Before revision:  We also introduce the stochastic k-secretary -- effectively reducing online blackbox  attacks to a k-secretary problem under noise -- and prove theoretical bounds on the competitive ratios of any online algorithms adapted to this setting.
After revision:  We also introduce the stochastic k-secretary -- effectively reducing online blackbox transfer attacks to a k-secretary problem under noise -- and prove theoretical bounds on the competitive ratios of any online algorithms adapted to this setting.