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##

Expected Total Reward

where,

*X*_{t}- State in time *t*

*Y*_{t}- Action in time *t*

Under the assumption that
*M*>|*r*_{t}(*s*,*a*)| for each
and that *A* and *S* are discrete then
is well defined for all
.
(
is the group of stochastic, history-depended decision rules). Namely, for each decision rule there is a well defined value.

*Yishay Mansour*

*1999-11-15*