Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets

ArXi:2512.10906v2 Announce Type: replace-cross We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose mean and covariance lie within norm balls centered at given nominal values. To cope with this ambiguity, we design causal affine control policies to minimize the worst-case expected regret over all distributions in the ambiguity set.