I have always thought of the LambdaRank objective (https://www.microsoft.com/en-us/research/publication/from-ranknet-to-lambdarank-to-lambdamart-an-overview/ ht

I have always thought of the LambdaRank objective (https://www.microsoft.com/en-us/research/publication/from-ranknet-to-lambdarank-to-lambdamart-an-overview/ https://www.microsoft.com/en-us/research/publication/from-ra...) as mapping the scores to a probability distribution over rankings, or as they call it "projections onto the permutahedron".