47 research outputs found
Bounded regret in stochastic multi-armed bandits
We study the stochastic multi-armed bandit problem when one knows the value
of an optimal arm, as a well as a positive lower bound on the
smallest positive gap . We propose a new randomized policy that attains
a regret {\em uniformly bounded over time} in this setting. We also prove
several lower bounds, which show in particular that bounded regret is not
possible if one only knows , and bounded regret of order is
not possible if one only knows $\mu^{(\star)}
Nonparametric Stochastic Contextual Bandits
We analyze the -armed bandit problem where the reward for each arm is a
noisy realization based on an observed context under mild nonparametric
assumptions. We attain tight results for top-arm identification and a sublinear
regret of , where is the
context dimension, for a modified UCB algorithm that is simple to implement
(NN-UCB). We then give global intrinsic dimension dependent and ambient
dimension independent regret bounds. We also discuss recovering topological
structures within the context space based on expected bandit performance and
provide an extension to infinite-armed contextual bandits. Finally, we
experimentally show the improvement of our algorithm over existing multi-armed
bandit approaches for both simulated tasks and MNIST image classification.Comment: AAAI 201
DTR Bandit: Learning to Make Response-Adaptive Decisions With Low Regret
Dynamic treatment regimes (DTRs) are personalized, adaptive, multi-stage
treatment plans that adapt treatment decisions both to an individual's initial
features and to intermediate outcomes and features at each subsequent stage,
which are affected by decisions in prior stages. Examples include personalized
first- and second-line treatments of chronic conditions like diabetes, cancer,
and depression, which adapt to patient response to first-line treatment,
disease progression, and individual characteristics. While existing literature
mostly focuses on estimating the optimal DTR from offline data such as from
sequentially randomized trials, we study the problem of developing the optimal
DTR in an online manner, where the interaction with each individual affect both
our cumulative reward and our data collection for future learning. We term this
the DTR bandit problem. We propose a novel algorithm that, by carefully
balancing exploration and exploitation, is guaranteed to achieve rate-optimal
regret when the transition and reward models are linear. We demonstrate our
algorithm and its benefits both in synthetic experiments and in a case study of
adaptive treatment of major depressive disorder using real-world data