Universal induction solves in principle the problem of choosing a prior to achieve optimal inductive inference. The AIXI theory, which combines control theory and universal induction, solves in principle the problem of optimal behavior of an intelligent agent. A practically most important and very challenging problem is to find a computationally efficient (if not optimal) approximation for the optimal but incomputable AIXI theory. We propose such an approximation based on a Monte Carlo algorithm that samples programs according to their algorithmic probability. The approach is specifically designed to deal with real world problems (the agent processes observed data and makes plans over range of divergent time scales) under limited computational resources.