3 research outputs found
RELEAF: An Algorithm for Learning and Exploiting Relevance
Recommender systems, medical diagnosis, network security, etc., require
on-going learning and decision-making in real time. These -- and many others --
represent perfect examples of the opportunities and difficulties presented by
Big Data: the available information often arrives from a variety of sources and
has diverse features so that learning from all the sources may be valuable but
integrating what is learned is subject to the curse of dimensionality. This
paper develops and analyzes algorithms that allow efficient learning and
decision-making while avoiding the curse of dimensionality. We formalize the
information available to the learner/decision-maker at a particular time as a
context vector which the learner should consider when taking actions. In
general the context vector is very high dimensional, but in many settings, the
most relevant information is embedded into only a few relevant dimensions. If
these relevant dimensions were known in advance, the problem would be simple --
but they are not. Moreover, the relevant dimensions may be different for
different actions. Our algorithm learns the relevant dimensions for each
action, and makes decisions based in what it has learned. Formally, we build on
the structure of a contextual multi-armed bandit by adding and exploiting a
relevance relation. We prove a general regret bound for our algorithm whose
time order depends only on the maximum number of relevant dimensions among all
the actions, which in the special case where the relevance relation is
single-valued (a function), reduces to ; in the
absence of a relevance relation, the best known contextual bandit algorithms
achieve regret , where is the full dimension of
the context vector.Comment: to appear in IEEE Journal of Selected Topics in Signal Processing,
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