Browsing by Subject "Minimax optimal"
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Item Open Access Minimax optimal algorithms for adversarial bandit problem with multiple plays(IEEE, 2019) Vural, Nuri Mert; Gökçesu, Hakan; Gökçesu, K.; Kozat, Süleyman SerdarWe investigate the adversarial bandit problem with multiple plays under semi-bandit feedback. We introduce a highly efficient algorithm that asymptotically achieves the performance of the best switching m-arm strategy with minimax optimal regret bounds. To construct our algorithm, we introduce a new expert advice algorithm for the multiple-play setting. By using our expert advice algorithm, we additionally improve the best-known high-probability bound for the multi-play setting by O(√(m)). Our results are guaranteed to hold in an individual sequence manner since we have no statistical assumption on the bandit arm gains. Through an extensive set of experiments involving synthetic and real data, we demonstrate significant performance gains achieved by the proposed algorithm with respect to the state-of-the-art algorithms.Item Open Access Online anomaly detection with minimax optimal density estimation in nonstationary environments(Institute of Electrical and Electronics Engineers, 2018) Gokcesu, K.; Kozat, Süleyman SerdarWe introduce a truly online anomaly detection algorithm that sequentially processes data to detect anomalies in time series. In anomaly detection, while the anomalous data are arbitrary, the normal data have similarities and generally conforms to a particular model. However, the particular model that generates the normal data is generally unknown (even nonstationary) and needs to be learned sequentially. Therefore, a two stage approach is needed, where in the first stage, we construct a probability density function to model the normal data in the time series. Then, in the second stage, we threshold the density estimation of the newly observed data to detect anomalies. We approach this problem from an information theoretic perspective and propose minimax optimal schemes for both stages to create an optimal anomaly detection algorithm in a strong deterministic sense. To this end, for the first stage, we introduce a completely online density estimation algorithm that is minimax optimal with respect to the log-loss and achieves Merhav's lower bound for general nonstationary exponential-family of distributions without any assumptions on the observation sequence. For the second stage, we propose a threshold selection scheme that is minimax optimal (with logarithmic performance bounds) against the best threshold chosen in hindsight with respect to the surrogate logistic loss. Apart from the regret bounds, through synthetic and real life experiments, we demonstrate substantial performance gains with respect to the state-of-the-art density estimation based anomaly detection algorithms in the literature.Item Open Access An online minimax optimal algorithm for adversarial multiarmed bandit problem(Institute of Electrical and Electronics Engineers, 2018) Gökçesu, Kaan; Kozat, Süleyman SerdarWe investigate the adversarial multiarmed bandit problem and introduce an online algorithm that asymptotically achieves the performance of the best switching bandit arm selection strategy. Our algorithms are truly online such that we do not use the game length or the number of switches of the best arm selection strategy in their constructions. Our results are guaranteed to hold in an individual sequence manner, since we have no statistical assumptions on the bandit arm losses. Our regret bounds, i.e., our performance bounds with respect to the best bandit arm selection strategy, are minimax optimal up to logarithmic terms. We achieve the minimax optimal regret with computational complexity only log-linear in the game length. Thus, our algorithms can be efficiently used in applications involving big data. Through an extensive set of experiments involving synthetic and real data, we demonstrate significant performance gains achieved by the proposed algorithm with respect to the state-of-the-art switching bandit algorithms. We also introduce a general efficiently implementable bandit arm selection framework, which can be adapted to various applications.