COVARIANCE MATRIX OF MULTIVARIATE REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

asymptotic behavior of multivariate reward processes with nonlinear reward functions

A correction term for the covariance of renewal-reward processes with multivariate rewards

We consider a renewal-reward process with multivariate rewards. Such a process is constructed from an i.i.d. sequence of time periods, to each of which there is associated a multivariate reward vector. The rewards in each time period may depend on each other and on the period length, but not on the other time periods. Rewards are accumulated to form a vector valued process that exhibits jumps i...

On Markov Decision Processes with Pseudo-Boolean Reward Functions

Asymptotics for renewal-reward processes with retrospective reward structure

Let {(Xi; Yi): i= : : : ;−1; 0; 1; : : :} be a doubly in nite renewal-reward process, where {Xi: i= : : :− 1; 0; 1; : : :} is an i.i.d. sequence of renewal cycle lengths and Yi= g(Xi−q; Xi−q+1; : : : ; Xi) is the lump reward earned at the end of the ith renewal cycle, with some function g :R q+1 → R . Starting with the rst renewal cycle (of duration X1) at the time origin, let C(t) denote the e...

Markov Decision Processes with Arbitrary Reward Processes

We consider a learning problem where the decision maker interacts with a standard Markov decision process, with the exception that the reward functions vary arbitrarily over time. We show that, against every possible realization of the reward process, the agent can perform as well—in hindsight—as every stationary policy. This generalizes the classical no-regret result for repeated games. Specif...