# %% [markdown]
# ## Describe the problem
# In this example, we look to find the minimum value of the two-dimensional Branin function over the hypercube $[0, 1]^2$. We can represent the search space using a `Box`, and plot contours of the Branin over this space.
#
#
# %%
from trieste.objectives import scaled_branin, SCALED_BRANIN_MINIMUM
from trieste.objectives.utils import mk_observer
from util.plotting_plotly import plot_function_plotly
from trieste.space import Box
search_space = Box([0, 0], [1, 1])
fig = plot_function_plotly(scaled_branin,
search_space.lower,
search_space.upper,
grid_density=20)
fig.update_layout(height=400, width=400)
fig.show()
# %% [markdown]
# ## Sample the observer over the search space
#
# Sometimes we don't have direct access to the objective function. We only have an observer that indirectly observes it. In _Trieste_, an observer can output a number of datasets. In our case, we only have one dataset, the objective. We can convert a function with `branin`'s signature to a single-output observer using `mk_observer`.
#
# The optimization procedure will benefit from having some starting data from the objective function to base its search on. We sample a five point space-filling design from the search space and evaluate it with the observer. For continuous search spaces, Trieste supports random, Sobol and Halton initial designs.
# %%
import trieste
observer = trieste.objectives.utils.mk_observer(scaled_branin)
# %% [markdown]
# As mentioned, we'll search over the hypercube $[0, 1]^2$ ...
# %%
search_space = trieste.space.Box([0, 0], [1, 1])
# %% [markdown]
# ... where the `masked_branin` now looks as follows. The white area in the centre shows the failure
# region.
# %%
from util.plotting_plotly import plot_function_plotly
fig = plot_function_plotly(masked_branin,
search_space.lower,
search_space.upper,
grid_density=70)
fig.update_layout(height=400, width=400)
fig.show()
# %% [markdown]
# ## Define the data sets
#
# We'll work with two data sets
#
# - one containing only those query_points and observations where the observations are finite.
# We'll label this with `OBJECTIVE`.
# - the other containing all the query points, but whose observations indicate if evaluating the
# observer failed at that point, using `1` if the evaluation failed, else `0`. We'll label this
# with `FAILURE`.
#
MICHALEWICZ_2_MINIMUM,
MICHALEWICZ_5_MINIMUM,
MICHALEWICZ_2_SEARCH_SPACE,
MICHALEWICZ_5_SEARCH_SPACE
)
from trieste.objectives.utils import mk_observer
from util.plotting_plotly import plot_function_plotly
function = michalewicz_2
F_MINIMIZER = MICHALEWICZ_2_MINIMUM
search_space = MICHALEWICZ_2_SEARCH_SPACE
fig = plot_function_plotly(
function,
search_space.lower,
search_space.upper,
grid_density=100
)
fig.update_layout(height=800, width=800)
fig.show()
# %% [markdown]
# ## Sample the observer over the search space
#
# We set up the observer as usual, using Sobol sampling to sample the initial points.
# %%
import trieste
observer = mk_observer(function)
# As mentioned, we'll search over the hypercube $[0, 1]^2$ ... # %% mins = [0.0, 0.0] maxs = [1.0, 1.0] lower_bound = tf.constant(mins, gpflow.default_float()) upper_bound = tf.constant(maxs, gpflow.default_float()) search_space = trieste.space.Box(lower_bound, upper_bound) # %% [markdown] # ... where the `masked_branin` now looks as follows. The white area in the centre shows the failure # region. # %% fig = plot_function_plotly(masked_branin, mins, maxs, grid_density=70) fig.update_layout(height=400, width=400) fig.show() # %% [markdown] # ## Define the data sets # # We'll work with two data sets # # - one containing only those query_points and observations where the observations are finite. # We'll label this with `OBJECTIVE`. # - the other containing all the query points, but whose observations indicate if evaluating the # observer failed at that point, using `1` if the evaluation failed, else `0`. We'll label this # with `FAILURE`. # # Let's define an observer that outputs the data in these formats.
from util.plotting import plot_function_2d, plot_bo_points, plot_regret # %% gpflow.config.set_default_float(np.float64) np.random.seed(1793) tf.random.set_seed(1793) # %% [markdown] # ## Describe the problem # In this example, we look to find the minimum value of the two-dimensional Branin function over the hypercube $[0, 1]^2$. We can plot contours of the Branin over this space. # %% mins = [0.0, 0.0] maxs = [1.0, 1.0] fig = plot_function_plotly(branin, mins, maxs, grid_density=20) fig.update_layout(height=400, width=400) fig.show() # %% [markdown] # ## Sample the observer over the search space # # Sometimes we don't have direct access to the objective function. We only have an observer that indirectly observes it. In _Trieste_, the observer outputs a number of datasets, each of which must be labelled so the optimization process knows which is which. In our case, we only have one dataset, the objective. We'll use _Trieste_'s default label for single-model setups, `OBJECTIVE`. We can convert a function with `branin`'s signature to a single-output observer using `mk_observer`. # # The optimization procedure will benefit from having some starting data from the objective function to base its search on. We sample five points from the search space and evaluate them on the observer. We can represent the search space using a `Box`. # %% observer = mk_observer(branin, OBJECTIVE) lower_bound = tf.cast(mins, gpflow.default_float()) upper_bound = tf.cast(maxs, gpflow.default_float()) search_space = trieste.space.Box(lower_bound, upper_bound)
