Stochastic rising rested bandit (SRRB) is a setting where the arms' expected rewards increase as they are pulled. It models scenarios in which the performances of the different options grow as an effect of an underlying learning process (e.g., online model selection). Even if the bandit literature provides specifically crafted algorithms based on upper-confidence bounds for such a setting, no study about Thompson sampling TS-like algorithms has been performed so far. The strong regularity of the expected rewards in the SRRB setting suggests that specific instances may be tackled effectively using adapted and sliding-window TS approaches. This work provides novel regret analyses for such algorithms in SRRBs, highlighting the challenges and providing new technical tools of independent interest. Our results allow us to identify under which assumptions TS-like algorithms succeed in achieving sublinear regret and which properties of the environment govern the complexity of the regret minimization problem when approached with TS. Furthermore, we provide a regret lower bound based on a complexity index we introduce. Finally, we conduct numerical simulations comparing TS-like algorithms with state-of-the-art approaches for SRRBs in synthetic and real-world settings.

This paper contains analysis of concept of a class within different object-oriented knowledge representation models. The main attention is paid to structure of the class and its efficiency in the context of data storage, using object-relational mapping. The main achievement of the paper is extension of concept of homogeneous class of objects by introducing concepts of single-core and multi-core inhomogeneous classes of objects, which allow simultaneous defining of a few different types within one class of objects, avoiding duplication of properties and methods in representation of types, decreasing sizes of program codes and providing more efficient information storage in the databases. In addition, the paper contains results of experiment, which show that data storage in relational database, using proposed extensions of the class, in some cases is more efficient in contrast to usage of homogeneous classes of objects.