Fast Minimization of Expected Logarithmic Loss via Stochastic Dual Averaging

arXiv:2311.02557v2 Announce Type: replace-cross
Abstract: Consider the problem of minimizing an expected logarithmic loss over either the probability simplex or the set of quantum density matrices. This problem includes tasks such as solving the Poisson inverse problem, computing the maximum-likelihood estimate for quantum state tomography, and approximating positive semi-definite matrix permanents with the currently tightest approximation ratio. Although the optimization problem is convex, standard iteration complexity guarantees for first-order methods do not directly apply due to the absence of Lipschitz …

abstract arxiv computing cs.lg likelihood loss math.oc matrix maximum-likelihood positive probability quant-ph quantum set state stochastic tasks type via