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Nonstochastic Multiarmed Bandits with Unrestricted Delays

NeurIPS 2019 · Bandits and online learning › Online convex optimization and games · approach: Best-of-both-worlds bandit algorithms · 3 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use DEW for variable bounded delays with a known delay upper boundDelayed Exp3 · Nonstochastic bandits, variable bounded delaysexpected regret bound: 2 \sqrt{ \left ( \frac{KTe}{2} + D \right) \ln K}Helped
Skip rounds whose delays meet or exceed betaDEW · Nonstochastic bandits, unrestricted delaysexpected regret bound: 2\sqrt{ \left ( \frac{KTe}{2} + (1 + 4e)D \right) \ln K}Helped
Tune the skipping threshold by doubling when delays are available at action timeSkipper + DEW · Nonstochastic bandits, unrestricted delays available at action timeexpected regret bound: 15 \min_{\beta} \left \{ \vert S_{\beta} \vert + 4e\beta \ln K + \frac{KT + D_{\beta}}{4e\beta} \right \} + 10 e^{2} K \Helped
Use the oracle bound rather than the explicit bound when D_beta is much smaller than DDoubling + Skipper + DEW · Example with a large delay on early rounds and zero delay on later roundsregret bound: explicit: \mathcal{O} \left (\sqrt{KT\ln K + T\sqrt{KT}} \right ) = \mathcal{O}\big(T^{3/4}\big); oracle: \mathcal{O} \lHelped

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