Browsing by Subject "Individual sequence manner"

Now showing 1 - 3 of 3

Open Access
Estimating distributions varying in time in a universal manner
(IEEE, 2017) Gökçesu, Kaan; Manış, Eren; Kurt, Ali Emirhan; Yar, Ersin
We investigate the estimation of distributions with time-varying parameters. We introduce an algorithm that achieves the optimal negative likelihood performance against the true probability distribution. We achieve this optimum regret performance without any knowledge about the total change of the parameters of true distribution. Our results are guaranteed to hold in an individual sequence manner such that we have no assumptions on the underlying sequences. Apart from the regret bounds, through synthetic and real life experiments, we demonstrate substantial performance gains with respect to the state-of-the-art probability density estimation algorithms in the literature.
Open Access
Minimax optimal algorithms for adversarial bandit problem with multiple plays
(IEEE, 2019) Vural, Nuri Mert; Gökçesu, Hakan; Gökçesu, K.; Kozat, Süleyman Serdar
We 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.
Open Access
An online minimax optimal algorithm for adversarial multiarmed bandit problem
(Institute of Electrical and Electronics Engineers, 2018) Gökçesu, Kaan; Kozat, Süleyman Serdar
We 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.