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• W3097432087 abstract "We consider a natural model of online preference aggregation, where sets of preferred items $R_1, R_2, ldots, R_t$ along with a demand for $k_t$ items in each $R_t$, appear online. Without prior knowledge of $(R_t, k_t)$, the learner maintains a ranking $pi_t$ aiming that at least $k_t$ items from $R_t$ appear high in $pi_t$. This is a fundamental problem in preference aggregation with applications to, e.g., ordering product or news items in web pages based on user scrolling and click patterns. The widely studied Generalized Min-Sum-Set-Cover (GMSSC) problem serves as a formal model for the setting above. GMSSC is NP-hard and the standard application of no-regret online learning algorithms is computationally inefficient, because they operate in the space of rankings. In this work, we show how to achieve low regret for GMSSC in polynomial-time. We employ dimensionality reduction from rankings to the space of doubly stochastic matrices, where we apply Online Gradient Descent. A key step is to show how subgradients can be computed efficiently, by solving the dual of a configuration LP. Using oblivious deterministic and randomized rounding schemes, we map doubly stochastic matrices back to rankings with a small loss in the GMSSC objective." @default.
• W3097432087 created "2020-11-09" @default.
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• W3097432087 date "2020-11-05" @default.
• W3097432087 modified "2023-09-27" @default.
• W3097432087 title "Efficient Online Learning of Optimal Rankings: Dimensionality Reduction via Gradient Descent" @default.
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• W3097432087 hasPublicationYear "2020" @default.
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