Discrete Optimal Stopping Task

A Discrete Optimal Stopping Task is an optimal stopping task that is a discrete sequential task.

• See: Stopping Rule, Filtration (Mathematics), Probability Space, Adapted Process, Stopping Time, Value Function, Markov Process, Probability Measure, Stochastic Process.

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References

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/optimal_stopping#Discrete_time_case Retrieved:2017-1-30.
  • Stopping rule problems are associated with two objects:
    1. A sequence of random variables [math]\displaystyle{ X_1, X_2, \ldots }[/math] , whose joint distribution is something assumed to be known
    2. A sequence of 'reward' functions [math]\displaystyle{ (y_i)_{i\ge 1} }[/math] which depend on the observed values of the random variables in 1.:

       [math]\displaystyle{ y_i=y_i (x_1, \ldots ,x_i) }[/math] Given those objects, the problem is as follows:

    • You are observing the sequence of random variables, and at each step [math]\displaystyle{ i }[/math] , you can choose to either stop observing or continue
    • If you stop observing at step [math]\displaystyle{ i }[/math] , you will receive reward [math]\displaystyle{ y_i }[/math] * You want to choose a stopping rule to maximise your expected reward (or equivalently, minimise your expected loss)

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