Table 2 Examples of test function η _t (z,d) for different update rules (recall that \(d=d_{t}(z)=|q_{t}(z|\mathcal {S}_{t})-\pi (z)|\))

Rule 1

η _t (d)=1−e^−βd

Rule 2

\(\eta _{t}(d)=\left \{ \begin {array}{ll} 1, \text {if} ~d> \varepsilon _{t},\\ 0, \text {if}~ d\leq \varepsilon _{t} \end {array} \right.\)

Rule 3

\(\eta _{t}(z,d)=\frac {d}{\max \{\pi (z),q_{t}(z|\mathcal {S}_{t})\}}\)