The key insights and findings of this work are:
For Pairwise Loss (PL) and Discounted Cumulative Gain (DCG), the minimax regret rate is Θ(T^(2/3)) for k = 1, 2, ..., m-2, and Θ(T^(1/2)) for k = m-1, m. This improves upon and generalizes previous results.
For Precision@n Gain (P@n), the minimax regret rate is Θ(T^(1/2)) for all 1 ≤ k ≤ m. This is a significant improvement over the previous O(T^(2/3)) regret bound.
An efficient algorithm is provided that achieves the Θ(T^(1/2)) minimax regret rate for P@n, with a per-round time complexity that is polynomial in m.
The analysis leverages the theory of finite partial monitoring games, specifically the concepts of global and local observability. The authors show that the games for PL, DCG, and P@n satisfy the appropriate observability conditions, leading to the characterization of the minimax regret rates.
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by Mingyuan Zha... at arxiv.org 04-15-2024
https://arxiv.org/pdf/2309.02425.pdfDeeper Inquiries