1,900 research outputs found
Corrupt Bandits for Preserving Local Privacy
We study a variant of the stochastic multi-armed bandit (MAB) problem in
which the rewards are corrupted. In this framework, motivated by privacy
preservation in online recommender systems, the goal is to maximize the sum of
the (unobserved) rewards, based on the observation of transformation of these
rewards through a stochastic corruption process with known parameters. We
provide a lower bound on the expected regret of any bandit algorithm in this
corrupted setting. We devise a frequentist algorithm, KLUCB-CF, and a Bayesian
algorithm, TS-CF and give upper bounds on their regret. We also provide the
appropriate corruption parameters to guarantee a desired level of local privacy
and analyze how this impacts the regret. Finally, we present some experimental
results that confirm our analysis
Channel Selection for Network-assisted D2D Communication via No-Regret Bandit Learning with Calibrated Forecasting
We consider the distributed channel selection problem in the context of
device-to-device (D2D) communication as an underlay to a cellular network.
Underlaid D2D users communicate directly by utilizing the cellular spectrum but
their decisions are not governed by any centralized controller. Selfish D2D
users that compete for access to the resources construct a distributed system,
where the transmission performance depends on channel availability and quality.
This information, however, is difficult to acquire. Moreover, the adverse
effects of D2D users on cellular transmissions should be minimized. In order to
overcome these limitations, we propose a network-assisted distributed channel
selection approach in which D2D users are only allowed to use vacant cellular
channels. This scenario is modeled as a multi-player multi-armed bandit game
with side information, for which a distributed algorithmic solution is
proposed. The solution is a combination of no-regret learning and calibrated
forecasting, and can be applied to a broad class of multi-player stochastic
learning problems, in addition to the formulated channel selection problem.
Analytically, it is established that this approach not only yields vanishing
regret (in comparison to the global optimal solution), but also guarantees that
the empirical joint frequencies of the game converge to the set of correlated
equilibria.Comment: 31 pages (one column), 9 figure
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
Regret Minimisation in Multi-Armed Bandits Using Bounded Arm Memory
In this paper, we propose a constant word (RAM model) algorithm for regret
minimisation for both finite and infinite Stochastic Multi-Armed Bandit (MAB)
instances. Most of the existing regret minimisation algorithms need to remember
the statistics of all the arms they encounter. This may become a problem for
the cases where the number of available words of memory is limited. Designing
an efficient regret minimisation algorithm that uses a constant number of words
has long been interesting to the community. Some early attempts consider the
number of arms to be infinite, and require the reward distribution of the arms
to belong to some particular family. Recently, for finitely many-armed bandits
an explore-then-commit based algorithm~\citep{Liau+PSY:2018} seems to escape
such assumption. However, due to the underlying PAC-based elimination their
method incurs a high regret. We present a conceptually simple, and efficient
algorithm that needs to remember statistics of at most arms, and for any
-armed finite bandit instance it enjoys a upper-bound on regret. We extend it to achieve sub-linear
\textit{quantile-regret}~\citep{RoyChaudhuri+K:2018} and empirically verify the
efficiency of our algorithm via experiments
A Survey of Monte Carlo Tree Search Methods
Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work
Learning in A Changing World: Restless Multi-Armed Bandit with Unknown Dynamics
We consider the restless multi-armed bandit (RMAB) problem with unknown
dynamics in which a player chooses M out of N arms to play at each time. The
reward state of each arm transits according to an unknown Markovian rule when
it is played and evolves according to an arbitrary unknown random process when
it is passive. The performance of an arm selection policy is measured by
regret, defined as the reward loss with respect to the case where the player
knows which M arms are the most rewarding and always plays the M best arms. We
construct a policy with an interleaving exploration and exploitation epoch
structure that achieves a regret with logarithmic order when arbitrary (but
nontrivial) bounds on certain system parameters are known. When no knowledge
about the system is available, we show that the proposed policy achieves a
regret arbitrarily close to the logarithmic order. We further extend the
problem to a decentralized setting where multiple distributed players share the
arms without information exchange. Under both an exogenous restless model and
an endogenous restless model, we show that a decentralized extension of the
proposed policy preserves the logarithmic regret order as in the centralized
setting. The results apply to adaptive learning in various dynamic systems and
communication networks, as well as financial investment.Comment: 33 pages, 5 figures, submitted to IEEE Transactions on Information
Theory, 201
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