Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Online learning over a finite action set with limited switching   This paper studies the value of switching actions in the Prediction From
Experts (PFE) problem and Adversarial Multi-Armed Bandits (MAB) problem. First,
we revisit the well-studied and practically motivated setting of PFE with
switching costs. Many algorithms are known to achieve the minimax optimal order
of $O(\sqrt{T \log n})$ in expectation for both regret and number of switches,
where $T$ is the number of iterations and $n$ the number of actions. However,
no high probability (h.p.) guarantees are known. Our main technical
contribution is the first algorithms which with h.p. achieve this optimal order
for both regret and switches. This settles an open problem of [Devroye et al.,
2015], and directly implies the first h.p. guarantees for several problems of
interest.
  Next, to investigate the value of switching actions at a more granular level,
we introduce the setting of switching budgets, in which algorithms are limited
to $S \leq T$ switches between actions. This entails a limited number of free
switches, in contrast to the unlimited number of expensive switches in the
switching cost setting. Using the above result and several reductions, we unify
previous work and completely characterize the complexity of this switching
budget setting up to small polylogarithmic factors: for both PFE and MAB, for
all switching budgets $S \leq T$, and for both expectation and h.p. guarantees.
For PFE, we show the optimal rate is $\tilde{\Theta}(\sqrt{T\log n})$ for $S =
\Omega(\sqrt{T\log n})$, and $\min(\tilde{\Theta}(\tfrac{T\log n}{S}), T)$ for
$S = O(\sqrt{T \log n})$. Interestingly, the bandit setting does not exhibit
such a phase transition; instead we show the minimax rate decays steadily as
$\min(\tilde{\Theta}(\tfrac{T\sqrt{n}}{\sqrt{S}}), T)$ for all ranges of $S
\leq T$. These results recover and generalize the known minimax rates for the
(arbitrary) switching cost setting.

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The categories of this paper are: nlin
29
The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat