open access

https://hdl.handle.net/2115/80332

A bad arm existence checking problem: How to utilize asymmetric problem structure?

英語

Best arm identification

2019-10-30

Springer

Machine learning

109

327-372

We study a bad arm existence checking problem in a stochastic K-armed bandit setting, in which a player's task is to judge whether a positive arm exists or all the arms are negative among given K arms by drawing as small number of arms as possible. Here, an arm is positive if its expected loss suffered by drawing the arm is at least a given threshold theta(U), and it is negative if that is less than another given threshold theta(L) (<= theta(U)). This problem is a formalization of diagnosis of disease or machine failure. An interesting structure of this problem is the asymmetry of positive and negative arms' roles; finding one positive arm is enough to judge positive existence while all the arms must be discriminated as negative to judge whole negativity. In the case with Delta = theta(U) - theta(L) > 0, we propose elimination algorithms with arm selection policy (policy to determine the next arm to draw) and decision condition (condition to conclude positive arm's existence or the drawn arm's negativity) utilizing this asymmetric problem structure and prove its effectiveness theoretically and empirically.

学術雑誌論文

Accepted Manuscript

This is a post-peer-review, pre-copyedit version of an article published in Machine learning. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10994-019-05854-7

0885-6125

1573-0565

AA10692766