  This letter presents a combination of searches for Higgs boson pair
production using up to 36.1 fb$^{-1}$ of proton-proton collision data at a
centre-of-mass energy $\sqrt{s} = 13$ TeV recorded with the ATLAS detector at
the LHC. The combination is performed using six analyses searching for Higgs
boson pairs decaying into the bbbb, bbWW, bb$\tau\tau$, WWWW, bb$\gamma \gamma$
and WW$\gamma\gamma$ final states. Results are presented for non-resonant and
resonant Higgs boson pair production modes. No statistically significant excess
in data above the Standard Model predictions is found. The combined observed
(expected) limit at 95% confidence level on the non-resonant Higgs boson pair
production cross-section is 6.9 (10) times the predicted Standard Model
cross-section. Limits are also set on the ratio ($ \kappa_{\lambda} $) of the
Higgs boson self-coupling to its Standard Model value. This ratio is
constrained at 95% confidence level in observation (expectation) to $ -5.0 <
\kappa_{\lambda} <12.0 $ ($ -5.8 < \kappa_{\lambda} <12.0 $). In addition,
limits are set on the production of narrow scalar resonances and spin-2
Kaluza-Klein Randall-Sundrum gravitons. Exclusion regions are also provided in
the parameter space of the habemus Minimal Supersymmetric Standard Model and
the Electroweak Singlet Model.
