  We consider the minimization problem of a sum of a number of functions having
Lipshitz $p$-th order derivatives with different Lipschitz constants. In this
case, to accelerate optimization, we propose a general framework allowing to
obtain near-optimal oracle complexity for each function in the sum separately,
meaning, in particular, that the oracle for a function with lower Lipschitz
constant is called a smaller number of times. As a building block, we extend
the current theory of tensor methods and show how to generalize near-optimal
tensor methods to work with inexact tensor step. Further, we investigate the
situation when the functions in the sum have Lipschitz derivatives of a
different order. For this situation, we propose a generic way to separate the
oracle complexity between the parts of the sum. Our method is not optimal,
which leads to an open problem of the optimal combination of oracles of a
different order.
