[CUDA] Potential missed inversion of discounts within CUDA implementation of LambdarankNDCG

[DJ-Hayden]

Description

Hello, I believe there might be a missed discount inversion within the CUDA implementation of LightGBM's LambdarankNDCG rank objective class? I'm unfortunately better at math than optimized C++/CUDA so I may be missing something simple. I'll try to link to the appropriate code/lines to justify my thoughts.

1. Within the normal, non-CUDA implementation of GetGradientsForOneQuery within rank_objective.hpp here there are two calls to DCGCalculator::GetDiscount to get the discounts.

2. I believe those calls go to DCGCalculator::GetDiscount here, which looks up pre-computed discounts.

3. Those pre-computed discounts seem to occur here during the DCGCalculator::Init call. Notably, the discounts are 1.0 / std::log2(2.0 + i), which aligns with the math (that the discounts are inverted).

4. Within the CUDA implementation of GetGradientsKernel_LambdarankNDCG within cuda_rank_objective.cu here the discounts are not precomputed.

5. Instead, each discount here and here directly compute the discount as log2(2.0f + i).

It does not appear to invert the discount later in the code. In fact, both the non-CUDA and CUDA implementation are nigh-identical within that lambda gradient calculation loop (besides the above inversion discrepancy and a pre-computed sigmoid lookup table).

Reproducible example

The code runs, trains, and seemingly works fine even without the inversion. So in all likelihood I might just be misunderstanding something.

Environment info

LightGBM Version 4.6.0

Additional Comments

Since the ranks should always be 0+, I believe the bug can be fixed with simple inversions within the function:

• const double high_discount = log2(2.0f + high_rank); -> const double high_discount = 1.0f / log2(2.0f + high_rank);
• const double low_discount = log2(2.0f + low_rank); -> const double low_discount = 1.0f / log2(2.0f + low_rank);

[jameslamb]

@shiyu1994 or @metpavel can you please investigate this one?