Information based approach to stochastic control problems

An information based method for solving stochastic control problems with partial observation has been proposed. First, the information-theoretic lower bounds of the cost function has been analysed. It has been shown, under rather weak assumptions, that reduction of the expected cost with closed-loop control compared to the best open-loop strategy is upper bounded by non-decreasing function of mutual information between control variables and the state trajectory. On the basis of this result, an Information Based Control method has been developed. The main idea of the IBC consists in replacing the original control task by a sequence of control problems that are relatively easy to solve and such that information about the state of the system is actively generated. Two examples of the operation of the IBC are given. It has been shown that the IBC is able to find the optimal solution without using dynamic programming at least in these examples. Hence the computational complexity of the IBC is substantially smaller than complexity of dynamic programming, which is the main advantage of the proposed method.