def _update_pareto_Y(self) -> bool:
r"""Update the non-dominated front."""
# is_non_dominated assumes maximization
non_dominated_mask = is_non_dominated(-self.Y)
pf = self.Y[non_dominated_mask]
# sort by first objective
new_pareto_Y = pf[torch.argsort(pf[:, 0])]
if not hasattr(self, "_pareto_Y") or not torch.equal(
new_pareto_Y, self._pareto_Y
):
self.register_buffer("_pareto_Y", new_pareto_Y)
return True
return False
def _update_pareto_Y(self) -> bool:
r"""Update the non-dominated front."""
# is_non_dominated assumes maximization
pareto_mask = is_non_dominated(-self.Y)
if len(self.batch_shape) > 0:
# Note: in the batch case, the Pareto frontier is padded by repeating
# a Pareto point. This ensures that the padded box-decomposition has
# the same number of points, which enables fast batch operations.
max_n_pareto = pareto_mask.sum(dim=-1).max().item()
pareto_Y = torch.empty(
*self.batch_shape,
max_n_pareto,
self.Y.shape[-1],
dtype=self.Y.dtype,
device=self.Y.device,
)
for i in range(self.Y.shape[0]):
pareto_i = self.Y[i, pareto_mask[i]]
n_pareto = pareto_i.shape[0]
pareto_Y[i, :n_pareto] = pareto_i
# pad pareto_Y, so that all batches have the same size Pareto set
pareto_Y[i, n_pareto:] = pareto_i[-1]
# sort by first objective
new_pareto_Y = pareto_Y.gather(
index=torch.argsort(pareto_Y[..., :1], dim=-2).expand(pareto_Y.shape),
dim=-2,
)
else:
pareto_Y = self.Y[pareto_mask]
# sort by first objective
new_pareto_Y = pareto_Y[torch.argsort(pareto_Y[:, 0])]
if not hasattr(self, "_pareto_Y") or not torch.equal(
new_pareto_Y, self._pareto_Y
):
self.register_buffer("_pareto_Y", new_pareto_Y)
return True
return False
def update(self, Y: Tensor) -> None:
r"""Update non-dominated front and decomposition.
Args:
Y: A `(batch_shape) x n x m`-dim tensor of new, incremental outcomes.
"""
if self._update_neg_Y(Y=Y):
self.reset()
else:
if self.num_outcomes == 2 or self._neg_pareto_Y.shape[-2] == 0:
# If there are two objective, recompute the box decomposition
# because the partitions can be computed analytically.
# If the current pareto set has no points, recompute the box
# decomposition.
self.reset()
else:
# only include points that are better than the reference point
better_than_ref = (Y > self.ref_point).all(dim=-1)
Y = Y[better_than_ref]
Y_all = torch.cat([self._neg_pareto_Y, -Y], dim=-2)
pareto_mask = is_non_dominated(-Y_all)
# determine the number of points in Y that are Pareto optimal
num_new_pareto = pareto_mask[-Y.shape[-2] :].sum()
self._neg_pareto_Y = Y_all[pareto_mask]
if num_new_pareto > 0:
# update local upper bounds for the minimization problem
self._U, self._Z = update_local_upper_bounds_incremental(
# this assumes minimization
new_pareto_Y=self._neg_pareto_Y[-num_new_pareto:],
U=self._U,
Z=self._Z,
)
# use the negative local upper bounds as the new pareto
# frontier for the minimization problem and perform
# box decomposition on dominated space.
self._get_partitioning()
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 test_is_non_dominated(self) -> None:
tkwargs = {"device": self.device}
Y = torch.tensor(
[
[1.0, 5.0],
[10.0, 3.0],
[4.0, 5.0],
[4.0, 5.0],
[5.0, 5.0],
[8.5, 3.5],
[8.5, 3.5],
[8.5, 3.0],
[9.0, 1.0],
]
)
expected_nondom_Y = torch.tensor([[10.0, 3.0], [5.0, 5.0], [8.5, 3.5]])
Yb = Y.clone()
Yb[1] = 0
expected_nondom_Yb = torch.tensor([[5.0, 5.0], [8.5, 3.5], [9.0, 1.0]])
Y3 = torch.tensor(
[
[4.0, 2.0, 3.0],
[2.0, 4.0, 1.0],
[3.0, 5.0, 1.0],
[2.0, 4.0, 2.0],
[2.0, 4.0, 2.0],
[1.0, 3.0, 4.0],
[1.0, 2.0, 4.0],
[1.0, 2.0, 6.0],
]
)
Y3b = Y3.clone()
Y3b[0] = 0
expected_nondom_Y3 = 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],
[1.0, 2.0, 6.0],
]
)
expected_nondom_Y3b = expected_nondom_Y3[1:]
for dtype in (torch.float, torch.double):
tkwargs["dtype"] = dtype
Y = Y.to(**tkwargs)
expected_nondom_Y = expected_nondom_Y.to(**tkwargs)
Yb = Yb.to(**tkwargs)
expected_nondom_Yb = expected_nondom_Yb.to(**tkwargs)
Y3 = Y3.to(**tkwargs)
expected_nondom_Y3 = expected_nondom_Y3.to(**tkwargs)
Y3b = Y3b.to(**tkwargs)
expected_nondom_Y3b = expected_nondom_Y3b.to(**tkwargs)
# test 2d
nondom_Y = Y[is_non_dominated(Y)]
self.assertTrue(torch.equal(expected_nondom_Y, nondom_Y))
# test deduplicate=False
expected_nondom_Y_no_dedup = torch.cat(
[expected_nondom_Y, expected_nondom_Y[-1:]], dim=0
)
nondom_Y = Y[is_non_dominated(Y, deduplicate=False)]
self.assertTrue(torch.equal(expected_nondom_Y_no_dedup, nondom_Y))
# test batch
batch_Y = torch.stack([Y, Yb], dim=0)
nondom_mask = is_non_dominated(batch_Y)
self.assertTrue(torch.equal(batch_Y[0][nondom_mask[0]], expected_nondom_Y))
self.assertTrue(torch.equal(batch_Y[1][nondom_mask[1]], expected_nondom_Yb))
# test deduplicate=False
expected_nondom_Yb_no_dedup = torch.cat(
[expected_nondom_Yb[:-1], expected_nondom_Yb[-2:]], dim=0
)
nondom_mask = is_non_dominated(batch_Y, deduplicate=False)
self.assertTrue(
torch.equal(batch_Y[0][nondom_mask[0]], expected_nondom_Y_no_dedup)
)
self.assertTrue(
torch.equal(batch_Y[1][nondom_mask[1]], expected_nondom_Yb_no_dedup)
)
# test 3d
nondom_Y3 = Y3[is_non_dominated(Y3)]
self.assertTrue(torch.equal(expected_nondom_Y3, nondom_Y3))
# test deduplicate=False
expected_nondom_Y3_no_dedup = torch.cat(
[expected_nondom_Y3[:3], expected_nondom_Y3[2:]], dim=0
)
nondom_Y3 = Y3[is_non_dominated(Y3, deduplicate=False)]
self.assertTrue(torch.equal(expected_nondom_Y3_no_dedup, nondom_Y3))
# test batch
batch_Y3 = torch.stack([Y3, Y3b], dim=0)
nondom_mask3 = is_non_dominated(batch_Y3)
self.assertTrue(
torch.equal(batch_Y3[0][nondom_mask3[0]], expected_nondom_Y3)
)
self.assertTrue(
torch.equal(batch_Y3[1][nondom_mask3[1]], expected_nondom_Y3b)
)
# test deduplicate=False
nondom_mask3 = is_non_dominated(batch_Y3, deduplicate=False)
self.assertTrue(
torch.equal(batch_Y3[0][nondom_mask3[0]], expected_nondom_Y3_no_dedup)
)
expected_nondom_Y3b_no_dedup = torch.cat(
[expected_nondom_Y3b[:2], expected_nondom_Y3b[1:]], dim=0
)
self.assertTrue(
torch.equal(batch_Y3[1][nondom_mask3[1]], expected_nondom_Y3b_no_dedup)
)
# test empty pareto
mask = is_non_dominated(Y3[:0])
expected_mask = torch.zeros(0, dtype=torch.bool, device=Y3.device)
self.assertTrue(torch.equal(expected_mask, mask))
mask = is_non_dominated(batch_Y3[:, :0])
expected_mask = torch.zeros(
*batch_Y3.shape[:-2], 0, dtype=torch.bool, device=Y3.device
)
self.assertTrue(torch.equal(expected_mask, mask))
def _get_pareto_points(self):
# taken from https://botorch.org/tutorials/constrained_multi_objective_bo
y_tensor = torch.stack(self._torch_model.train_targets, dim=1)
pareto_mask = is_non_dominated(y_tensor)
pareto_y = y_tensor[pareto_mask]
return pareto_y
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)
objs = [-y for y in res['objs']]
return objs
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 = generate_initial_data(initial_runs,
objective_function, time_list,
global_start_time)
mll, model = initialize_model(train_x, train_obj)
# 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(initial_runs):
train_obj_i = train_obj[:i + 1]
# compute pareto front
pareto_mask = is_non_dominated(train_obj_i)
pareto_y = 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 - initial_runs) rounds of BayesOpt after the initial random batch
for iteration in range(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)
# partition non-dominated space into disjoint rectangles
partitioning = NondominatedPartitioning(
num_outcomes=problem.num_objs, Y=train_obj)
qEHVI = qExpectedHypervolumeImprovement(
model=model,
ref_point=problem.ref_point.tolist(
), # use known reference point
partitioning=partitioning,
sampler=sampler,
)
# optimize and get new observation
new_x, new_obj = optimize_acqf_and_get_observation(
qEHVI, objective_function, time_list, global_start_time)
except Exception as e:
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])
else:
mll, model = initialize_model(
train_x[::step],
train_obj[::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)
# partition non-dominated space into disjoint rectangles
partitioning = NondominatedPartitioning(
num_outcomes=problem.num_objs, Y=train_obj[::step])
qEHVI = qExpectedHypervolumeImprovement(
model=model,
ref_point=problem.ref_point.tolist(
), # use known reference point
partitioning=partitioning,
sampler=sampler,
)
# optimize and get new observation
new_x, new_obj = 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])
# update progress
# compute pareto front
pareto_mask = is_non_dominated(train_obj)
pareto_y = 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)
else:
mll, model = initialize_model(
train_x,
train_obj,
model.state_dict(),
)
t1 = time.time()
print(
"Iter %d: x=%s, perf=%s, hv_diff=%f, time=%.2f, global_time=%.2f" %
(iteration, unnormalize(new_x, bounds=problem_bounds), -new_obj,
hv_diff, t1 - t0, time_list[-1]),
flush=True)
# Save result
X = unnormalize(train_x, bounds=problem_bounds).cpu().numpy().astype(
np.float64) # caution
Y = -1 * train_obj.cpu().numpy().astype(np.float64)
# compute pareto front
pareto_mask = is_non_dominated(train_obj)
pareto_y = train_obj[pareto_mask]
pf = -1 * pareto_y.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]
def get_mvar_set_cpu(self, Y: Tensor) -> Tensor:
r"""Find MVaR set based on the definition in [Prekopa2012MVaR]_.
NOTE: This is much faster on CPU for large `n_w` than the alternative but it
is significantly slower on GPU. Based on empirical evidence, this is recommended
when running on CPU with `n_w > 64`.
This first calculates the CDF for each point on the extended domain of the
random variable (the grid defined by the given samples), then takes the
values with CDF equal to (rounded if necessary) `alpha`. The non-dominated
subset of these form the MVaR set.
Args:
Y: A `batch x n_w x m`-dim tensor of outcomes. This is currently
restricted to `m = 2` objectives.
TODO: Support `m > 2` objectives.
Returns:
A `batch` length list of `k x m`-dim tensor of MVaR values, where `k`
depends on the corresponding batch inputs. Note that MVaR values in general
are not in-sample points.
"""
if Y.dim() == 3:
return [self.get_mvar_set_cpu(y_) for y_ in Y]
m = Y.shape[-1]
if m != 2: # pragma: no cover
raise ValueError(
"`get_mvar_set_cpu` only supports `m=2` outcomes!")
# Generate sets of all unique values in each output dimension.
# Note that points in MVaR are bounded from above by the
# independent VaR of each objective. Hence, we only need to
# consider the unique outcomes that are less than or equal to
# the VaR of the independent objectives
var_alpha_idx = ceil(self.alpha * self.n_w) - 1
Y_sorted = Y.topk(Y.shape[0] - var_alpha_idx, dim=0,
largest=False).values
unique_outcomes_list = [
Y_sorted[:, i].unique().tolist()[::-1] for i in range(m)
]
# Convert this into a list of m dictionaries mapping values to indices.
unique_outcomes = [
dict(zip(outcomes, range(len(outcomes))))
for outcomes in unique_outcomes_list
]
# Initialize a tensor counting the number of points in Y that a given grid point
# is dominated by. This will essentially be a non-normalized CDF.
counter_tensor = torch.zeros(
[len(outcomes) for outcomes in unique_outcomes],
dtype=torch.long,
device=Y.device,
)
# populate the tensor, counting the dominated points.
# we only need to consider points in Y where at least one
# objective is less than the max objective value in
# unique_outcomes_list
max_vals = torch.tensor([o[0] for o in unique_outcomes_list],
dtype=Y.dtype,
device=Y.device)
mask = (Y < max_vals).any(dim=-1)
counter_tensor += self.n_w - mask.sum()
Y_pruned = Y[mask]
for y_ in Y_pruned:
starting_idcs = [
unique_outcomes[i].get(y_[i].item(), 0) for i in range(m)
]
counter_tensor[starting_idcs[0]:, starting_idcs[1]:] += 1
# Get the count alpha-level points should have.
alpha_count = ceil(self.alpha * self.n_w)
# Get the alpha level indices.
alpha_level_indices = (counter_tensor == alpha_count).nonzero(
as_tuple=False)
# If there are no exact alpha level points, get the smallest alpha' > alpha
# and find the corresponding alpha level indices.
if alpha_level_indices.numel() == 0:
min_greater_than_alpha = counter_tensor[
counter_tensor > alpha_count].min()
alpha_level_indices = (
counter_tensor == min_greater_than_alpha).nonzero(
as_tuple=False)
unique_outcomes = [
torch.as_tensor(list(outcomes.keys()),
device=Y.device,
dtype=Y.dtype) for outcomes in unique_outcomes
]
alpha_level_points = torch.stack(
[
unique_outcomes[i][alpha_level_indices[:, i]]
for i in range(len(unique_outcomes))
],
dim=-1,
)
# MVaR is simply the non-dominated subset of alpha level points.
if self.filter_dominated:
mask = is_non_dominated(alpha_level_points)
mvar = alpha_level_points[mask]
else:
mvar = alpha_level_points
return mvar
def test_is_non_dominated(self) -> None:
tkwargs = {"device": self.device}
Y = torch.tensor([
[1.0, 5.0],
[10.0, 3.0],
[4.0, 5.0],
[4.0, 5.0],
[5.0, 5.0],
[8.5, 3.5],
[8.5, 3.0],
[9.0, 1.0],
])
expected_nondom_Y = torch.tensor([[10.0, 3.0], [5.0, 5.0], [8.5, 3.5]])
Yb = Y.clone()
Yb[1] = 0
expected_nondom_Yb = torch.tensor([[5.0, 5.0], [8.5, 3.5], [9.0, 1.0]])
Y3 = torch.tensor([
[4.0, 2.0, 3.0],
[2.0, 4.0, 1.0],
[3.0, 5.0, 1.0],
[2.0, 4.0, 2.0],
[1.0, 3.0, 4.0],
[1.0, 2.0, 4.0],
[1.0, 2.0, 6.0],
])
Y3b = Y3.clone()
Y3b[0] = 0
expected_nondom_Y3 = 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],
[1.0, 2.0, 6.0],
])
expected_nondom_Y3b = expected_nondom_Y3[1:]
for dtype in (torch.float, torch.double):
tkwargs["dtype"] = dtype
Y = Y.to(**tkwargs)
expected_nondom_Y = expected_nondom_Y.to(**tkwargs)
Yb = Yb.to(**tkwargs)
expected_nondom_Yb = expected_nondom_Yb.to(**tkwargs)
Y3 = Y3.to(**tkwargs)
expected_nondom_Y3 = expected_nondom_Y3.to(**tkwargs)
Y3b = Y3b.to(**tkwargs)
expected_nondom_Y3b = expected_nondom_Y3b.to(**tkwargs)
# test 2d
nondom_Y = Y[is_non_dominated(Y)]
self.assertTrue(torch.equal(expected_nondom_Y, nondom_Y))
# test batch
batch_Y = torch.stack([Y, Yb], dim=0)
nondom_mask = is_non_dominated(batch_Y)
self.assertTrue(
torch.equal(batch_Y[0][nondom_mask[0]], expected_nondom_Y))
self.assertTrue(
torch.equal(batch_Y[1][nondom_mask[1]], expected_nondom_Yb))
# test 3d
nondom_Y3 = Y3[is_non_dominated(Y3)]
self.assertTrue(torch.equal(expected_nondom_Y3, nondom_Y3))
# test batch
batch_Y3 = torch.stack([Y3, Y3b], dim=0)
nondom_mask3 = is_non_dominated(batch_Y3)
self.assertTrue(
torch.equal(batch_Y3[0][nondom_mask3[0]], expected_nondom_Y3))
self.assertTrue(
torch.equal(batch_Y3[1][nondom_mask3[1]], expected_nondom_Y3b))
def test_infer_objective_thresholds(self, _, cuda=False):
# lightweight test
exp = get_branin_experiment_with_multi_objective(
has_optimization_config=True,
with_batch=True,
with_status_quo=True,
)
for trial in exp.trials.values():
trial.mark_running(no_runner_required=True).mark_completed()
exp.attach_data(
get_branin_data_multi_objective(trial_indices=exp.trials.keys())
)
data = exp.fetch_data()
modelbridge = TorchModelBridge(
search_space=exp.search_space,
model=MultiObjectiveBotorchModel(),
optimization_config=exp.optimization_config,
transforms=Cont_X_trans + Y_trans,
torch_device=torch.device("cuda" if cuda else "cpu"),
experiment=exp,
data=data,
)
fixed_features = ObservationFeatures(parameters={"x1": 0.0})
search_space = exp.search_space.clone()
param_constraints = [
ParameterConstraint(constraint_dict={"x1": 1.0}, bound=10.0)
]
search_space.add_parameter_constraints(param_constraints)
oc = exp.optimization_config.clone()
oc.objective._objectives[0].minimize = True
expected_base_gen_args = modelbridge._get_transformed_gen_args(
search_space=search_space.clone(),
optimization_config=oc,
fixed_features=fixed_features,
)
with ExitStack() as es:
mock_model_infer_obj_t = es.enter_context(
patch(
"ax.modelbridge.torch.infer_objective_thresholds",
wraps=infer_objective_thresholds,
)
)
mock_get_transformed_gen_args = es.enter_context(
patch.object(
modelbridge,
"_get_transformed_gen_args",
wraps=modelbridge._get_transformed_gen_args,
)
)
mock_get_transformed_model_gen_args = es.enter_context(
patch.object(
modelbridge,
"_get_transformed_model_gen_args",
wraps=modelbridge._get_transformed_model_gen_args,
)
)
mock_untransform_objective_thresholds = es.enter_context(
patch.object(
modelbridge,
"_untransform_objective_thresholds",
wraps=modelbridge._untransform_objective_thresholds,
)
)
obj_thresholds = modelbridge.infer_objective_thresholds(
search_space=search_space,
optimization_config=oc,
fixed_features=fixed_features,
)
expected_obj_weights = torch.tensor([-1.0, 1.0])
ckwargs = mock_model_infer_obj_t.call_args[1]
self.assertTrue(
torch.equal(ckwargs["objective_weights"], expected_obj_weights)
)
# check that transforms have been applied (at least UnitX)
self.assertEqual(ckwargs["bounds"], [(0.0, 1.0), (0.0, 1.0)])
lc = ckwargs["linear_constraints"]
self.assertTrue(torch.equal(lc[0], torch.tensor([[15.0, 0.0]])))
self.assertTrue(torch.equal(lc[1], torch.tensor([[15.0]])))
self.assertEqual(ckwargs["fixed_features"], {0: 1.0 / 3.0})
mock_get_transformed_gen_args.assert_called_once()
mock_get_transformed_model_gen_args.assert_called_once_with(
search_space=expected_base_gen_args.search_space,
fixed_features=expected_base_gen_args.fixed_features,
pending_observations=expected_base_gen_args.pending_observations,
optimization_config=expected_base_gen_args.optimization_config,
)
mock_untransform_objective_thresholds.assert_called_once()
ckwargs = mock_untransform_objective_thresholds.call_args[1]
self.assertTrue(
torch.equal(ckwargs["objective_weights"], expected_obj_weights)
)
self.assertEqual(ckwargs["bounds"], [(0.0, 1.0), (0.0, 1.0)])
self.assertEqual(ckwargs["fixed_features"], {0: 1.0 / 3.0})
self.assertEqual(obj_thresholds[0].metric.name, "branin_a")
self.assertEqual(obj_thresholds[1].metric.name, "branin_b")
self.assertEqual(obj_thresholds[0].op, ComparisonOp.LEQ)
self.assertEqual(obj_thresholds[1].op, ComparisonOp.GEQ)
self.assertFalse(obj_thresholds[0].relative)
self.assertFalse(obj_thresholds[1].relative)
df = exp_to_df(exp)
Y = np.stack([df.branin_a.values, df.branin_b.values]).T
Y = torch.from_numpy(Y)
Y[:, 0] *= -1
pareto_Y = Y[is_non_dominated(Y)]
nadir = pareto_Y.min(dim=0).values
self.assertTrue(
np.all(
np.array([-obj_thresholds[0].bound, obj_thresholds[1].bound])
< nadir.numpy()
)
)
# test using MTGP
sobol_generator = get_sobol(
search_space=exp.search_space,
seed=TEST_SOBOL_SEED,
# set initial position equal to the number of sobol arms generated
# so far. This means that new sobol arms will complement the previous
# arms in a space-filling fashion
init_position=len(exp.arms_by_name) - 1,
)
sobol_run = sobol_generator.gen(n=2)
trial = exp.new_batch_trial(optimize_for_power=True)
trial.add_generator_run(sobol_run)
trial.mark_running(no_runner_required=True).mark_completed()
data = exp.fetch_data()
torch.manual_seed(0) # make model fitting deterministic
modelbridge = TorchModelBridge(
search_space=exp.search_space,
model=MultiObjectiveBotorchModel(),
optimization_config=exp.optimization_config,
transforms=ST_MTGP_trans,
experiment=exp,
data=data,
)
fixed_features = ObservationFeatures(parameters={}, trial_index=1)
expected_base_gen_args = modelbridge._get_transformed_gen_args(
search_space=search_space.clone(),
optimization_config=exp.optimization_config,
fixed_features=fixed_features,
)
with ExitStack() as es:
mock_model_infer_obj_t = es.enter_context(
patch(
"ax.modelbridge.torch.infer_objective_thresholds",
wraps=infer_objective_thresholds,
)
)
mock_untransform_objective_thresholds = es.enter_context(
patch.object(
modelbridge,
"_untransform_objective_thresholds",
wraps=modelbridge._untransform_objective_thresholds,
)
)
obj_thresholds = modelbridge.infer_objective_thresholds(
search_space=search_space,
optimization_config=exp.optimization_config,
fixed_features=fixed_features,
)
ckwargs = mock_model_infer_obj_t.call_args[1]
self.assertEqual(ckwargs["fixed_features"], {2: 1.0})
mock_untransform_objective_thresholds.assert_called_once()
ckwargs = mock_untransform_objective_thresholds.call_args[1]
self.assertEqual(ckwargs["fixed_features"], {2: 1.0})
self.assertEqual(obj_thresholds[0].metric.name, "branin_a")
self.assertEqual(obj_thresholds[1].metric.name, "branin_b")
self.assertEqual(obj_thresholds[0].op, ComparisonOp.GEQ)
self.assertEqual(obj_thresholds[1].op, ComparisonOp.GEQ)
self.assertFalse(obj_thresholds[0].relative)
self.assertFalse(obj_thresholds[1].relative)
df = exp_to_df(exp)
trial_mask = df.trial_index == 1
Y = np.stack([df.branin_a.values[trial_mask], df.branin_b.values[trial_mask]]).T
Y = torch.from_numpy(Y)
pareto_Y = Y[is_non_dominated(Y)]
nadir = pareto_Y.min(dim=0).values
self.assertTrue(
np.all(
np.array([obj_thresholds[0].bound, obj_thresholds[1].bound])
< nadir.numpy()
)
)
def test_infer_objective_thresholds(self, _, cuda=False):
# lightweight test
exp = get_branin_experiment_with_multi_objective(
has_optimization_config=True,
with_batch=True,
with_status_quo=True,
)
for trial in exp.trials.values():
trial.mark_running(no_runner_required=True).mark_completed()
exp.attach_data(
get_branin_data_multi_objective(trial_indices=exp.trials.keys()))
data = exp.fetch_data()
modelbridge = MultiObjectiveTorchModelBridge(
search_space=exp.search_space,
model=MultiObjectiveBotorchModel(),
optimization_config=exp.optimization_config,
transforms=Cont_X_trans + Y_trans,
torch_device=torch.device("cuda" if cuda else "cpu"),
experiment=exp,
data=data,
)
fixed_features = ObservationFeatures(parameters={"x1": 0.0})
search_space = exp.search_space.clone()
param_constraints = [
ParameterConstraint(constraint_dict={"x1": 1.0}, bound=10.0)
]
outcome_constraints = [
OutcomeConstraint(
metric=exp.metrics["branin_a"],
op=ComparisonOp.GEQ,
bound=-40.0,
relative=False,
)
]
search_space.add_parameter_constraints(param_constraints)
exp.optimization_config.outcome_constraints = outcome_constraints
oc = exp.optimization_config.clone()
oc.objective._objectives[0].minimize = True
expected_base_gen_args = modelbridge._get_transformed_gen_args(
search_space=search_space.clone(),
optimization_config=oc,
fixed_features=fixed_features,
)
with ExitStack() as es:
mock_model_infer_obj_t = es.enter_context(
patch(
"ax.modelbridge.multi_objective_torch.infer_objective_thresholds",
wraps=infer_objective_thresholds,
))
mock_get_transformed_gen_args = es.enter_context(
patch.object(
modelbridge,
"_get_transformed_gen_args",
wraps=modelbridge._get_transformed_gen_args,
))
mock_get_transformed_model_gen_args = es.enter_context(
patch.object(
modelbridge,
"_get_transformed_model_gen_args",
wraps=modelbridge._get_transformed_model_gen_args,
))
mock_untransform_objective_thresholds = es.enter_context(
patch.object(
modelbridge,
"untransform_objective_thresholds",
wraps=modelbridge.untransform_objective_thresholds,
))
obj_thresholds = modelbridge.infer_objective_thresholds(
search_space=search_space,
optimization_config=oc,
fixed_features=fixed_features,
)
expected_obj_weights = torch.tensor([-1.0, 1.0])
ckwargs = mock_model_infer_obj_t.call_args[1]
self.assertTrue(
torch.equal(ckwargs["objective_weights"],
expected_obj_weights))
# check that transforms have been applied (at least UnitX)
self.assertEqual(ckwargs["bounds"], [(0.0, 1.0), (0.0, 1.0)])
oc = ckwargs["outcome_constraints"]
self.assertTrue(torch.equal(oc[0], torch.tensor([[-1.0, 0.0]])))
self.assertTrue(torch.equal(oc[1], torch.tensor([[45.0]])))
lc = ckwargs["linear_constraints"]
self.assertTrue(torch.equal(lc[0], torch.tensor([[15.0, 0.0]])))
self.assertTrue(torch.equal(lc[1], torch.tensor([[15.0]])))
self.assertEqual(ckwargs["fixed_features"], {0: 1.0 / 3.0})
mock_get_transformed_gen_args.assert_called_once()
mock_get_transformed_model_gen_args.assert_called_once_with(
search_space=expected_base_gen_args.search_space,
fixed_features=expected_base_gen_args.fixed_features,
pending_observations=expected_base_gen_args.
pending_observations,
optimization_config=expected_base_gen_args.optimization_config,
)
mock_untransform_objective_thresholds.assert_called_once()
ckwargs = mock_untransform_objective_thresholds.call_args[1]
self.assertTrue(
torch.equal(ckwargs["objective_weights"],
expected_obj_weights))
self.assertEqual(ckwargs["bounds"], [(0.0, 1.0), (0.0, 1.0)])
self.assertEqual(ckwargs["fixed_features"], {0: 1.0 / 3.0})
self.assertEqual(obj_thresholds[0].metric.name, "branin_a")
self.assertEqual(obj_thresholds[1].metric.name, "branin_b")
self.assertEqual(obj_thresholds[0].op, ComparisonOp.LEQ)
self.assertEqual(obj_thresholds[1].op, ComparisonOp.GEQ)
self.assertFalse(obj_thresholds[0].relative)
self.assertFalse(obj_thresholds[1].relative)
df = exp_to_df(exp)
Y = np.stack([df.branin_a.values, df.branin_b.values]).T
Y = torch.from_numpy(Y)
Y[:, 0] *= -1
pareto_Y = Y[is_non_dominated(Y)]
nadir = pareto_Y.min(dim=0).values
self.assertTrue(
np.all(
np.array([-obj_thresholds[0].bound, obj_thresholds[1].bound]) <
nadir.numpy()))
# test using MTGP
sobol_generator = get_sobol(search_space=exp.search_space)
sobol_run = sobol_generator.gen(n=5)
trial = exp.new_batch_trial(optimize_for_power=True)
trial.add_generator_run(sobol_run)
trial.mark_running(no_runner_required=True).mark_completed()
data = exp.fetch_data()
modelbridge = MultiObjectiveTorchModelBridge(
search_space=exp.search_space,
model=MultiObjectiveBotorchModel(),
optimization_config=exp.optimization_config,
transforms=ST_MTGP_trans,
experiment=exp,
data=data,
)
fixed_features = ObservationFeatures(parameters={}, trial_index=1)
expected_base_gen_args = modelbridge._get_transformed_gen_args(
search_space=search_space.clone(),
optimization_config=exp.optimization_config,
fixed_features=fixed_features,
)
with self.assertRaises(ValueError):
# Check that a ValueError is raised when MTGP is being used
# and trial_index is not specified as a fixed features.
# Note: this error is raised by StratifiedStandardizeY
modelbridge.infer_objective_thresholds(
search_space=search_space,
optimization_config=exp.optimization_config,
)
with ExitStack() as es:
mock_model_infer_obj_t = es.enter_context(
patch(
"ax.modelbridge.multi_objective_torch.infer_objective_thresholds",
wraps=infer_objective_thresholds,
))
mock_untransform_objective_thresholds = es.enter_context(
patch.object(
modelbridge,
"untransform_objective_thresholds",
wraps=modelbridge.untransform_objective_thresholds,
))
obj_thresholds = modelbridge.infer_objective_thresholds(
search_space=search_space,
optimization_config=exp.optimization_config,
fixed_features=fixed_features,
)
ckwargs = mock_model_infer_obj_t.call_args[1]
self.assertEqual(ckwargs["fixed_features"], {2: 1.0})
mock_untransform_objective_thresholds.assert_called_once()
ckwargs = mock_untransform_objective_thresholds.call_args[1]
self.assertEqual(ckwargs["fixed_features"], {2: 1.0})
self.assertEqual(obj_thresholds[0].metric.name, "branin_a")
self.assertEqual(obj_thresholds[1].metric.name, "branin_b")
self.assertEqual(obj_thresholds[0].op, ComparisonOp.GEQ)
self.assertEqual(obj_thresholds[1].op, ComparisonOp.GEQ)
self.assertFalse(obj_thresholds[0].relative)
self.assertFalse(obj_thresholds[1].relative)
df = exp_to_df(exp)
trial_mask = df.trial_index == 1
Y = np.stack(
[df.branin_a.values[trial_mask], df.branin_b.values[trial_mask]]).T
Y = torch.from_numpy(Y)
pareto_Y = Y[is_non_dominated(Y)]
nadir = pareto_Y.min(dim=0).values
self.assertTrue(
np.all(
np.array([obj_thresholds[0].bound, obj_thresholds[1].bound]) <
nadir.numpy()))
def test_mvar(self):
with self.assertRaises(ValueError):
MVaR(n_w=5, alpha=3.0)
def set_equals(t1: Tensor, t2: Tensor) -> bool:
r"""Check if two `k x m`-dim tensors are equivalent after possibly
reordering the `k` dimension. Ignores duplicate entries.
"""
t1 = t1.unique(dim=0)
t2 = t2.unique(dim=0)
if t1.shape != t2.shape:
return False
equals_sum = (t1.unsqueeze(-2) == t2).all(dim=-1).sum(dim=-1)
return torch.equal(equals_sum, torch.ones_like(equals_sum))
for dtype in (torch.float, torch.double):
tkwargs = {"device": self.device, "dtype": dtype}
mvar = MVaR(n_w=5, alpha=0.6)
# a simple negatively correlated example
Y = torch.stack(
[torch.linspace(1, 5, 5), torch.linspace(5, 1, 5)],
dim=-1,
).to(**tkwargs)
expected_set = torch.stack(
[torch.linspace(1, 3, 3), torch.linspace(3, 1, 3)],
dim=-1,
).to(Y)
# check that both versions produce the correct set
cpu_mvar = mvar.get_mvar_set_cpu(Y) # For 2d input, returns k x m
gpu_mvar = mvar.get_mvar_set_gpu(Y)[0] # returns a batch list of k x m
self.assertTrue(set_equals(cpu_mvar, gpu_mvar))
self.assertTrue(set_equals(cpu_mvar, expected_set))
# check that the `filter_dominated` works correctly
mvar = MVaR(
n_w=5,
alpha=0.4,
filter_dominated=False,
)
# negating the input to treat large values as undesirable
Y = -torch.tensor(
[
[1, 4],
[2, 3],
[3, 2],
[4, 1],
[3.5, 3.5],
],
**tkwargs
)
cpu_mvar = mvar.get_mvar_set_cpu(Y)
gpu_mvar = mvar.get_mvar_set_gpu(Y)[0]
self.assertTrue(set_equals(cpu_mvar, gpu_mvar))
# negating here as well
expected_w_dominated = -torch.tensor(
[
[2, 4],
[3, 3],
[3.5, 3],
[3, 3.5],
[4, 2],
],
**tkwargs
)
self.assertTrue(set_equals(cpu_mvar, expected_w_dominated))
expected_non_dominated = expected_w_dominated[
is_non_dominated(expected_w_dominated)
]
mvar.filter_dominated = True
cpu_mvar = mvar.get_mvar_set_cpu(Y)
gpu_mvar = mvar.get_mvar_set_gpu(Y)[0]
self.assertTrue(set_equals(cpu_mvar, gpu_mvar))
self.assertTrue(set_equals(cpu_mvar, expected_non_dominated))
# test batched w/ random input
mvar = MVaR(
n_w=10,
alpha=0.5,
filter_dominated=False,
)
Y = torch.rand(4, 10, 2, **tkwargs)
cpu_mvar = mvar.get_mvar_set_cpu(Y)
gpu_mvar = mvar.get_mvar_set_gpu(Y)
# check that the two agree
self.assertTrue(
all([set_equals(cpu_mvar[i], gpu_mvar[i]) for i in range(4)])
)
# check that the MVaR is dominated by `alpha` fraction (maximization).
dominated_count = (Y[0].unsqueeze(-2) >= cpu_mvar[0]).all(dim=-1).sum(dim=0)
expected_count = (
torch.ones(cpu_mvar[0].shape[0], device=self.device, dtype=torch.long)
* 5
)
self.assertTrue(torch.equal(dominated_count, expected_count))
# test forward pass
# with `expectation=True`
mvar = MVaR(
n_w=10,
alpha=0.5,
expectation=True,
)
samples = torch.rand(2, 20, 2, **tkwargs)
mvar_exp = mvar(samples)
expected = [
mvar.get_mvar_set_cpu(Y).mean(dim=0) for Y in samples.view(4, 10, 2)
]
self.assertTrue(
torch.allclose(mvar_exp, torch.stack(expected).view(2, 2, 2))
)
# m > 2
samples = torch.rand(2, 20, 3, **tkwargs)
mvar_exp = mvar(samples)
expected = [
mvar.get_mvar_set_gpu(Y)[0].mean(dim=0) for Y in samples.view(4, 10, 3)
]
self.assertTrue(torch.equal(mvar_exp, torch.stack(expected).view(2, 2, 3)))
# with `expectation=False`
mvar = MVaR(
n_w=10,
alpha=0.5,
expectation=False,
pad_to_n_w=True,
)
samples = torch.rand(2, 20, 2, **tkwargs)
mvar_vals = mvar(samples)
self.assertTrue(mvar_vals.shape == samples.shape)
expected = [mvar.get_mvar_set_cpu(Y) for Y in samples.view(4, 10, 2)]
for i in range(4):
batch_idx = i // 2
q_idx_start = 10 * (i % 2)
expected_ = expected[i]
# check that the actual values are there
self.assertTrue(
set_equals(
mvar_vals[
batch_idx, q_idx_start : q_idx_start + expected_.shape[0]
],
expected_,
)
)
# check for correct padding
self.assertTrue(
torch.equal(
mvar_vals[
batch_idx,
q_idx_start + expected_.shape[0] : q_idx_start + 10,
],
mvar_vals[
batch_idx, q_idx_start + expected_.shape[0] - 1
].expand(10 - expected_.shape[0], -1),
)
)
# Test the no-exact alpha level points case.
# This happens when there are duplicates in the input.
Y = torch.ones(10, 2, **tkwargs)
cpu_mvar = mvar.get_mvar_set_cpu(Y)
gpu_mvar = mvar.get_mvar_set_gpu(Y)[0]
self.assertTrue(torch.equal(cpu_mvar, Y[:1]))
self.assertTrue(torch.equal(gpu_mvar, Y[:1]))
# Test grad warning
with self.assertWarnsRegex(RuntimeWarning, "requires grad"):
mvar(Y.requires_grad_())
def infer_objective_thresholds(
model: Model,
objective_weights: Tensor, # objective_directions
bounds: Optional[List[Tuple[float, float]]] = None,
outcome_constraints: Optional[Tuple[Tensor, Tensor]] = None,
linear_constraints: Optional[Tuple[Tensor, Tensor]] = None,
fixed_features: Optional[Dict[int, float]] = None,
subset_idcs: Optional[Tensor] = None,
Xs: Optional[List[Tensor]] = None,
X_observed: Optional[Tensor] = None,
) -> Tensor:
"""Infer objective thresholds.
This method uses the model-estimated Pareto frontier over the in-sample points
to infer absolute (not relativized) objective thresholds.
This uses a heuristic that sets the objective threshold to be a scaled nadir
point, where the nadir point is scaled back based on the range of each
objective across the current in-sample Pareto frontier.
See `botorch.utils.multi_objective.hypervolume.infer_reference_point` for
details on the heuristic.
Args:
model: A fitted botorch Model.
objective_weights: The objective is to maximize a weighted sum of
the columns of f(x). These are the weights. These should not
be subsetted.
bounds: A list of (lower, upper) tuples for each column of X.
outcome_constraints: A tuple of (A, b). For k outcome constraints
and m outputs at f(x), A is (k x m) and b is (k x 1) such that
A f(x) <= b. These should not be subsetted.
linear_constraints: A tuple of (A, b). For k linear constraints on
d-dimensional x, A is (k x d) and b is (k x 1) such that
A x <= b.
fixed_features: A map {feature_index: value} for features that
should be fixed to a particular value during generation.
subset_idcs: The indices of the outcomes that are modeled by the
provided model. If subset_idcs not None, this method infers
whether the model is subsetted.
Xs: A list of m (k_i x d) feature tensors X. Number of rows k_i can
vary from i=1,...,m.
X_observed: A `n x d`-dim tensor of in-sample points to use for
determining the current in-sample Pareto frontier.
Returns:
A `m`-dim tensor of objective thresholds, where the objective
threshold is `nan` if the outcome is not an objective.
"""
if X_observed is None:
if bounds is None:
raise ValueError("bounds is required if X_observed is None.")
elif Xs is None:
raise ValueError("Xs is required if X_observed is None.")
_, X_observed = _get_X_pending_and_observed(
Xs=Xs,
objective_weights=objective_weights,
outcome_constraints=outcome_constraints,
bounds=bounds,
linear_constraints=linear_constraints,
fixed_features=fixed_features,
)
num_outcomes = objective_weights.shape[0]
if subset_idcs is None:
# check if only a subset of outcomes are modeled
nonzero = objective_weights != 0
if outcome_constraints is not None:
A, _ = outcome_constraints
nonzero = nonzero | torch.any(A != 0, dim=0)
expected_subset_idcs = nonzero.nonzero().view(-1)
if model.num_outputs > expected_subset_idcs.numel():
# subset the model so that we only compute the posterior
# over the relevant outcomes
subset_model_results = subset_model(
model=model,
objective_weights=objective_weights,
outcome_constraints=outcome_constraints,
)
model = subset_model_results.model
objective_weights = subset_model_results.objective_weights
outcome_constraints = subset_model_results.outcome_constraints
subset_idcs = subset_model_results.indices
else:
# model is already subsetted.
subset_idcs = expected_subset_idcs
# subset objective weights and outcome constraints
objective_weights = objective_weights[subset_idcs]
if outcome_constraints is not None:
outcome_constraints = (
outcome_constraints[0][:, subset_idcs],
outcome_constraints[1],
)
else:
objective_weights = objective_weights[subset_idcs]
if outcome_constraints is not None:
outcome_constraints = (
outcome_constraints[0][:, subset_idcs],
outcome_constraints[1],
)
with torch.no_grad():
pred = not_none(model).posterior(not_none(X_observed)).mean
if outcome_constraints is not None:
cons_tfs = get_outcome_constraint_transforms(outcome_constraints)
# pyre-ignore [16]
feas = torch.stack([c(pred) <= 0 for c in cons_tfs],
dim=-1).all(dim=-1)
pred = pred[feas]
if pred.shape[0] == 0:
raise AxError("There are no feasible observed points.")
obj_mask = objective_weights.nonzero().view(-1)
obj_weights_subset = objective_weights[obj_mask]
obj = pred[..., obj_mask] * obj_weights_subset
pareto_obj = obj[is_non_dominated(obj)]
objective_thresholds = infer_reference_point(
pareto_Y=pareto_obj,
scale=0.1,
)
# multiply by objective weights to return objective thresholds in the
# unweighted space
objective_thresholds = objective_thresholds * obj_weights_subset
full_objective_thresholds = torch.full(
(num_outcomes, ),
float("nan"),
dtype=objective_weights.dtype,
device=objective_weights.device,
)
obj_idcs = subset_idcs[obj_mask]
full_objective_thresholds[obj_idcs] = objective_thresholds.clone()
return full_objective_thresholds
def get_mvar_set_gpu(self, Y: Tensor) -> Tensor:
r"""Find MVaR set based on the definition in [Prekopa2012MVaR]_.
NOTE: This is much faster on GPU than the alternative but it scales very poorly
on CPU as `n_w` increases. This should be preferred if a GPU is available or
when `n_w <= 64`. In addition, this supports `m >= 2` outcomes (vs `m = 2` for
the CPU version) and it should be used if `m > 2`.
This first calculates the CDF for each point on the extended domain of the
random variable (the grid defined by the given samples), then takes the
values with CDF equal to (rounded if necessary) `alpha`. The non-dominated
subset of these form the MVaR set.
Args:
Y: A `batch x n_w x m`-dim tensor of observations.
Returns:
A `batch` length list of `k x m`-dim tensor of MVaR values, where `k`
depends on the corresponding batch inputs. Note that MVaR values in general
are not in-sample points.
"""
if Y.dim() == 2:
Y = Y.unsqueeze(0)
batch, m = Y.shape[0], Y.shape[-1]
# Note that points in MVaR are bounded from above by the
# independent VaR of each objective. Hence, we only need to
# consider the unique outcomes that are less than or equal to
# the VaR of the independent objectives
var_alpha_idx = ceil(self.alpha * self.n_w) - 1
n_points = Y.shape[-2] - var_alpha_idx
Y_sorted = Y.topk(n_points, dim=-2, largest=False).values
# `y_grid` is the grid formed by all inputs in each batch.
if m == 2:
# This is significantly faster but only works with m=2.
y_grid = torch.stack(
[
Y_sorted[..., 0].repeat_interleave(repeats=n_points,
dim=-1),
Y_sorted[..., 1].repeat(1, n_points),
],
dim=-1,
)
else:
y_grid = torch.stack(
[
torch.stack(
torch.meshgrid([Y_sorted[b, :, i] for i in range(m)]),
dim=-1,
).view(-1, m) for b in range(batch)
],
dim=0,
)
# Get the non-normalized CDF.
cdf = (Y.unsqueeze(-2) >= y_grid.unsqueeze(-3)).all(dim=-1).sum(dim=-2)
# Get the alpha level points
alpha_count = ceil(self.alpha * self.n_w)
# NOTE: Need to loop here since mvar may have different shapes.
mvar = []
for b in range(batch):
alpha_level_points = y_grid[b][cdf[b] == alpha_count]
# If there are no exact alpha level points, get the smallest alpha' > alpha
# and find the corresponding alpha level indices.
if alpha_level_points.numel() == 0:
min_greater_than_alpha = cdf[b][cdf[b] > alpha_count].min()
alpha_level_points = y_grid[b][cdf[b] ==
min_greater_than_alpha]
# MVaR is the non-dominated subset of alpha level points.
if self.filter_dominated:
mask = is_non_dominated(alpha_level_points)
mvar.append(alpha_level_points[mask])
else:
mvar.append(alpha_level_points)
return mvar
def pareto_frontier_evaluator(
model: TorchModel,
objective_weights: Tensor,
objective_thresholds: Optional[Tensor] = None,
X: Optional[Tensor] = None,
Y: Optional[Tensor] = None,
Yvar: Optional[Tensor] = None,
outcome_constraints: Optional[Tuple[Tensor, Tensor]] = None,
) -> Tuple[Tensor, Tensor, Tensor]:
"""Return outcomes predicted to lie on a pareto frontier.
Given a model and a points to evaluate use the model to predict which points
lie on the pareto frontier.
Args:
model: Model used to predict outcomes.
objective_weights: A `m` tensor of values indicating the weight to put
on different outcomes. For pareto frontiers only the sign matters.
objective_thresholds: A tensor containing thresholds forming a reference point
from which to calculate pareto frontier hypervolume. Points that do not
dominate the objective_thresholds contribute nothing to hypervolume.
X: A `n x d` tensor of features to evaluate.
Y: A `n x m` tensor of outcomes to use instead of predictions.
Yvar: A `n x m x m` tensor of input covariances (NaN if unobserved).
outcome_constraints: A tuple of (A, b). For k outcome constraints
and m outputs at f(x), A is (k x m) and b is (k x 1) such that
A f(x) <= b.
Returns:
3-element tuple containing
- A `j x m` tensor of outcome on the pareto frontier. j is the number
of frontier points.
- A `j x m x m` tensor of predictive covariances.
cov[j, m1, m2] is Cov[m1@j, m2@j].
- A `j` tensor of the index of each frontier point in the input Y.
"""
if X is not None:
Y, Yvar = model.predict(X)
elif Y is None or Yvar is None:
raise ValueError(
"Requires `X` to predict or both `Y` and `Yvar` to select a subset of "
"points on the pareto frontier.")
# Apply objective_weights to outcomes and objective_thresholds.
# If objective_thresholds is not None use a dummy tensor of zeros.
(
obj,
weighted_objective_thresholds,
) = get_weighted_mc_objective_and_objective_thresholds(
objective_weights=objective_weights,
objective_thresholds=(objective_thresholds
if objective_thresholds is not None else
torch.zeros(objective_weights.shape)),
)
Y_obj = obj(Y)
indx_frontier = torch.arange(Y.shape[0], dtype=torch.long, device=Y.device)
# Filter Y, Yvar, Y_obj to items that dominate all objective thresholds
if objective_thresholds is not None:
objective_thresholds_mask = (Y_obj >=
weighted_objective_thresholds).all(dim=1)
Y = Y[objective_thresholds_mask]
Yvar = Yvar[objective_thresholds_mask]
Y_obj = Y_obj[objective_thresholds_mask]
indx_frontier = indx_frontier[objective_thresholds_mask]
# Get feasible points that do not violate outcome_constraints
if outcome_constraints is not None:
cons_tfs = get_outcome_constraint_transforms(outcome_constraints)
# pyre-ignore [16]
feas = torch.stack([c(Y) <= 0 for c in cons_tfs], dim=-1).all(dim=-1)
Y = Y[feas]
Yvar = Yvar[feas]
Y_obj = Y_obj[feas]
indx_frontier = indx_frontier[feas]
if Y.shape[0] == 0:
# if there are no feasible points that are better than the reference point
# return empty tensors
return Y, Yvar, indx_frontier
# calculate pareto front with only objective outcomes:
frontier_mask = is_non_dominated(Y_obj)
# Apply masks
Y_frontier = Y[frontier_mask]
Yvar_frontier = Yvar[frontier_mask]
indx_frontier = indx_frontier[frontier_mask]
return Y_frontier, Yvar_frontier, indx_frontier
def sample_points_around_best(
acq_function: AcquisitionFunction,
n_discrete_points: int,
sigma: float,
bounds: Tensor,
best_pct: float = 5.0,
subset_sigma: float = 1e-1,
prob_perturb: Optional[float] = None,
) -> Optional[Tensor]:
r"""Find best points and sample nearby points.
Args:
acq_function: The acquisition function.
n_discrete_points: The number of points to sample.
sigma: The standard deviation of the additive gaussian noise for
perturbing the best points.
bounds: A `2 x d`-dim tensor containing the bounds.
best_pct: The percentage of best points to perturb.
subset_sigma: The standard deviation of the additive gaussian
noise for perturbing a subset of dimensions of the best points.
prob_perturb: The probability of perturbing each dimension.
Returns:
An optional `n_discrete_points x d`-dim tensor containing the
sampled points. This is None if no baseline points are found.
"""
X = get_X_baseline(acq_function=acq_function)
if X is None:
return
with torch.no_grad():
try:
posterior = acq_function.model.posterior(X)
except AttributeError:
warnings.warn(
"Failed to sample around previous best points.",
BotorchWarning,
)
return
mean = posterior.mean
while mean.ndim > 2:
# take average over batch dims
mean = mean.mean(dim=0)
try:
f_pred = acq_function.objective(mean)
# Some acquisition functions do not have an objective
# and for some acquisition functions the objective is None
except (AttributeError, TypeError):
f_pred = mean
if hasattr(acq_function, "maximize"):
# make sure that the optimiztaion direction is set properly
if not acq_function.maximize:
f_pred = -f_pred
try:
# handle constraints for EHVI-based acquisition functions
constraints = acq_function.constraints
if constraints is not None:
neg_violation = -torch.stack(
[c(mean).clamp_min(0.0) for c in constraints], dim=-1
).sum(dim=-1)
feas = neg_violation == 0
if feas.any():
f_pred[~feas] = float("-inf")
else:
# set objective equal to negative violation
f_pred = neg_violation
except AttributeError:
pass
if f_pred.ndim == mean.ndim and f_pred.shape[-1] > 1:
# multi-objective
# find pareto set
is_pareto = is_non_dominated(f_pred)
best_X = X[is_pareto]
else:
if f_pred.shape[-1] == 1:
f_pred = f_pred.squeeze(-1)
n_best = max(1, round(X.shape[0] * best_pct / 100))
# the view() is to ensure that best_idcs is not a scalar tensor
best_idcs = torch.topk(f_pred, n_best).indices.view(-1)
best_X = X[best_idcs]
n_trunc_normal_points = (
n_discrete_points // 2 if best_X.shape[-1] >= 20 else n_discrete_points
)
perturbed_X = sample_truncated_normal_perturbations(
X=best_X,
n_discrete_points=n_trunc_normal_points,
sigma=sigma,
bounds=bounds,
)
if best_X.shape[-1] > 20 or prob_perturb is not None:
perturbed_subset_dims_X = sample_perturbed_subset_dims(
X=best_X,
bounds=bounds,
# ensure that we return n_discrete_points
n_discrete_points=n_discrete_points - n_trunc_normal_points,
sigma=sigma,
prob_perturb=prob_perturb,
)
perturbed_X = torch.cat([perturbed_X, perturbed_subset_dims_X], dim=0)
# shuffle points
perm = torch.randperm(perturbed_X.shape[0], device=X.device)
perturbed_X = perturbed_X[perm]
return perturbed_X
def _pad_batch_pareto_frontier(
Y: Tensor,
ref_point: Tensor,
is_pareto: bool = False,
feasibility_mask: Optional[Tensor] = None,
) -> Tensor:
r"""Get a batch Pareto frontier by padding the pareto frontier with repeated points.
This assumes maximization.
Args:
Y: A `(batch_shape) x n x m`-dim tensor of points
ref_point: a `(batch_shape) x m`-dim tensor containing the reference point
is_pareto: a boolean indicating whether the points in Y are already
non-dominated.
feasibility_mask: A `(batch_shape) x n`-dim tensor of booleans indicating
whether each point is feasible.
Returns:
A `(batch_shape) x max_num_pareto x m`-dim tensor of padded Pareto
frontiers.
"""
tkwargs = {"dtype": Y.dtype, "device": Y.device}
ref_point = ref_point.unsqueeze(-2)
batch_shape = Y.shape[:-2]
if len(batch_shape) > 1:
raise UnsupportedError(
"_pad_batch_pareto_frontier only supports a single "
f"batch dimension, but got {len(batch_shape)} "
"batch dimensions.")
if feasibility_mask is not None:
# set infeasible points to be the reference point (corresponding to the batch)
Y = torch.where(feasibility_mask.unsqueeze(-1), Y, ref_point)
if not is_pareto:
pareto_mask = is_non_dominated(Y)
else:
pareto_mask = torch.ones(Y.shape[:-1],
dtype=torch.bool,
device=Y.device)
better_than_ref = (Y > ref_point).all(dim=-1)
# is_non_dominated assumes maximization
# TODO: filter out points that are worse than the reference point first here
pareto_mask = pareto_mask & better_than_ref
if len(batch_shape) == 0:
return Y[pareto_mask]
# Note: in the batch case, the Pareto frontier is padded by repeating
# a Pareto point. This ensures that the padded box-decomposition has
# the same number of points, which enables fast batch operations.
max_n_pareto = pareto_mask.sum(dim=-1).max().item()
pareto_Y = torch.empty(*batch_shape, max_n_pareto, Y.shape[-1], **tkwargs)
for i, pareto_i in enumerate(pareto_mask):
pareto_i = Y[i, pareto_mask[i]]
n_pareto = pareto_i.shape[0]
if n_pareto > 0:
pareto_Y[i, :n_pareto] = pareto_i
# pad pareto_Y, so that all batches have the same size Pareto set
pareto_Y[i, n_pareto:] = pareto_i[-1]
else:
# if there are no pareto points in this batch, use the reference
# point
pareto_Y[i, :] = ref_point[i]
return pareto_Y
print(f"\nTrial {trial:>2} of {N_TRIALS} ", end="")
hvs_qparego, hvs_qehvi, hvs_random = [], [], []
# call helper functions to generate initial training data and initialize model
train_x_qparego, train_obj_qparego = generate_initial_data(n=6)
mll_qparego, model_qparego = initialize_model(train_x_qparego,
train_obj_qparego)
train_x_qehvi, train_obj_qehvi = train_x_qparego, train_obj_qparego
train_x_random, train_obj_random = train_x_qparego, train_obj_qparego
# compute hypervolume
mll_qehvi, model_qehvi = initialize_model(train_x_qehvi, train_obj_qehvi)
# compute pareto front
pareto_mask = is_non_dominated(train_obj_qparego)
pareto_y = train_obj_qparego[pareto_mask]
# compute hypervolume
volume = hv.compute(pareto_y)
hvs_qparego.append(volume)
hvs_qehvi.append(volume)
hvs_random.append(volume)
# run N_BATCH rounds of BayesOpt after the initial random batch
for iteration in range(1, N_BATCH + 1):
t0 = time.time()
# fit the models
