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- W2971305908 abstract "We propose computationally efficient algorithms for textit{online linear optimization with bandit feedback}, in which a player chooses an textit{action vector} from a given (possibly infinite) set $mathcal{A} subseteq mathbb{R}^d$, and then suffers a loss that can be expressed as a linear function in action vectors. Although existing algorithms achieve an optimal regret bound of $tilde{O}(sqrt{T})$ for $T$ rounds (ignoring factors of $mathrm{poly} (d, log T)$), computationally efficient ways of implementing them have not yet been specified, in particular when $|mathcal{A}|$ is not bounded by a polynomial size in $d$. A standard way to pursue computational efficiency is to assume that we have an efficient algorithm referred to as textit{oracle} that solves (offline) linear optimization problems over $mathcal{A}$. Under this assumption, the computational efficiency of a bandit algorithm can then be measured in terms of textit{oracle complexity}, i.e., the number of oracle calls. Our contribution is to propose algorithms that offer optimal regret bounds of $tilde{O}(sqrt{T})$ as well as low oracle complexity for both textit{non-stochastic settings} and textit{stochastic settings}. Our algorithm for non-stochastic settings has an oracle complexity of $tilde{O}( T )$ and is the first algorithm that achieves both a regret bound of $tilde{O}( sqrt{T} )$ and an oracle complexity of $tilde{O} ( mathrm{poly} ( T ) )$, given only linear optimization oracles. Our algorithm for stochastic settings calls the oracle only $O( mathrm{poly} (d, log T))$ times, which is smaller than the current best oracle complexity of $O( T )$ if $T$ is sufficiently large." @default.
- W2971305908 created "2019-09-05" @default.
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- W2971305908 date "2019-01-01" @default.
- W2971305908 modified "2023-10-16" @default.
- W2971305908 title "Oracle-Efficient Algorithms for Online Linear Optimization with Bandit Feedback" @default.
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