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Sufficient Classes of Strategies in Discrete Dynamic Programming Ii . Locally Stationary Strategies
| Content Provider | Semantic Scholar |
|---|---|
| Author | Fainberg, Eugene A. |
| Abstract | (Translated by Merle Ellis) 6. The main results. This paper is a continuation of [1]. Throughout we examine a homogeneous controlled Markov model d {X, A(.), p, r} with discrete time, count-able state space X, sets of controls A(x), x X, transition function p and payoff function r. For the initial state x X and strategy r H, where H is the set of all strategies, the value of the criterion w(x) is the expectation of the total payoff on the infinite horizon. The price of the model is denoted by v, and the price of the class of stationary strategies S is denoted by s. If the payoff function is replaced by its negative part r-, then the value of the criterion is denoted by w-; the corresponding prices are denoted by v_ and s_. v+ is defined similarly when r is replaced by r + (according to [2], v+ s+). As before, we assume fulfilled the general convergence condition (4.7), which according to [3], [4] is equivalent to v+ < eo (if in some relation for the functions the argument is omitted, this means that the relation holds for all values of the argument). Since the price of the model coincides with the price of the class of nonrandomized strategies (this follows from Corollary 4.3), we shall understand throughout what follows by II the set of nonrandomized strategies. define the strategy/nr obtained from r if the control is performed at time n + 1 and prior to this time the sequence of states and controls hn was observed, i.e., hr and for any prehistory hi Xoao" return under the strategy r from the step n under the condition of the prehistory h,. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ams.sunysb.edu/~feinberg/public/TV1987.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
