Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuum armed bandit problem of few variables in high dimensions   We consider the stochastic and adversarial settings of continuum armed
bandits where the arms are indexed by [0,1]^d. The reward functions r:[0,1]^d
-> R are assumed to intrinsically depend on at most k coordinate variables
implying r(x_1,..,x_d) = g(x_{i_1},..,x_{i_k}) for distinct and unknown
i_1,..,i_k from {1,..,d} and some locally Holder continuous g:[0,1]^k -> R with
exponent 0 < alpha <= 1. Firstly, assuming (i_1,..,i_k) to be fixed across
time, we propose a simple modification of the CAB1 algorithm where we construct
the discrete set of sampling points to obtain a bound of
O(n^((alpha+k)/(2*alpha+k)) (log n)^((alpha)/(2*alpha+k)) C(k,d)) on the
regret, with C(k,d) depending at most polynomially in k and sub-logarithmically
in d. The construction is based on creating partitions of {1,..,d} into k
disjoint subsets and is probabilistic, hence our result holds with high
probability. Secondly we extend our results to also handle the more general
case where (i_1,...,i_k) can change over time and derive regret bounds for the
same.

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The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
17
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: eess
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat