def test_identity_mc_multi_output_objective(self):
objective = IdentityMCMultiOutputObjective()
with self.assertRaises(BotorchTensorDimensionError):
IdentityMCMultiOutputObjective(outcomes=[0])
# test negative outcome without specifying num_outcomes
with self.assertRaises(BotorchError):
IdentityMCMultiOutputObjective(outcomes=[0, -1])
for batch_shape, m, dtype in itertools.product(
([], [3]), (2, 3), (torch.float, torch.double)):
samples = torch.rand(*batch_shape,
2,
m,
device=self.device,
dtype=dtype)
self.assertTrue(torch.equal(objective(samples), samples))
def __init__(
self,
model: Model,
sampler: Optional[MCSampler] = None,
objective: Optional[MCMultiOutputObjective] = None,
X_pending: Optional[Tensor] = None,
) -> None:
r"""Constructor for the MCAcquisitionFunction base class.
Args:
model: A fitted model.
sampler: The sampler used to draw base samples. Defaults to
`SobolQMCNormalSampler(num_samples=128, collapse_batch_dims=True)`.
objective: The MCMultiOutputObjective under which the samples are
evaluated. Defaults to `IdentityMultiOutputObjective()`.
X_pending: A `m x d`-dim Tensor of `m` design points that have
points that have been submitted for function evaluation
but have not yet been evaluated.
"""
super().__init__(model=model)
if sampler is None:
sampler = SobolQMCNormalSampler(num_samples=128,
collapse_batch_dims=True)
self.add_module("sampler", sampler)
if objective is None:
objective = IdentityMCMultiOutputObjective()
elif not isinstance(objective, MCMultiOutputObjective):
raise UnsupportedError(
"Only objectives of type MCMultiOutputObjective are supported for "
"Multi-Objective MC acquisition functions.")
self.add_module("objective", objective)
self.X_pending = None
if X_pending is not None:
self.set_X_pending(X_pending)
def test_identity_mc_multi_output_objective(self):
objective = IdentityMCMultiOutputObjective()
for batch_shape, m, dtype in itertools.product(
([], [3]), (2, 3), (torch.float, torch.double)):
samples = torch.rand(*batch_shape,
2,
m,
device=self.device,
dtype=dtype)
self.assertTrue(torch.equal(objective(samples), samples))
def construct_inputs_qEHVI(
model: Model,
training_data: TrainingData,
objective_thresholds: Tensor,
objective: Optional[AcquisitionObjective] = None,
**kwargs: Any,
) -> Dict[str, Any]:
r"""Construct kwargs for `qExpectedHypervolumeImprovement` constructor."""
X_observed = training_data.X
# compute posterior mean (for ref point computation ref pareto frontier)
with torch.no_grad():
Y_pmean = model.posterior(X_observed).mean
outcome_constraints = kwargs.pop("outcome_constraints", None)
# For HV-based acquisition functions we pass the constraint transform directly
if outcome_constraints is None:
cons_tfs = None
else:
cons_tfs = get_outcome_constraint_transforms(outcome_constraints)
# Adjust `Y_pmean` to contrain feasible points only.
feas = torch.stack([c(Y_pmean) <= 0 for c in cons_tfs], dim=-1).all(dim=-1)
Y_pmean = Y_pmean[feas]
if objective is None:
objective = IdentityMCMultiOutputObjective()
ehvi_kwargs = construct_inputs_EHVI(
model=model,
training_data=training_data,
objective_thresholds=objective_thresholds,
objective=objective,
# Pass `Y_pmean` that accounts for constraints to `construct_inputs_EHVI`
# to ensure that correct non-dominated partitioning is produced.
Y_pmean=Y_pmean,
**kwargs,
)
sampler = kwargs.get("sampler")
if sampler is None:
sampler = _get_sampler(
mc_samples=kwargs.get("mc_samples", 128), qmc=kwargs.get("qmc", True)
)
add_qehvi_kwargs = {
"sampler": sampler,
"X_pending": kwargs.get("X_pending"),
"constraints": cons_tfs,
"eta": kwargs.get("eta", 1e-3),
}
return {**ehvi_kwargs, **add_qehvi_kwargs}
def __init__(
self,
model: Model,
sampler: Optional[MCSampler] = None,
objective: Optional[MCMultiOutputObjective] = None,
constraints: Optional[List[Callable[[Tensor], Tensor]]] = None,
X_pending: Optional[Tensor] = None,
) -> None:
r"""Constructor for the MCAcquisitionFunction base class.
Args:
model: A fitted model.
sampler: The sampler used to draw base samples. Defaults to
`SobolQMCNormalSampler(num_samples=128, collapse_batch_dims=True)`.
objective: The MCMultiOutputObjective under which the samples are
evaluated. Defaults to `IdentityMultiOutputObjective()`.
constraints: A list of callables, each mapping a Tensor of dimension
`sample_shape x batch-shape x q x m` to a Tensor of dimension
`sample_shape x batch-shape x q`, where negative values imply
feasibility.
X_pending: A `m x d`-dim Tensor of `m` design points that have
points that have been submitted for function evaluation
but have not yet been evaluated.
"""
super().__init__(model=model)
if sampler is None:
sampler = SobolQMCNormalSampler(num_samples=128,
collapse_batch_dims=True)
self.add_module("sampler", sampler)
if objective is None:
objective = IdentityMCMultiOutputObjective()
elif not isinstance(objective, MCMultiOutputObjective):
raise UnsupportedError(
"Only objectives of type MCMultiOutputObjective are supported for "
"Multi-Objective MC acquisition functions.")
if (hasattr(model, "input_transform")
and isinstance(model.input_transform, InputPerturbation)
and constraints is not None):
raise UnsupportedError(
"Constraints are not supported with input perturbations, due to"
"sample q-batch shape being different than that of the inputs."
"Use a composite objective that applies feasibility weighting to"
"samples before calculating the risk measure.")
self.add_module("objective", objective)
self.constraints = constraints
self.X_pending = None
if X_pending is not None:
self.set_X_pending(X_pending)
def test_init(self):
mm = MockModel(MockPosterior(mean=torch.rand(2, 1)))
# test default init
acqf = DummyMultiObjectiveAnalyticAcquisitionFunction(model=mm)
self.assertIsInstance(acqf.objective,
IdentityAnalyticMultiOutputObjective)
# test custom init
objective = DummyAnalyticMultiOutputObjective()
acqf = DummyMultiObjectiveAnalyticAcquisitionFunction(
model=mm, objective=objective)
self.assertEqual(acqf.objective, objective)
# test unsupported objective
with self.assertRaises(UnsupportedError):
DummyMultiObjectiveAnalyticAcquisitionFunction(
model=mm, objective=IdentityMCMultiOutputObjective())
acqf = DummyMultiObjectiveAnalyticAcquisitionFunction(model=mm)
# test set_X_pending
with self.assertRaises(UnsupportedError):
acqf.set_X_pending()
def construct_inputs_qNEHVI(
model: Model,
training_data: TrainingData,
objective_thresholds: Tensor,
objective: Optional[AcquisitionObjective] = None,
**kwargs: Any,
) -> Dict[str, Any]:
r"""Construct kwargs for `qNoisyExpectedHypervolumeImprovement` constructor."""
# This selects the objectives (a subset of the outcomes) and set each
# objective threhsold to have the proper optimization direction.
if objective is None:
objective = IdentityMCMultiOutputObjective()
outcome_constraints = kwargs.pop("outcome_constraints", None)
if outcome_constraints is None:
cons_tfs = None
else:
cons_tfs = get_outcome_constraint_transforms(outcome_constraints)
sampler = kwargs.get("sampler")
if sampler is None:
sampler = _get_sampler(
mc_samples=kwargs.get("mc_samples", 128), qmc=kwargs.get("qmc", True)
)
return {
"model": model,
"ref_point": objective(objective_thresholds),
"X_baseline": kwargs.get("X_baseline", training_data.X),
"sampler": sampler,
"objective": objective,
"constraints": cons_tfs,
"X_pending": kwargs.get("X_pending"),
"eta": kwargs.get("eta", 1e-3),
"prune_baseline": kwargs.get("prune_baseline", True),
"alpha": kwargs.get("alpha", 0.0),
"cache_pending": kwargs.get("cache_pending", True),
"max_iep": kwargs.get("max_iep", 0),
"incremental_nehvi": kwargs.get("incremental_nehvi", True),
}
def test_q_expected_hypervolume_improvement(self):
tkwargs = {"device": self.device}
for dtype in (torch.float, torch.double):
ref_point = [0.0, 0.0]
tkwargs["dtype"] = dtype
pareto_Y = torch.tensor(
[[4.0, 5.0], [5.0, 5.0], [8.5, 3.5], [8.5, 3.0], [9.0, 1.0]],
**tkwargs)
partitioning = NondominatedPartitioning(num_outcomes=2)
# the event shape is `b x q x m` = 1 x 1 x 2
samples = torch.zeros(1, 1, 2, **tkwargs)
mm = MockModel(MockPosterior(samples=samples))
# test error if there is not pareto_Y initialized in partitioning
with self.assertRaises(BotorchError):
qExpectedHypervolumeImprovement(model=mm,
ref_point=ref_point,
partitioning=partitioning)
partitioning.update(Y=pareto_Y)
# test error if ref point has wrong shape
with self.assertRaises(ValueError):
qExpectedHypervolumeImprovement(model=mm,
ref_point=ref_point[:1],
partitioning=partitioning)
X = torch.zeros(1, 1, **tkwargs)
# basic test
sampler = IIDNormalSampler(num_samples=1)
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
res = acqf(X)
self.assertEqual(res.item(), 0.0)
# check ref point
self.assertTrue(
torch.equal(acqf.ref_point, torch.tensor(ref_point,
**tkwargs)))
# check cached indices
self.assertTrue(hasattr(acqf, "q_subset_indices"))
self.assertIn("q_choose_1", acqf.q_subset_indices)
self.assertTrue(
torch.equal(
acqf.q_subset_indices["q_choose_1"],
torch.tensor([[0]], device=self.device),
))
# test q=2
X2 = torch.zeros(2, 1, **tkwargs)
samples2 = torch.zeros(1, 2, 2, **tkwargs)
mm2 = MockModel(MockPosterior(samples=samples2))
acqf.model = mm2
res = acqf(X2)
self.assertEqual(res.item(), 0.0)
# check cached indices
self.assertTrue(hasattr(acqf, "q_subset_indices"))
self.assertIn("q_choose_1", acqf.q_subset_indices)
self.assertTrue(
torch.equal(
acqf.q_subset_indices["q_choose_1"],
torch.tensor([[0], [1]], device=self.device),
))
self.assertIn("q_choose_2", acqf.q_subset_indices)
self.assertTrue(
torch.equal(
acqf.q_subset_indices["q_choose_2"],
torch.tensor([[0, 1]], device=self.device),
))
self.assertNotIn("q_choose_3", acqf.q_subset_indices)
# now back to 1 and sure all caches were cleared
acqf.model = mm
res = acqf(X)
self.assertNotIn("q_choose_2", acqf.q_subset_indices)
self.assertIn("q_choose_1", acqf.q_subset_indices)
self.assertTrue(
torch.equal(
acqf.q_subset_indices["q_choose_1"],
torch.tensor([[0]], device=self.device),
))
X = torch.zeros(1, 1, **tkwargs)
samples = torch.zeros(1, 1, 2, **tkwargs)
mm = MockModel(MockPosterior(samples=samples))
# basic test, no resample
sampler = IIDNormalSampler(num_samples=2, seed=12345)
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
res = acqf(X)
self.assertEqual(res.item(), 0.0)
self.assertEqual(acqf.sampler.base_samples.shape,
torch.Size([2, 1, 1, 2]))
bs = acqf.sampler.base_samples.clone()
res = acqf(X)
self.assertTrue(torch.equal(acqf.sampler.base_samples, bs))
# basic test, qmc, no resample
sampler = SobolQMCNormalSampler(num_samples=2)
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
res = acqf(X)
self.assertEqual(res.item(), 0.0)
self.assertEqual(acqf.sampler.base_samples.shape,
torch.Size([2, 1, 1, 2]))
bs = acqf.sampler.base_samples.clone()
acqf(X)
self.assertTrue(torch.equal(acqf.sampler.base_samples, bs))
# basic test, qmc, resample
sampler = SobolQMCNormalSampler(num_samples=2, resample=True)
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
res = acqf(X)
self.assertEqual(res.item(), 0.0)
self.assertEqual(acqf.sampler.base_samples.shape,
torch.Size([2, 1, 1, 2]))
bs = acqf.sampler.base_samples.clone()
acqf(X)
self.assertFalse(torch.equal(acqf.sampler.base_samples, bs))
# basic test for X_pending and warning
acqf.set_X_pending()
self.assertIsNone(acqf.X_pending)
acqf.set_X_pending(None)
self.assertIsNone(acqf.X_pending)
acqf.set_X_pending(X)
self.assertEqual(acqf.X_pending, X)
res = acqf(X)
X2 = torch.zeros(1, 1, 1, requires_grad=True, **tkwargs)
with warnings.catch_warnings(
record=True) as ws, settings.debug(True):
acqf.set_X_pending(X2)
self.assertEqual(acqf.X_pending, X2)
self.assertEqual(len(ws), 1)
self.assertTrue(issubclass(ws[-1].category, BotorchWarning))
# test objective
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
objective=IdentityMCMultiOutputObjective(),
)
res = acqf(X)
self.assertEqual(res.item(), 0.0)
# Test that the hypervolume improvement is correct for given sample
# test q = 1
X = torch.zeros(1, 1, **tkwargs)
# basic test
samples = torch.tensor([[[6.5, 4.5]]], **tkwargs)
mm = MockModel(MockPosterior(samples=samples))
sampler = IIDNormalSampler(num_samples=1)
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
res = acqf(X)
self.assertEqual(res.item(), 1.5)
# test q = 1, does not contribute
samples = torch.tensor([0.0, 1.0], **tkwargs).view(1, 1, 2)
sampler = IIDNormalSampler(1)
mm = MockModel(MockPosterior(samples=samples))
acqf.model = mm
res = acqf(X)
self.assertEqual(res.item(), 0.0)
# test q = 2, both points contribute
X = torch.zeros(2, 1, **tkwargs)
samples = torch.tensor([[6.5, 4.5], [7.0, 4.0]],
**tkwargs).unsqueeze(0)
mm = MockModel(MockPosterior(samples=samples))
acqf.model = mm
res = acqf(X)
self.assertEqual(res.item(), 1.75)
# test q = 2, only 1 point contributes
samples = torch.tensor([[6.5, 4.5], [6.0, 4.0]],
**tkwargs).unsqueeze(0)
mm = MockModel(MockPosterior(samples=samples))
acqf.model = mm
res = acqf(X)
self.assertEqual(res.item(), 1.5)
# test q = 2, neither contributes
samples = torch.tensor([[2.0, 2.0], [0.0, 0.1]],
**tkwargs).unsqueeze(0)
mm = MockModel(MockPosterior(samples=samples))
acqf.model = mm
res = acqf(X)
self.assertEqual(res.item(), 0.0)
# test q = 2, test point better than current best second objective
samples = torch.tensor([[6.5, 4.5], [6.0, 6.0]],
**tkwargs).unsqueeze(0)
mm = MockModel(MockPosterior(samples=samples))
acqf.model = mm
res = acqf(X)
self.assertEqual(res.item(), 8.0)
# test q = 2, test point better than current-best first objective
samples = torch.tensor([[6.5, 4.5], [9.0, 2.0]],
**tkwargs).unsqueeze(0)
mm = MockModel(MockPosterior(samples=samples))
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
res = acqf(X)
self.assertEqual(res.item(), 2.0)
# test q = 3, all contribute
X = torch.zeros(3, 1, **tkwargs)
samples = torch.tensor([[6.5, 4.5], [9.0, 2.0], [7.0, 4.0]],
**tkwargs).unsqueeze(0)
mm = MockModel(MockPosterior(samples=samples))
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
res = acqf(X)
self.assertEqual(res.item(), 2.25)
# test q = 3, not all contribute
samples = torch.tensor([[6.5, 4.5], [9.0, 2.0], [7.0, 5.0]],
**tkwargs).unsqueeze(0)
mm = MockModel(MockPosterior(samples=samples))
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
res = acqf(X)
self.assertEqual(res.item(), 3.5)
# test q = 3, none contribute
samples = torch.tensor([[0.0, 4.5], [1.0, 2.0], [3.0, 0.0]],
**tkwargs).unsqueeze(0)
mm = MockModel(MockPosterior(samples=samples))
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
res = acqf(X)
self.assertEqual(res.item(), 0.0)
# test m = 3, q=1
pareto_Y = torch.tensor(
[[4.0, 2.0, 3.0], [3.0, 5.0, 1.0], [2.0, 4.0, 2.0],
[1.0, 3.0, 4.0]],
**tkwargs,
)
partitioning = NondominatedPartitioning(num_outcomes=3, Y=pareto_Y)
samples = torch.tensor([[1.0, 2.0, 6.0]], **tkwargs).unsqueeze(0)
mm = MockModel(MockPosterior(samples=samples))
ref_point = [-1.0] * 3
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
X = torch.zeros(1, 2, **tkwargs)
res = acqf(X)
self.assertEqual(res.item(), 12.0)
# change reference point
ref_point = [0.0] * 3
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
res = acqf(X)
self.assertEqual(res.item(), 4.0)
# test m = 3, no contribution
ref_point = [1.0] * 3
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
res = acqf(X)
self.assertEqual(res.item(), 0.0)
# test m = 3, q = 2
pareto_Y = torch.tensor(
[[4.0, 2.0, 3.0], [3.0, 5.0, 1.0], [2.0, 4.0, 2.0]], **tkwargs)
samples = torch.tensor([[1.0, 2.0, 6.0], [1.0, 3.0, 4.0]],
**tkwargs).unsqueeze(0)
mm = MockModel(MockPosterior(samples=samples))
ref_point = [-1.0] * 3
partitioning = NondominatedPartitioning(num_outcomes=3, Y=pareto_Y)
acqf = qExpectedHypervolumeImprovement(
model=mm,
ref_point=ref_point,
partitioning=partitioning,
sampler=sampler,
)
X = torch.zeros(2, 2, **tkwargs)
res = acqf(X)
self.assertEqual(res.item(), 22.0)
def qehvi_candidates_func(
train_x: "torch.Tensor",
train_obj: "torch.Tensor",
train_con: Optional["torch.Tensor"],
bounds: "torch.Tensor",
) -> "torch.Tensor":
"""Quasi MC-based batch Expected Hypervolume Improvement (qEHVI).
The default value of ``candidates_func`` in :class:`~optuna.integration.BoTorchSampler`
with multi-objective optimization when the number of objectives is three or less.
.. seealso::
:func:`~optuna.integration.botorch.qei_candidates_func` for argument and return value
descriptions.
"""
n_objectives = train_obj.size(-1)
if train_con is not None:
train_y = torch.cat([train_obj, train_con], dim=-1)
is_feas = (train_con <= 0).all(dim=-1)
train_obj_feas = train_obj[is_feas]
constraints = []
n_constraints = train_con.size(1)
for i in range(n_constraints):
constraints.append(lambda Z, i=i: Z[..., -n_constraints + i])
additional_qehvi_kwargs = {
"objective":
IdentityMCMultiOutputObjective(outcomes=list(range(n_objectives))),
"constraints":
constraints,
}
else:
train_y = train_obj
train_obj_feas = train_obj
additional_qehvi_kwargs = {}
train_x = normalize(train_x, bounds=bounds)
model = SingleTaskGP(train_x,
train_y,
outcome_transform=Standardize(m=train_y.shape[-1]))
mll = ExactMarginalLogLikelihood(model.likelihood, model)
fit_gpytorch_model(mll)
# Approximate box decomposition similar to Ax when the number of objectives is large.
# https://github.com/facebook/Ax/blob/master/ax/models/torch/botorch_moo_defaults
if n_objectives > 2:
alpha = 10**(-8 + n_objectives)
else:
alpha = 0.0
partitioning = NondominatedPartitioning(num_outcomes=n_objectives,
Y=train_obj_feas,
alpha=alpha)
ref_point = train_obj.min(dim=0).values - 1e-8
ref_point_list = ref_point.tolist()
acqf = qExpectedHypervolumeImprovement(
model=model,
ref_point=ref_point_list,
partitioning=partitioning,
sampler=SobolQMCNormalSampler(num_samples=256),
**additional_qehvi_kwargs,
)
standard_bounds = torch.zeros_like(bounds)
standard_bounds[1] = 1
candidates, _ = optimize_acqf(
acq_function=acqf,
bounds=standard_bounds,
q=1,
num_restarts=20,
raw_samples=1024,
options={
"batch_limit": 5,
"maxiter": 200,
"nonnegative": True
},
sequential=True,
)
candidates = unnormalize(candidates.detach(), bounds=bounds)
return candidates
def evaluate(mth, run_i, seed):
print(mth, run_i, seed, '===== start =====', flush=True)
def objective_function(x: torch.Tensor):
# Caution: unnormalize and maximize
x = unnormalize(x, bounds=problem_bounds)
x = x.cpu().numpy().astype(np.float64) # caution
res = problem.evaluate(x)
res['objs'] = [-y for y in res['objs']]
return res # Caution: negative values imply feasibility in botorch
hv_diffs = []
time_list = []
global_start_time = time.time()
# random seed
np.random.seed(seed)
torch.manual_seed(seed)
# call helper functions to generate initial training data and initialize model
train_x, train_obj, train_con = generate_initial_data(
initial_runs, objective_function, time_list, global_start_time)
# fix bug: find feasible
real_initial_runs = initial_runs
while real_initial_runs < max_runs:
# compute feasible observations
is_feas = (train_con <= 0).all(dim=-1)
# compute points that are better than the known reference point
better_than_ref = (train_obj > problem.ref_point).all(dim=-1)
if (is_feas & better_than_ref).any():
break
train_x, train_obj, train_con = expand_initial_data(
train_x, train_obj, train_con, objective_function, time_list,
global_start_time)
real_initial_runs += 1
print('=== Expand initial data to find feasible. Iter =',
real_initial_runs)
mll, model = initialize_model(train_x, train_obj, train_con)
# for plot
X_init = train_x.cpu().numpy().astype(np.float64)
Y_init = -1 * train_obj.cpu().numpy().astype(np.float64)
# calculate hypervolume of init data
for i in range(real_initial_runs):
train_obj_i = train_obj[:i + 1]
train_con_i = train_con[:i + 1]
# compute pareto front
is_feas_i = (train_con_i <= 0).all(dim=-1)
feas_train_obj_i = train_obj_i[is_feas_i]
pareto_mask = is_non_dominated(feas_train_obj_i)
pareto_y = feas_train_obj_i[pareto_mask]
# compute hypervolume
volume = hv.compute(pareto_y)
hv_diff = problem.max_hv - volume
hv_diffs.append(hv_diff)
# run (max_runs - real_initial_runs) rounds of BayesOpt after the initial random batch
for iteration in range(real_initial_runs + 1, max_runs + 1):
t0 = time.time()
try:
# fit the models
fit_gpytorch_model(mll)
# define the qEHVI acquisition modules using a QMC sampler
sampler = SobolQMCNormalSampler(num_samples=MC_SAMPLES)
# compute feasible observations
is_feas = (train_con <= 0).all(dim=-1)
# compute points that are better than the known reference point
better_than_ref = (train_obj > problem.ref_point).all(dim=-1)
# partition non-dominated space into disjoint rectangles
partitioning = NondominatedPartitioning(
num_outcomes=problem.num_objs,
# use observations that are better than the specified reference point and feasible
Y=train_obj[better_than_ref & is_feas],
)
qEHVI = qExpectedHypervolumeImprovement(
model=model,
ref_point=problem.ref_point.tolist(
), # use known reference point
partitioning=partitioning,
sampler=sampler,
# define an objective that specifies which outcomes are the objectives
objective=IdentityMCMultiOutputObjective(
outcomes=list(range(problem.num_objs))),
# specify that the constraint is on the last outcome
constraints=constraint_callable_list(
problem.num_constraints, num_objs=problem.num_objs),
)
# optimize and get new observation
new_x, new_obj, new_con = optimize_acqf_and_get_observation(
qEHVI, objective_function, time_list, global_start_time)
except Exception as e: # handle numeric problem
step = 2
print(
'===== Exception in optimization loop, restart with 1/%d of training data: %s'
% (step, str(e)))
if refit == 1:
mll, model = initialize_model(train_x[::step],
train_obj[::step],
train_con[::step])
else:
mll, model = initialize_model(
train_x[::step],
train_obj[::step],
train_con[::step],
model.state_dict(),
)
# fit the models
fit_gpytorch_model(mll)
# define the qEHVI acquisition modules using a QMC sampler
sampler = SobolQMCNormalSampler(num_samples=MC_SAMPLES)
# compute feasible observations
is_feas = (train_con[::step] <= 0).all(dim=-1)
# compute points that are better than the known reference point
better_than_ref = (train_obj[::step] > problem.ref_point).all(
dim=-1)
# partition non-dominated space into disjoint rectangles
partitioning = NondominatedPartitioning(
num_outcomes=problem.num_objs,
# use observations that are better than the specified reference point and feasible
Y=train_obj[::step][better_than_ref & is_feas],
)
qEHVI = qExpectedHypervolumeImprovement(
model=model,
ref_point=problem.ref_point.tolist(
), # use known reference point
partitioning=partitioning,
sampler=sampler,
# define an objective that specifies which outcomes are the objectives
objective=IdentityMCMultiOutputObjective(
outcomes=list(range(problem.num_objs))),
# specify that the constraint is on the last outcome
constraints=constraint_callable_list(
problem.num_constraints, num_objs=problem.num_objs),
)
# optimize and get new observation
new_x, new_obj, new_con = optimize_acqf_and_get_observation(
qEHVI, objective_function, time_list, global_start_time)
assert len(time_list) == iteration
# update training points
train_x = torch.cat([train_x, new_x])
train_obj = torch.cat([train_obj, new_obj])
train_con = torch.cat([train_con, new_con])
# update progress
# compute pareto front
is_feas = (train_con <= 0).all(dim=-1)
feas_train_obj = train_obj[is_feas]
pareto_mask = is_non_dominated(feas_train_obj)
pareto_y = feas_train_obj[pareto_mask]
# compute hypervolume
volume = hv.compute(pareto_y)
hv_diff = problem.max_hv - volume
hv_diffs.append(hv_diff)
# reinitialize the models so they are ready for fitting on next iteration
# use the current state dict to speed up fitting
# Note: they find improved performance from not warm starting the model hyperparameters
# using the hyperparameters from the previous iteration
if refit == 1:
mll, model = initialize_model(train_x, train_obj, train_con)
else:
mll, model = initialize_model(
train_x,
train_obj,
train_con,
model.state_dict(),
)
t1 = time.time()
print(
"Iter %d: x=%s, perf=%s, con=%s, hv_diff=%f, time=%.2f, global_time=%.2f"
% (iteration, unnormalize(new_x, bounds=problem_bounds), -new_obj,
new_con, hv_diff, t1 - t0, time_list[-1]),
flush=True)
# compute pareto front
is_feas = (train_con <= 0).all(dim=-1)
feas_train_obj = train_obj[is_feas]
pareto_mask = is_non_dominated(feas_train_obj)
pareto_y = feas_train_obj[pareto_mask]
pf = -1 * pareto_y.cpu().numpy().astype(np.float64)
# Save result
X = unnormalize(train_x, bounds=problem_bounds).cpu().numpy().astype(
np.float64) # caution
train_obj[~is_feas] = -INFEASIBLE_OBJ_VALUE # set infeasible
Y = -1 * train_obj.cpu().numpy().astype(np.float64)
# plot for debugging
if plot_mode == 1:
plot_pf(problem, problem_str, mth, pf, Y_init)
return hv_diffs, pf, X, Y, time_list
def prune_inferior_points_multi_objective(
model: Model,
X: Tensor,
ref_point: Tensor,
objective: Optional[MCMultiOutputObjective] = None,
constraints: Optional[List[Callable[[Tensor], Tensor]]] = None,
num_samples: int = 2048,
max_frac: float = 1.0,
marginalize_dim: Optional[int] = None,
) -> Tensor:
r"""Prune points from an input tensor that are unlikely to be pareto optimal.
Given a model, an objective, and an input tensor `X`, this function returns
the subset of points in `X` that have some probability of being pareto
optimal, better than the reference point, and feasible. This function uses
sampling to estimate the probabilities, the higher the number of points `n`
in `X` the higher the number of samples `num_samples` should be to obtain
accurate estimates.
Args:
model: A fitted model. Batched models are currently not supported.
X: An input tensor of shape `n x d`. Batched inputs are currently not
supported.
ref_point: The reference point.
objective: The objective under which to evaluate the posterior.
constraints: A list of callables, each mapping a Tensor of dimension
`sample_shape x batch-shape x q x m` to a Tensor of dimension
`sample_shape x batch-shape x q`, where negative values imply
feasibility.
num_samples: The number of samples used to compute empirical
probabilities of being the best point.
max_frac: The maximum fraction of points to retain. Must satisfy
`0 < max_frac <= 1`. Ensures that the number of elements in the
returned tensor does not exceed `ceil(max_frac * n)`.
marginalize_dim: A batch dimension that should be marginalized.
For example, this is useful when using a batched fully Bayesian
model.
Returns:
A `n' x d` with subset of points in `X`, where
n' = min(N_nz, ceil(max_frac * n))
with `N_nz` the number of points in `X` that have non-zero (empirical,
under `num_samples` samples) probability of being pareto optimal.
"""
if X.ndim > 2:
# TODO: support batched inputs (req. dealing with ragged tensors)
raise UnsupportedError(
"Batched inputs `X` are currently unsupported by "
"prune_inferior_points_multi_objective")
max_points = math.ceil(max_frac * X.size(-2))
if max_points < 1 or max_points > X.size(-2):
raise ValueError(f"max_frac must take values in (0, 1], is {max_frac}")
with torch.no_grad():
posterior = model.posterior(X=X)
if posterior.event_shape.numel() > SobolEngine.MAXDIM:
if settings.debug.on():
warnings.warn(
f"Sample dimension q*m={posterior.event_shape.numel()} exceeding Sobol "
f"max dimension ({SobolEngine.MAXDIM}). Using iid samples instead.",
SamplingWarning,
)
sampler = IIDNormalSampler(num_samples=num_samples)
else:
sampler = SobolQMCNormalSampler(num_samples=num_samples)
samples = sampler(posterior)
if objective is None:
objective = IdentityMCMultiOutputObjective()
obj_vals = objective(samples, X=X)
if obj_vals.ndim > 3:
if obj_vals.ndim == 4 and marginalize_dim is not None:
obj_vals = obj_vals.mean(dim=marginalize_dim)
else:
# TODO: support batched inputs (req. dealing with ragged tensors)
raise UnsupportedError(
"Models with multiple batch dims are currently unsupported by"
" prune_inferior_points_multi_objective.")
if constraints is not None:
infeas = torch.stack([c(samples) > 0 for c in constraints],
dim=0).any(dim=0)
if infeas.ndim == 3 and marginalize_dim is not None:
# make sure marginalize_dim is not negative
if marginalize_dim < 0:
# add 1 to the normalize marginalize_dim since we have already
# removed the output dim
marginalize_dim = (
1 + normalize_indices([marginalize_dim], d=infeas.ndim)[0])
infeas = infeas.float().mean(dim=marginalize_dim).round().bool()
# set infeasible points to be the ref point
obj_vals[infeas] = ref_point
pareto_mask = is_non_dominated(
obj_vals, deduplicate=False) & (obj_vals > ref_point).all(dim=-1)
probs = pareto_mask.to(dtype=X.dtype).mean(dim=0)
idcs = probs.nonzero().view(-1)
if idcs.shape[0] > max_points:
counts, order_idcs = torch.sort(probs, descending=True)
idcs = order_idcs[:max_points]
return X[idcs]