  Optimization metrics are crucial for building recommendation systems at
scale. However, an effective and efficient metric for practical use remains
elusive. While Top-K ranking metrics are the gold standard for optimization,
they suffer from significant computational overhead. Alternatively, the more
efficient accuracy and AUC metrics often fall short of capturing the true
targets of recommendation tasks, leading to suboptimal performance. To overcome
this dilemma, we propose a new optimization metric, Lower-Left Partial AUC
(LLPAUC), which is computationally efficient like AUC but strongly correlates
with Top-K ranking metrics. Compared to AUC, LLPAUC considers only the partial
area under the ROC curve in the Lower-Left corner to push the optimization
focus on Top-K. We provide theoretical validation of the correlation between
LLPAUC and Top-K ranking metrics and demonstrate its robustness to noisy user
feedback. We further design an efficient point-wise recommendation loss to
maximize LLPAUC and evaluate it on three datasets, validating its effectiveness
and robustness.
