Linearly Solvable Optimal Control

We summarize the recently-developed framework of linearly-solvable stochastic optimal control. Using an exponential transformation, the (Hamilton-Jacobi) Bellman equation for such problems can bemade linear, giving rise to efficient numericalmethods. Extensions to game theory are also possible and lead to linear Isaacs equations. The key restriction that makes a stochastic optimal control problem linearly-solvable is that the noise and the controls must act in the same subspace. Apart from being linearly solvable, problems in this class have a number of unique properties including: path-integral interpretation of the exponentiated value function; compositionality of optimal control laws; duality with Bayesian inference; trajectory-based Maximum Principle for stochastic control. Development of a general class of more easily solvable problems tends to accelerate progress – as linear systems theory has done. The new framework may have similar impact in fields where stochastic optimal control is relevant.