3,566 research outputs found
The Simulator: Understanding Adaptive Sampling in the Moderate-Confidence Regime
We propose a novel technique for analyzing adaptive sampling called the {\em
Simulator}. Our approach differs from the existing methods by considering not
how much information could be gathered by any fixed sampling strategy, but how
difficult it is to distinguish a good sampling strategy from a bad one given
the limited amount of data collected up to any given time. This change of
perspective allows us to match the strength of both Fano and change-of-measure
techniques, without succumbing to the limitations of either method. For
concreteness, we apply our techniques to a structured multi-arm bandit problem
in the fixed-confidence pure exploration setting, where we show that the
constraints on the means imply a substantial gap between the
moderate-confidence sample complexity, and the asymptotic sample complexity as
found in the literature. We also prove the first instance-based
lower bounds for the top-k problem which incorporate the appropriate
log-factors. Moreover, our lower bounds zero-in on the number of times each
\emph{individual} arm needs to be pulled, uncovering new phenomena which are
drowned out in the aggregate sample complexity. Our new analysis inspires a
simple and near-optimal algorithm for the best-arm and top-k identification,
the first {\em practical} algorithm of its kind for the latter problem which
removes extraneous log factors, and outperforms the state-of-the-art in
experiments
Rebels Leading London: the mayoralties of Ken Livingstone and Boris Johnson compared
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link
Generalized HydroDynamics on an Atom Chip
The emergence of a special type of fluid-like behavior at large scales in
one-dimensional (1d) quantum integrable systems, theoretically predicted in
2016, is established experimentally, by monitoring the time evolution of the in
situ density profile of a single 1d cloud of atoms trapped on
an atom chip after a quench of the longitudinal trapping potential. The theory
can be viewed as a dynamical extension of the thermodynamics of Yang and Yang,
and applies to the whole range of repulsion strength and temperature of the
gas. The measurements, performed on weakly interacting atomic clouds that lie
at the crossover between the quasicondensate and the ideal Bose gas regimes,
are in very good agreement with the 2016 theory. This contrasts with the
previously existing 'conventional' hydrodynamic approach---that relies on the
assumption of local thermal equilibrium---, which is unable to reproduce the
experimental data.Comment: v1: 6+11 pages, 4+4 figures. v2: published version, 6+11 pages, 4+6
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