  Since the adoption of VP9 by Netflix in 2016, royalty-free coding standards
continued to gain prominence through the activities of the AOMedia consortium.
AV1, the latest open source standard, is now widely supported. In the early
years after standardisation, HDR video tends to be under served in open source
encoders for a variety of reasons including the relatively small amount of true
HDR content being broadcast and the challenges in RD optimisation with that
material. AV1 codec optimisation has been ongoing since 2020 including
consideration of the computational load. In this paper, we explore the idea of
direct optimisation of the Lagrangian $\lambda$ parameter used in the rate
control of the encoders to estimate the optimal Rate-Distortion trade-off
achievable for a High Dynamic Range signalled video clip. We show that by
adjusting the Lagrange multiplier in the RD optimisation process on a
frame-hierarchy basis, we are able to increase the Bjontegaard difference rate
gains by more than 3.98$\times$ on average without visually affecting the
quality.
