not take into consideration long-term plans. Sometimes, taking short-term risks (by making moves that are not fully bullet-proof) can result in long-term positions that are far superior. Highly skilled players weigh these in their decision making.
Similarly, making bold moves can also jeopardize the opponent's plans and thus, in the end can result in very good moves (that was Fisher's specialty).
As of the brain, it uses learning rules that are local (Page, 2000) and probably favors reinforcement (e.g., Sutton & Barto, 2015). It might mimick minimax in some situations, but it can probably also mimick other optimization procedures based on internal settings, biases, and predisposition.
We wished the brain was so "rationale" as to adopt a single, well-understood algorithm, but nop, no such luck!