Browsing by Subject "Regret analysis"
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Item Open Access Generalized global bandit and its application in cellular coverage optimization(Institute of Electrical and Electronics Engineers, 2018) Shen, C.; Zhou, R.; Tekin, Cem; Schaar, M. V. D.Motivated by the engineering problem of cellular coverage optimization, we propose a novel multiarmed bandit model called generalized global bandit. We develop a series of greedy algorithms that have the capability to handle nonmonotonic but decomposable reward functions, multidimensional global parameters, and switching costs. The proposed algorithms are rigorously analyzed under the multiarmed bandit framework, where we show that they achieve bounded regret, and hence, they are guaranteed to converge to the optimal arm in finite time. The algorithms are then applied to the cellular coverage optimization problem to achieve the optimal tradeoff between sufficient small cell coverage and limited macroleakage without prior knowledge of the deployment environment. The performance advantage of the new algorithms over existing bandits solutions is revealed analytically and further confirmed via numerical simulations. The key element behind the performance improvement is a more efficient 'trial and error' mechanism, in which any trial will help improve the knowledge of all candidate power levels.Item Open Access Global bandits(Institute of Electrical and Electronics Engineers, 2018) Atan, O.; Tekin, Cem; Schaar, M. V. D.Multiarmed bandits (MABs) model sequential decision-making problems, in which a learner sequentially chooses arms with unknown reward distributions in order to maximize its cumulative reward. Most of the prior works on MAB assume that the reward distributions of each arm are independent. But in a wide variety of decision problems - from drug dosage to dynamic pricing - the expected rewards of different arms are correlated, so that selecting one arm provides information about the expected rewards of other arms as well. We propose and analyze a class of models of such decision problems, which we call global bandits (GB). In the case in which rewards of all arms are deterministic functions of a single unknown parameter, we construct a greedy policy that achieves bounded regret, with a bound that depends on the single true parameter of the problem. Hence, this policy selects suboptimal arms only finitely many times with probability one. For this case, we also obtain a bound on regret that is independent of the true parameter; this bound is sublinear, with an exponent that depends on the informativeness of the arms. We also propose a variant of the greedy policy that achieves O(√T) worst case and O(1) parameter-dependent regret. Finally, we perform experiments on dynamic pricing and show that the proposed algorithms achieve significant gains with respect to the well-known benchmarks.Item Open Access Online anomaly detection with bandwidth optimized hierarchical kernel density estimators(IEEE, 2020) Kerpicci, M.; Ozkan, H.; Kozat, Süleyman SerdarWe propose a novel unsupervised anomaly detection algorithm that can work for sequential data from any complex distribution in a truly online framework with mathematically proven strong performance guarantees. First, a partitioning tree is constructed to generate a doubly exponentially large hierarchical class of observation space partitions, and every partition region trains an online kernel density estimator (KDE) with its own unique dynamical bandwidth. At each time, the proposed algorithm optimally combines the class estimators to sequentially produce the final density estimation. We mathematically prove that the proposed algorithm learns the optimal partition with kernel bandwidths that are optimized in both region-specific and time-varying manner. The estimated density is then compared with a data-adaptive threshold to detect anomalies. Overall, the computational complexity is only linear in both the tree depth and data length. In our experiments, we observe significant improvements in anomaly detection accuracy compared with the state-of-the-art techniques.Item Open Access Online anomaly detection with kernel density estimators(Bilkent University, 2019-07) Kerpiççi, MineWe study online anomaly detection in an unsupervised framework and introduce an algorithm to detect the anomalies in sequential data. We first sequentially learn the density for the observed data with a novel kernel based hierarchical approach for which we also provide a regret bound in a competitive manner against an exponentially large class of estimators. In our approach, we use a binary partitioning tree and apply the nonparametric Kernel Density Estimation (KDE) method at each node of the introduced tree. The use of the partitioning tree allows us not only to generate a large class of estimators of size doubly exponential in the depth that we compete against in estimating the density, but also to hierarchically organize the class to obtain a computationally efficient final estimation. Moreover, we do not assume any underlying distribution for the data so that our algorithm can work for data coming from any unknown arbitrarily complex distribution. Note that the end-to-end processing in our work is truly online. For this, we exploit a random Fourier kernel expansion for sequentially exact kernel evaluations without a repetitive access to past data. Our algorithm learns not only the optimal partitioning of the observation space but also the optimal bandwidth, which is locally tuned for the optimal partition. Thus, we solve the bandwidth selection problem in KDE methods in a highly novel and computationally efficient way. Finally, as the data density is sequentially being learned in the stream, we compare the estimated density with a threshold to detect the anomalies. We also adaptively learn the threshold in time to achieve the optimal threshold. In our experiments with synthetic and real datasets, we illustrate significant performance improvements achieved by our method against the state-of-the-art anomaly detection algorithms.