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Efficient Online Linear Optimization with Approximation Algorithms

NeurIPS 2017 · Bandits and online learning › Online convex optimization and games · approach: Online allocation with constraints

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use the new infeasible-projection algorithm instead of the KKL approachFull-information online linear optimization with an approximation oracle · Full informationapproximation-oracle calls per iteration: T -> \log(T)Helped
Use the new infeasible-projection algorithm instead of the KKL approachBandit online linear optimization with a barycentric spanner · Bandit informationexpected approximation-oracle calls per iteration: T^{2/3} -> \log(T)Helped
Use the new full-information algorithm with low-oracle-complexity parameter settingsFull-information online linear optimization with an approximation oracle · Full informationexpected α-regret: T^{-1/2} -> O(T^{-1/3})Mixed
Use the new bandit algorithm with a barycentric spannerBandit online linear optimization with an approximation oracle · Bandit informationexpected α-regret: T^{-1/3} -> T^{-1/3}No clear effect
Choose the alternative learning rate and projection error for the optimal-regret guaranteeFull-information algorithm · Full informationexpected α-regret: O(αRFT^{-1/3}) -> O(αRFT^{-1/2})Helped
Choose the alternative learning rate and projection error for the optimal-regret guaranteeFull-information algorithm · Full informationapproximation-oracle calls per iteration: O(d^2\ln\left({\frac{\alpha+1}{\alpha}T}\right)) -> O(\sqrt{T}d^2\ln\left({\frac{\alpha+1}{\alpha}T}\right))Hurt
Use a barycentric-spanner-based exploration reduction to estimate loss vectorsBandit algorithm · Bandit informationexpected α-regret: O((αβdCR+αRF+C)T^{-1/3})Helped

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