Two-choice optimal stopping

Two Choice Optimal Stopping∗†

Let Xn, . . . , X1 be i.i.d. random variables with distribution function F . A statistician, knowing F , observes the X values sequentially and is given two chances to choose X’s using stopping rules. The statistician’s goal is to stop at a value of X as small as possible. Let V 2 n equal the expectation of the smaller of the two values chosen by the statistician when proceeding optimally. We o...

Optimal Two-Choice Stopping on an Exponential Sequence

Let X1 X2 Xn be independent and identically distributed with distribution function F . A statistician may choose two X values from the sequence by means of two stopping rules t1 t2, with the goal of maximizing E Xt1 ∨ Xt2 . We describe the optimal stopping rules and the asymptotic behavior of the optimal expected stopping values, V 2 n , as n → , when F is the exponential distribution. Specific...

Two Choi e Optimal Stopping

Optimal Stopping Policy for Multivariate Sequences a Generalized Best Choice Problem

  In the classical versions of “Best Choice Problem”, the sequence of offers is a random sample from a single known distribution. We present an extension of this problem in which the sequential offers are random variables but from multiple independent distributions. Each distribution function represents a class of investment or offers. Offers appear without any specified order. The objective is...

Optimal Stopping Problems

In the last lecture, we have analyzed the behavior of TD(λ) for approximating the cost­to­go function in autonomous systems. Recall that much of the analysis was based on the idea of sampling states according to their stationary distribution. This was done either explicitly, as was assumed in approximate value iteration, or implicitly through the simulation or observation of system trajectories...