On the relation between Bayesian inference and certain solvable problems of stochastic control

Optimal control for nonlinear stochastic dynamical systems requires thesolution of a nonlinear PDE, the so - called Hamilton Jacobi Bellman equation.Recently, Bert Kappen and Emanuel Todorov have shown that for certain types of cost functions, this equationcan be transformed to a linear problem which is mathematically related to a Bayesian estimation problem. This has led to novel efficient algorithms for optimal control of such systems. I will show a simple proof for this surprising result and discuss some possible implications.