Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Fragility of Optimized Bandit Algorithms   Much of the literature on optimal design of bandit algorithms is based on
minimization of expected regret. It is well known that designs that are optimal
over certain exponential families can achieve expected regret that grows
logarithmically in the number of arm plays, at a rate governed by the
Lai-Robbins lower bound. In this paper, we show that when one uses such
optimized designs, the associated algorithms necessarily have the undesirable
feature that the tail of the regret distribution behaves like that of a
truncated Cauchy distribution. Furthermore, for $p>1$, the $p$'th moment of the
regret distribution grows much faster than poly-logarithmically, in particular
as a power of the number of sub-optimal arm plays. We show that optimized
Thompson sampling and UCB bandit designs are also fragile, in the sense that
when the problem is even slightly mis-specified, the regret can grow much
faster than the conventional theory suggests. Our arguments are based on
standard change-of-measure ideas, and indicate that the most likely way that
regret becomes larger than expected is when the optimal arm returns
below-average rewards in the first few arm plays that make that arm appear to
be sub-optimal, thereby causing the algorithm to sample a truly sub-optimal arm
much more than would be optimal.

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The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int