In this study, we consider the infinitely many-armed bandit problems in a rested rotting setting, where the mean reward of an arm may decrease with each pull, while otherwise, it remains unchanged. We explore two scenarios regarding the rotting of rewards: one in which the cumulative amount of rotting is bounded by $V_T$, referred to as the slow-rotting case, and the other in which the cumulative number of rotting instances is bounded by $S_T$, referred to as the abrupt-rotting case. To address the challenge posed by rotting rewards, we introduce an algorithm that utilizes UCB with an adaptive sliding window, designed to manage the bias and variance trade-off arising due to rotting rewards. Our proposed algorithm achieves tight regret bounds for both slow and abrupt rotting scenarios. Lastly, we demonstrate the performance of our algorithm using numerical experiments.

We study contextual linear bandit problems under feature uncertainty; they are noisy with missing entries. To address the challenges of the noise, we analyze Bayesian oracles given observed noisy features. Our Bayesian analysis finds that the optimal hypothesis can be far from the underlying realizability function, depending on the noise characteristics, which are highly non-intuitive and do not occur for classical noiseless setups. This implies that classical approaches cannot guarantee a non-trivial regret bound. Therefore, we propose an algorithm that aims at the Bayesian oracle from observed information under this model, achieving $\tilde{O}(d\sqrt{T})$ regret bound when there is a large number of arms. We demonstrate the proposed algorithm using synthetic and real-world datasets.

We consider the infinitely many-armed bandit problem with rotting rewards, where the mean reward of an arm decreases at each pull of the arm according to an arbitrary trend with maximum rotting rate $\varrho=o(1)$. We show that this learning problem has an $\Omega(\max\{\varrho^{1/3}T, \sqrt{T}\})$ worst-case regret lower bound where $T$ is the time horizon. We show that a matching upper bound $\tilde{O}(\max\{\varrho^{1/3}T, \sqrt{T}\})$, up to a poly-logarithmic factor, can be achieved by an algorithm that uses a UCB index for each arm and a threshold value to decide whether to continue pulling an arm or remove the arm from further consideration, when the algorithm knows the value of the maximum rotting rate $\varrho$. We also show that an $\tilde{O}(\max\{\varrho^{1/3}T, T^{3/4}\})$ regret upper bound can be achieved by an algorithm that does not know the value of $\varrho$, by using an adaptive UCB index along with an adaptive threshold value.

The large volume of scientific publications is likely to have hidden knowledge that can be used for suggesting new research topics. We propose an automatic method that is helpful for generating research hypotheses in the field of physics using the massive number of physics journal publications. We convert the text data of titles and abstract sections in publications to a bipartite graph, extracting words of physical matter composed of chemical elements and extracting related keywords in the articles. The proposed method predicts the formation of new links between matter and keyword nodes based on collaborative filtering and matter popularity. The formation of links represents research hypotheses, as it suggests the new possible relationships between physical matter and keywords for physical properties or phenomena. The suggested method has better performance than existing methods for link prediction in the entire bipartite graph and the subgraph that contains only a specific keyword, such as `antiferromagnetism' or `superconductivity.' Our suggested concept for generating research hypotheses can be easily extended to various other research topics or industrial topics using patent literature.