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This paper is about index policies for minimizing (frequentist) regret in a stochastic multi-armed bandit model, inspired by a Bayesian view on the problem. Our main contribution is to prove that the Bayes-UCB algorithm, which relies on quantiles of posterior distributions, is asymptotically optimal when the reward distributions belong to a one-dimensional exponential family, for a large class of prior distributions. We also show that the Bayesian literature gives new insight on what kind of exploration rates could be used in frequentist, UCB-type algorithms. Indeed, approximations of the Bayesian optimal solution or the Finite Horizon Gittins indices provide a justification for the kl-UCB+ and kl-UCB-H+ algorithms, whose asymptotic optimality is also established.
In this paper we introduce a class of Markov decision processes that arise as a natural model for many renewable resource allocation problems. Upon extending results from the inventory control literature, we prove that they admit a closed form soluti
We introduce a dynamic generative model, Bayesian allocation model (BAM), which establishes explicit connections between nonnegative tensor factorization (NTF), graphical models of discrete probability distributions and their Bayesian extensions, and
Due to spectrum scarcity, the coexistence of radar and wireless communication has gained substantial research interest recently. Among many scenarios, the heterogeneouslydistributed joint radar-communication system is promising due to its flexibility
We introduce Deep Adaptive Design (DAD), a method for amortizing the cost of adaptive Bayesian experimental design that allows experiments to be run in real-time. Traditional sequential Bayesian optimal experimental design approaches require substant
The Kalman filter (KF) is used in a variety of applications for computing the posterior distribution of latent states in a state space model. The model requires a linear relationship between states and observations. Extensions to the Kalman filter ha