Solving Stochastic Control under Multiplicative and Internal Noise via Constrained Optimization

Multiplicative motor and observation noise, along with internal noise corrupting computation, are central features of the sensorimotor system in biological and robotic agents. Yet, analytical solutions for stochastic optimal control are largely restricted to additive noise models and neglect internal noise. Here, we consider the problem of finding optimal control and filter laws for partially observable stochastic linear systems under quadratic costs with multiplicative control and observation noise, as well as internal noise. We provide an efficient, analytically derived coordinate-descent algorithm that computes mutually optimal linear control and filter laws by reformulating the problem as a constrained optimization. Our method provably guarantees monotonic decrease of the expected cost and convergence to a critical point, and overcomes the suboptimality and incompleteness of prior analytical approaches. Compared to state-of-the-art numerical methods, it achieves orders-of-magnitude computational speedups. Our solution also proves instrumental in revealing novel internal-noise-dependent, task-structured control strategies in a redundant arm control task.