The disparity between optimal and practical Lagrangian multiplier estimation in video encoders

With video streaming making up 80% of the global internet bandwidth, the need to deliver high-quality video at low bitrate, combined with the high complexity of modern codecs, has led to the idea of a per-clip optimisation approach in transcoding. In this paper, we revisit the Lagrangian multiplier parameter, which is at the core of rate-distortion optimisation. Currently, video encoders use prediction models to set this parameter but these models are agnostic to the video at hand. We explore the gains that could be achieved using a per-clip direct-search optimisation of the Lagrangian multiplier parameter. We evaluate this optimisation framework on a much larger corpus of videos than that has been attempted by previous research. Our results show that per-clip optimisation of the Lagrangian multiplier leads to BD-Rate average improvements of 1.87% for x265 across a 10 k clip corpus of modern videos, and up to 25% in a single clip. Average improvements of 0.69% are reported for libaom-av1 on a subset of 100 clips. However, we show that a per-clip, per-frame-type optimisation of λ for libaom-av1 can increase these average gains to 2.5% and up to 14.9% on a single clip. Our optimisation scheme requires about 50–250 additional encodes per-clip but we show that significant speed-up can be made using proxy videos in the optimisation. These computational gains (of up to ×200) incur a slight loss to BD-Rate improvement because the optimisation is conducted at lower resolutions. Overall, this paper highlights the value of re-examining the estimation of the Lagrangian multiplier in modern codecs as there are significant gains still available without changing the tools used in the standards.