2,931 research outputs found
Decoy Bandits Dueling on a Poset
We adress the problem of dueling bandits defined on partially ordered sets,
or posets. In this setting, arms may not be comparable, and there may be
several (incomparable) optimal arms. We propose an algorithm, UnchainedBandits,
that efficiently finds the set of optimal arms of any poset even when pairs of
comparable arms cannot be distinguished from pairs of incomparable arms, with a
set of minimal assumptions. This algorithm relies on the concept of decoys,
which stems from social psychology. For the easier case where the
incomparability information may be accessible, we propose a second algorithm,
SlicingBandits, which takes advantage of this information and achieves a very
significant gain of performance compared to UnchainedBandits. We provide
theoretical guarantees and experimental evaluation for both algorithms
Occupants in manifolds
Let K be a subset of a smooth manifold M. In some cases functor calculus
methods lead to a homotopical formula for M minus K in terms of the subspaces M
minus S, where S runs through the finite subsets of K.Comment: There is a sequel to this paper: title "Configuration categories and
homotopy automorphisms". v2: some typos corrected, v3: some errors in section
1 corrected. v4: more errors corrected and therefore number of authors
increased from 1 to 2. v5: more errors corrected especially in section 3. v6:
just a few typos corrected and pointers adde
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