A cost–based analysis for risk–averse explore–then–commit finite–time bandits

In this article, a multi–armed bandit problem is studied in an explore–then–commit setting where the cost of pulling arm experimentation (exploration) phase may not be negligible. Identifying best after pure to exploit it once or for given finite number times goal problem. Applications are prevalent personalized health-care and financial investments frequency exploitation limited. setting, we observe that with highest expected reward necessarily most desirable objective exploitation. Alternatively, advocate idea risk aversion, compete against risk–return trade–off. Additionally, trade–off between regret should considered case arms exploration incurs cost. considered, propose class hyper–parameter–free risk–averse algorithms, called OTE/FTE–MAB (One/Finite–Time Exploitation Multi–Armed Bandit), whose objectives select probable single finite–time exploitations. To analyze these define new notion our interest. We provide upper bound order ln (1∈r) minimum experiments done guarantee er regret. As compared existing algorithms do rely on hyper–parameters, resulting more robust behavior practice. has cost, c–OTE–MAB algorithm two–armed bandits addresses cost–regret trade–off, corresponding exploration–exploitation by minimizing linear combination cost– function, using hyper–parameter. This determines estimation optimal explorations value approaches function at rate 1ne associated confidence level, ne each arm.