yes, I know that the uniform distribution assigns probability zero to every point, that doesn’t mean I ever have to, which is why I specified ML random reals in the unit interval (Equivalently binary sequences). im well aware that many events have probability zero under some particular stochastic process (including the 0-1 laws), but in order to do that calculation you have to arrive at that stochastic process as a model and how will you assign it probability 1 in the first place?
The statement “0=1” is equivalent to the empty set, so also already covered in what I said.
In fact, assuming that the utility function is bounded solves many problems, such as pascal’s muggings and the saint Petersburg paradox. For history based RL, assuming continuity can also be useful, implying both boundedness and the existence of optimal policies.
yes, I know that the uniform distribution assigns probability zero to every point, that doesn’t mean I ever have to, which is why I specified ML random reals in the unit interval (Equivalently binary sequences). im well aware that many events have probability zero under some particular stochastic process (including the 0-1 laws), but in order to do that calculation you have to arrive at that stochastic process as a model and how will you assign it probability 1 in the first place?
The statement “0=1” is equivalent to the empty set, so also already covered in what I said.
In fact, assuming that the utility function is bounded solves many problems, such as pascal’s muggings and the saint Petersburg paradox. For history based RL, assuming continuity can also be useful, implying both boundedness and the existence of optimal policies.