1,389 research outputs found
Multi-Fidelity Multi-Armed Bandits Revisited
We study the multi-fidelity multi-armed bandit (MF-MAB), an extension of the
canonical multi-armed bandit (MAB) problem. MF-MAB allows each arm to be pulled
with different costs (fidelities) and observation accuracy. We study both the
best arm identification with fixed confidence (BAI) and the regret minimization
objectives. For BAI, we present (a) a cost complexity lower bound, (b) an
algorithmic framework with two alternative fidelity selection procedures, and
(c) both procedures' cost complexity upper bounds. From both cost complexity
bounds of MF-MAB, one can recover the standard sample complexity bounds of the
classic (single-fidelity) MAB. For regret minimization of MF-MAB, we propose a
new regret definition, prove its problem-independent regret lower bound
and problem-dependent lower bound , where is the number of arms and is the decision budget
in terms of cost, and devise an elimination-based algorithm whose worst-cost
regret upper bound matches its corresponding lower bound up to some logarithmic
terms and, whose problem-dependent bound matches its corresponding lower bound
in terms of
Optimizing Photonic Nanostructures via Multi-fidelity Gaussian Processes
We apply numerical methods in combination with finite-difference-time-domain
(FDTD) simulations to optimize transmission properties of plasmonic mirror
color filters using a multi-objective figure of merit over a five-dimensional
parameter space by utilizing novel multi-fidelity Gaussian processes approach.
We compare these results with conventional derivative-free global search
algorithms, such as (single-fidelity) Gaussian Processes optimization scheme,
and Particle Swarm Optimization---a commonly used method in nanophotonics
community, which is implemented in Lumerical commercial photonics software. We
demonstrate the performance of various numerical optimization approaches on
several pre-collected real-world datasets and show that by properly trading off
expensive information sources with cheap simulations, one can more effectively
optimize the transmission properties with a fixed budget.Comment: NIPS 2018 Workshop on Machine Learning for Molecules and Materials.
arXiv admin note: substantial text overlap with arXiv:1811.0075
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