Pure exploration in multi-armed bandits with low rank structure using oblivious sampler
This work addresses sample efficiency in bandit problems for scenarios like clinical trials or recommendation systems, but it is incremental as it builds on existing low-rank bandit frameworks.
The paper tackles pure exploration in multi-armed bandits with low-rank reward structures by proposing an oblivious sampler for a separated setting without feedback, achieving a regret bound of O(d√((ln N)/n)) and showing a lower bound with an O(√(ln N)) gap.
In this paper, we consider the low rank structure of the reward sequence of the pure exploration problems. Firstly, we propose the separated setting in pure exploration problem, where the exploration strategy cannot receive the feedback of its explorations. Due to this separation, it requires that the exploration strategy to sample the arms obliviously. By involving the kernel information of the reward vectors, we provide efficient algorithms for both time-varying and fixed cases with regret bound $O(d\sqrt{(\ln N)/n})$. Then, we show the lower bound to the pure exploration in multi-armed bandits with low rank sequence. There is an $O(\sqrt{\ln N})$ gap between our upper bound and the lower bound.