A measurement of the top quark mass (Mt) in the dileptonic tt decay channel is performed using data from proton-proton collisions at a center-of-mass energy of 8 TeV. The data was recorded by the CMS experiment at the LHC and corresponds to an integrated luminosity of 19.7 ± 0.5 fb-1. Events are selected with two oppositely charged leptons (l = e, μ) and two jets identified as originating from b quarks. The analysis is based on three kinematic observables whose distributions are sensitive to the value of Mt. An invariant mass observable, Mbl, and a "stransverse mass" observable, MT2, are employed in a simultaneous fit to determine the value of Mt and an overall jet energy scale factor (JSF). A complementary approach is used to construct an invariant mass observable, Mblν, that is combined with MT2 to measure Mt. The shapes of the observables, along with their evolutions in Mt and JSF, are modeled by a nonparametric Gaussian process regression technique. The sensitivity of the observables to the value of Mt is investigated using a Fisher information density method. The top quark mass is measured to be 172.22 ± 0.18(stat)-0.93 +0.89 (syst) GeV.