Interestingly, the gain function defined in the original MMR paper (Carbonell and Goldstein, 1998) satisfies diminishing returns, a fact apparently unnoticed until now.
carbonell and Goldstein (1998) define an objective function gain of adding element k to set S (k / ∈ S) as: where Sim 1 (s k , q) measures the similarity between unit s k to a query q, Sim 2 (s i , s k ) measures the similarity between unit s i and unit s k , and 0 ≤ λ ≤ 1 is a trade-off coefficient.