Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimax Regret for Cascading Bandits   Cascading bandits model the task of learning to rank $K$ out of $L$ items
over $n$ rounds of partial feedback. For this model, the minimax (i.e.,
gap-free) regret is poorly understood; in particular, the best known lower and
upper bounds are $\Omega(\sqrt{nL/K})$ and $\tilde{O}(\sqrt{nLK})$,
respectively. We improve the lower bound to $\Omega(\sqrt{nL})$ and show
CascadeKL-UCB (which ranks items by their KL-UCB indices) attains it up to log
terms. Surprisingly, we also show CascadeUCB1 (which ranks via UCB1) can suffer
suboptimal $\Omega(\sqrt{nLK})$ regret. This sharply contrasts with standard
$L$-armed bandits, where the corresponding algorithms both achieve the minimax
regret $\sqrt{nL}$ (up to log terms), and the main advantage of KL-UCB is only
to improve constants in the gap-dependent bounds. In essence, this contrast
occurs because Pinsker's inequality is tight for hard problems in the $L$-armed
case but loose (by a factor of $K$) in the cascading case.

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The categories of this paper are: dg-ga
19
The categories of this paper are: eess
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph