  The stochastic gravitational-wave background is a superposition of sources
that are either too weak or too numerous to detect individually. In this study
we present the results from a cross-correlation analysis on data from Advanced
LIGO's second observing run (O2), which we combine with the results of the
first observing run (O1). We do not find evidence for a stochastic background,
so we place upper limits on the normalized energy density in gravitational
waves at the 95% credible level of $\Omega_{\rm GW}<6.0\times 10^{-8}$ for a
frequency-independent (flat) background and $\Omega_{\rm GW}<4.8\times 10^{-8}$
at 25 Hz for a background of compact binary coalescences. The upper limit
improves over the O1 result by a factor of 2.8. Additionally, we place upper
limits on the energy density in an isotropic background of scalar- and
vector-polarized gravitational waves, and we discuss the implication of these
results for models of compact binaries and cosmic string backgrounds. Finally,
we present a conservative estimate of the correlated broadband noise due to the
magnetic Schumann resonances in O2, based on magnetometer measurements at both
the LIGO Hanford and LIGO Livingston observatories. We find that correlated
noise is well below the O2 sensitivity.
