Implement clamped Luus Jaakola search for function minimization. #1690
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Summary:
EmbeddingOffloadScaleupProposer attempts to find an approximately
optimal trade-off between using extra cache memory to reduce prefetch
delay and the additional plan cost resulting from a more challenging
bin-packing of larger shards.
Currently a binary search is used under the assumption that the
cost would consistently decrease in the evaluated region. However,
investigation revealed that the cost region can be non-smooth and
multi-modal, leading to poor results with the binary search.
This diff implements the Luus Jaakola search procedure which is much
more robust and capable of navigating 'rough terrain'. In a subsequent
diff EmbeddingOffloadScaleupProposer will be updated to utilize this
approach instead of the binary search.
See https://en.wikipedia.org/wiki/Luus-Jaakola for detail.
Reviewed By: henrylhtsang
Differential Revision: D52686075