Generalized maximum entropy estimation
This provides a computationally efficient solution for entropy estimation in noisy constraint settings, with applications in chemical master equations and constrained Markov decision processes, though it appears incremental as an extension of existing convex optimization techniques.
The paper tackles the problem of estimating maximum entropy distributions under noisy moment constraints by developing a novel approximation scheme using smoothed fast gradient methods with explicit error bounds, achieving computational efficiency with provable accuracy guarantees.
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel approximation scheme using a smoothed fast gradient method that is equipped with explicit bounds on the approximation error. We further demonstrate how the presented scheme can be used for approximating the chemical master equation through the zero-information moment closure method, and for an approximate dynamic programming approach in the context of constrained Markov decision processes with uncountable state and action spaces.