اصل جداسازی برای کنترل نیمه مشاهده شده فرآیندهای تصادفی منحصر به فرد

The analysis of partially observed stochastic control problems often replaces the unknown state process with its conditional distribution given the observations. This technique rewrites the dynamics in terms of knowable processes whose costs coincide with the original processes. This paper considers stochastic processes having singular behavior and presents an approach which separates the determination of the optimal control from the task of estimating the conditional distribution of the unknown process. It involves using a martingale problem characterization for the dynamics followed by a further characterization using occupation measures. This final characterization forms the basis for an equivalent linear programming formulation of the problem over the space of occupation measures.

The previous section has demonstrated that the problem of choosing a control for singular stochastic processes under the condition of partial observations so as to minimize the long-term average cost of the process is equivalent to solving the minimization linear program over the space of pairs of occupation measures. Moreover, the optimal control is given in terms of the conditional distribution on the control space given the state of the occupation measure. The adjustments to the control in order to meet the partial observation requirement occurs by averaging this control according to the conditional distribution of the state given the observations. This approach separates the task of optimization from the estimation of the conditional distribution. The major task remaining to solve the partially observed, singular control problem is the on-line requirement of determining the conditional distributions ππ given the observations GG.