This note presents a combination of searches for Higgs boson pairs 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 three analyses searching for the $HH \to b\bar{b}b\bar{b}$, $HH \to b\bar{b}\tau^{+}\tau^{-}$ and $HH \to b\bar{b}\gamma\gamma$ decay channels. Results are presented for both non-resonant and resonant Higgs boson pair production modes. The combined observed (expected) limit on the non-resonant Higgs boson pair cross-section is 0.22 pb (0.35 pb) at 95\% confidence level, which corresponds to 6.7 (10.4) times the predicted Standard Model cross-section. The ratio of the Higgs boson self-coupling to its Standard Model expectation $\left(\kappa_{\lambda} = \lambda_{HHH}/\lambda_{HHH}^{\text{SM}}\right)$ is observed (expected) to be constrained at 95\% confidence level to $-5.0 < \kappa_{\lambda} < 12.1$ $\left(-5.8< \kappa_{\lambda} < 12.0\right)$. Exclusion limits are also set on resonant Higgs boson pair production, probing a model with an extended Higgs sector based on two doublets, as well as a Randall--Sundrum bulk graviton model.

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