Sorry for the super late reply. I don't know if anyone will see this... But...
In minimax regret, you have a set of available decisions D, and a set of possible states of nature N, and a utility U(D,N). Each state of nature also has a probability P(N) (which can be influenced by the decision too in some problems).
States of nature include "interest rates rise 1%", "interest rates fall 1%", and "interest rates stay the same". Decisions include "invest in stocks" and "invest in bonds".
Minimax regret proposes to ignore the probabilities P(N), instead suggesting a way to make a decision purely based on the utilities of the outcomes. But that is actually an illusion.
Outside of math class word problems, we don't have N or U(D,N) handed to us on a silver platter. There is always an infinite range of possible states of nature, many of which have a probability approaching but never reaching zero, including states such as "win the lottery", "communist revolution", and "unexpected intergalactic nuclear war".
In commonsense decision-making we don't include those states of nature in our decision matrix, because our common sense rules them out as being implausible before we even think about our options. You wouldn't choose to invest in bonds just because stocks have the most regret in the event of a communist takeover.
So what actually happens is we intuitively apply some probability threshold that rules out states of nature falling below it from our consideration. Then we minimize max regret on the remaining "plausibly realistic" states of nature.
Humans are so good at doing probability mentally that this step happens before we even realize it. But if you are writing code that makes decisions, you'll need to do it, and so you'll need to have at least a rough stab at the probability distributions.
In minimax regret, you have a set of available decisions D, and a set of possible states of nature N, and a utility U(D,N). Each state of nature also has a probability P(N) (which can be influenced by the decision too in some problems).
States of nature include "interest rates rise 1%", "interest rates fall 1%", and "interest rates stay the same". Decisions include "invest in stocks" and "invest in bonds".
Minimax regret proposes to ignore the probabilities P(N), instead suggesting a way to make a decision purely based on the utilities of the outcomes. But that is actually an illusion.
Outside of math class word problems, we don't have N or U(D,N) handed to us on a silver platter. There is always an infinite range of possible states of nature, many of which have a probability approaching but never reaching zero, including states such as "win the lottery", "communist revolution", and "unexpected intergalactic nuclear war".
In commonsense decision-making we don't include those states of nature in our decision matrix, because our common sense rules them out as being implausible before we even think about our options. You wouldn't choose to invest in bonds just because stocks have the most regret in the event of a communist takeover.
So what actually happens is we intuitively apply some probability threshold that rules out states of nature falling below it from our consideration. Then we minimize max regret on the remaining "plausibly realistic" states of nature.
Humans are so good at doing probability mentally that this step happens before we even realize it. But if you are writing code that makes decisions, you'll need to do it, and so you'll need to have at least a rough stab at the probability distributions.