Algorithm 1 Open in new tab Standard...

Algorithm 1

Standard Optimization Algorithm

Require: r patient responses at each of c initial dose combinations,

D = {(d_{i}, y_{i})}_{i = 1}^{n_{0}}

n \leftarrow n_{0} = r \times c

1_{STOP} \leftarrow FALSE

3: Obtain

p (f ∣ D, \tilde{d})

and

p (d_{opt} ∣ D)

using fitted GP ⊳ Obtain posteriors

d^{*} \leftarrow {argmin}_{\tilde{d}} μ (\tilde{d}) + σ (\tilde{d})

⊳ Obtain effective best point

f^{*} \leftarrow μ (d^{*})

⊳ Obtain best value of f

6: Calculate

α_{AEI} (\tilde{d} ∣ D)

for

\tilde{d} \in D

⊳ Compute AEI

7: while

n < N

and

1_{STOP} = FALSE

d^{(c + 1)} \leftarrow {argmax}_{\tilde{d} \in D} α_{AEI} (\tilde{d} ∣ D)

⊳ Obtain next dose

9: for

i = 1, \dots, r

10: Evaluate

y_{i}

d^{(c + 1)}

⊳ Observe outcomes

11: end for

12:

n \leftarrow n + r

⁠;

c \leftarrow c + 1

⊳ Update

n, c

13:

D \leftarrow D \cup {(d_{i}^{(c + 1)}, y_{i})}_{i = 1}^{r}

⊳ Update data

14: Obtain

p (f ∣ D, \tilde{d})

and

p (d_{opt} ∣ D)

using fitted GP ⊳ Obtain posteriors

15:

d^{*} \leftarrow {argmin}_{\tilde{d}} μ (\tilde{d}) + σ (\tilde{d})

⊳ Obtain effective best point

16:

f^{*} \leftarrow μ (d^{*})

⊳ Obtain best value of f

17: Calculate

α_{AEI} (\tilde{d} ∣ D)

for

\tilde{d} \in D

⊳ Compute AEI

18: Update

1_{STOP}

using (4) ⊳ Update stopping rule

19: end while