Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit Best Arm Identification in Linear Bandits Using No-Regret
  Learners   We study the problem of best arm identification in linearly parameterised
multi-armed bandits. Given a set of feature vectors
$\mathcal{X}\subset\mathbb{R}^d,$ a confidence parameter $\delta$ and an
unknown vector $\theta^*,$ the goal is to identify
$\arg\max_{x\in\mathcal{X}}x^T\theta^*$, with probability at least $1-\delta,$
using noisy measurements of the form $x^T\theta^*.$ For this fixed confidence
($\delta$-PAC) setting, we propose an explicitly implementable and provably
order-optimal sample-complexity algorithm to solve this problem. Previous
approaches rely on access to minimax optimization oracles. The algorithm, which
we call the \textit{Phased Elimination Linear Exploration Game} (PELEG),
maintains a high-probability confidence ellipsoid containing $\theta^*$ in each
round and uses it to eliminate suboptimal arms in phases. PELEG achieves fast
shrinkage of this confidence ellipsoid along the most confusing (i.e., close
to, but not optimal) directions by interpreting the problem as a two player
zero-sum game, and sequentially converging to its saddle point using low-regret
learners to compute players' strategies in each round. We analyze the sample
complexity of PELEG and show that it matches, up to order, an
instance-dependent lower bound on sample complexity in the linear bandit
setting. We also provide numerical results for the proposed algorithm
consistent with its theoretical guarantees.

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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: math
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The categories of this paper are: gr-qc