We present a high probability complexity bound for a stochastic adaptive regularization method with cubics, also known as regularized Newton method. The method makes use of stochastic zeroth, first and second-order oracles that satisfy certain accuracy and reliability assumptions. Such oracles have been used in the literature by other adaptive stochastic methods, such as trust region and line search. These oracles capture many settings, such as expected risk minimization, stochastic zeroth order…