Continue Bayesian optimization from completed experiments

Use this function when initial experiments and their responses are already available. It fits a MaGP model, selects a new input with expected improvement, evaluates FUN, and adds the new result to the data. This process repeats for at most n_iter new evaluations.

Usage

magp_bayes_optimize(
  FUN,
  X,
  y = NULL,
  model = c("2d", "full"),
  direction = c("minimize", "maximize"),
  n_iter = 10L,
  xi = 0,
  stop_ei = 0,
  stop_patience = 3L,
  seed = NULL,
  fit_control = list(),
  acquisition_control = list(),
  objective_args = list(),
  verbose = TRUE
)

Arguments

FUN: Function that evaluates one experiment. Its argument names must match the columns of X. It must return one finite number, or a list with one finite number named Score or Value.
X: Initial inputs as a numeric matrix or data frame. The first half of the columns contains quantitative values. The second half contains the sequence positions, with each row forming a permutation of 1:q. X may also contain a response column named y.
y: Numeric responses for the rows of X. Leave this as NULL when X contains a column named y.
model: MaGP mapping to fit. Use "2d" for the compact mapping or "full" for the full mapping.
direction: Use "minimize" when smaller responses are better and "maximize" when larger responses are better.
n_iter: Maximum number of new experiments to evaluate.
xi: Nonnegative expected-improvement offset. The default, 0, uses the current best response as the improvement target. Larger values require a candidate to exceed that target by more.
stop_ei: Nonnegative early-stopping threshold for expected improvement.
stop_patience: Number of consecutive selected points with expected improvement less than or equal to stop_ei required to stop early.
seed: Optional nonnegative whole-number seed for reproducible model starts and acquisition searches. The caller's random-number state is preserved.
fit_control: Optional named list passed to magp2d_fit() or magpfull_fit(). Common choices include tau, maxeval, n_starts, and workers. This function supplies X, y, and seed.
acquisition_control: Optional named list passed to magp_next_point(). Common choices include lower, upper, sequences, n_starts, workers, and maxit. This function supplies the fitted model, direction, xi, current best response, and seed.
objective_args: Optional named list of fixed arguments passed to FUN in addition to the input columns.
verbose: If TRUE, print the observed response and expected improvement after each new evaluation.

Value

An object of class magp_bayes_opt. The final fitted model includes every completed evaluation.

How the loop works

The initial rows of X are treated as completed experiments and are not evaluated again. Each iteration performs four steps:

fit the selected MaGP model to all results collected so far;
use magp_next_point() to select an unobserved input;
call FUN at that input; and
add the response and refit the model.

FUN receives one named argument for each input column. For columns A, B, a, and b, for example, the call is equivalent to FUN(A = ..., B = ..., a = ..., b = ...).

Reading the result

The returned object contains:

call: the function call;
best_point: the input row with the best observed response;
best_value: the best observed response;
best_index: the row number of the best result in X and y;
history: the initial and newly evaluated rows in evaluation order;
model: the final fitted MaGP model;
X and y: all inputs and responses used by the final model;
acquisitions: details from each call to magp_next_point();
mapping and direction: the model and optimization direction;
iterations_requested and iterations_completed: the requested and completed numbers of new evaluations;
stop_reason: why the loop ended;
xi, stop_ei, and stop_patience: the acquisition and stopping settings; and
fit_control and acquisition_control: the control lists used in the search.

References

Jones, D. R., Schonlau, M., and Welch, W. J. (1998). Efficient Global Optimization of Expensive Black-Box Functions. Journal of Global Optimization, 13, 455-492. doi:10.1023/A:1008306431147 .

Examples

# \donttest{
design <- magp_initial_design(n = 6, q = 3, seed = 1)
objective <- function(quantity_1, quantity_2, quantity_3,
                      sequence_1, sequence_2, sequence_3) {
  quantities <- c(quantity_1, quantity_2, quantity_3)
  positions <- c(sequence_1, sequence_2, sequence_3)
  -sum((quantities - c(0.2, 0.6, 0.8))^2) -
    0.02 * sum((positions - c(1, 3, 2))^2)
}
initial_y <- apply(design$design, 1L, function(row) {
  do.call(objective, as.list(row))
})
result <- magp_bayes_optimize(
  FUN = objective,
  X = design$design,
  y = initial_y,
  direction = "maximize",
  n_iter = 1,
  seed = 2,
  fit_control = list(maxeval = 100),
  acquisition_control = list(n_starts = 2, maxit = 20),
  verbose = FALSE
)
result$best_point
#> quantity_1 quantity_2 quantity_3 sequence_1 sequence_2 sequence_3 
#> 0.08333333 0.58333333 0.91666667 1.00000000 2.00000000 3.00000000 
result$best_value
#> [1] -0.0675
result$history
#>   Iteration Initial quantity_1 quantity_2 quantity_3 sequence_1 sequence_2
#> 1         0    TRUE 0.08333333 0.58333333 0.91666667          1          2
#> 2         0    TRUE 0.75000000 0.08333333 0.75000000          3          1
#> 3         0    TRUE 0.41666667 0.75000000 0.08333333          2          1
#> 4         0    TRUE 0.58333333 0.91666667 0.58333333          1          3
#> 5         0    TRUE 0.25000000 0.25000000 0.41666667          2          3
#> 6         0    TRUE 0.91666667 0.41666667 0.25000000          3          2
#> 7         1   FALSE 0.00000000 1.00000000 1.00000000          2          3
#>   sequence_3      Value ExpectedImprovement PredictedMean
#> 1          3 -0.0675000                  NA            NA
#> 2          2 -0.7319444                  NA            NA
#> 3          3 -0.7030556                  NA            NA
#> 4          2 -0.2941667                  NA            NA
#> 5          1 -0.3119444                  NA            NA
#> 6          1 -0.9697222                  NA            NA
#> 7          1 -0.2800000            1.793363    -0.4690127
#>   PredictedStandardError
#> 1                     NA
#> 2                     NA
#> 3                     NA
#> 4                     NA
#> 5                     NA
#> 6                     NA
#> 7               4.982345
# }