  Variations in the instrumental noise of the Laser Interferometer Space
Antenna (LISA) over time are expected as a result of e.g. scheduled satellite
operations or unscheduled glitches. We demonstrate that these fluctuations can
be leveraged to improve the sensitivity to stochastic gravitational wave
backgrounds (SGWBs) compared to the stationary noise scenario. This requires
optimal use of data segments with downward noise fluctuations, and thus a data
analysis pipeline capable of analysing and combining shorter time segments of
mission data. We propose that simulation based inference is well suited for
this challenge. In an approximate, but state-of-the-art, modeling setup, we
show by comparison with Fisher Information Matrix estimates that the optimal
information gain can be achieved in practice.
