Allow TRs to be created with empty/single region

tests/unit/acquisition/test_rule.py

@@ -1274,6 +1274,41 @@ def test_trust_region_box_update_size(success: bool) -> None:
     npt.assert_allclose(trb.upper, np.minimum(trb.location + trb.eps, search_space.upper))
 
 
+# Check multi trust region works when no subspace is provided.
+@pytest.mark.parametrize(
+    "rule, exp_num_subspaces",
+    [
+        (EfficientGlobalOptimization(), 1),
+        (EfficientGlobalOptimization(ParallelContinuousThompsonSampling(), num_query_points=2), 2),
+        (RandomSampling(num_query_points=2), 1),
+    ],
+)
+def test_multi_trust_region_box_no_subspace(
+    rule: AcquisitionRule[TensorType, SearchSpace, ProbabilisticModel],
+    exp_num_subspaces: int,
+) -> None:
+    search_space = Box([0.0, 0.0], [1.0, 1.0])
+    mtb = BatchTrustRegionBox(rule=rule)
+    mtb.acquire(search_space, {})
+
+    assert mtb._tags is not None
+    assert mtb._init_subspaces is not None
+    assert len(mtb._init_subspaces) == exp_num_subspaces
+    for i, (subspace, tag) in enumerate(zip(mtb._init_subspaces, mtb._tags)):
+        assert isinstance(subspace, SingleObjectiveTrustRegionBox)
+        assert subspace.global_search_space == search_space
+        assert tag == f"{i}"
+
+
+# Check multi trust region works when a single subspace is provided.
+def test_multi_trust_region_box_single_subspace() -> None:
+    search_space = Box([0.0, 0.0], [1.0, 1.0])
+    subspace = SingleObjectiveTrustRegionBox(search_space)
+    mtb = BatchTrustRegionBox(subspace)  # type: ignore[var-annotated]
+    assert mtb._init_subspaces == (subspace,)
+    assert mtb._tags == ("0",)
+
+
 # When state is None, acquire returns a multi search space of the correct type.
 def test_multi_trust_region_box_acquire_no_state() -> None:
     search_space = Box([0.0, 0.0], [1.0, 1.0])

trieste/acquisition/rule.py

@@ -1166,19 +1166,30 @@ def __deepcopy__(self, memo: dict[int, object]) -> BatchTrustRegion.State:
 
     def __init__(
         self: "BatchTrustRegion[ProbabilisticModelType, UpdatableTrustRegionType]",
-        init_subspaces: Sequence[UpdatableTrustRegionType],
+        init_subspaces: Union[
+            None, UpdatableTrustRegionType, Sequence[UpdatableTrustRegionType]
+        ] = None,
         rule: AcquisitionRule[TensorType, SearchSpace, ProbabilisticModelType] | None = None,
     ):
         """
-        :param init_subspaces: The initial search spaces for each trust region.
+        :param init_subspaces: The initial search spaces for each trust region. If `None`, default
+            subspaces of type :class:`UpdatableTrustRegionType` will be created, with length
+            equal to the number of query points in the base `rule`.
         :param rule: The acquisition rule that defines how to search for a new query point in each
             subspace. Defaults to :class:`EfficientGlobalOptimization` with default arguments.
         """
         if rule is None:
             rule = EfficientGlobalOptimization()
 
-        self._init_subspaces = tuple(init_subspaces)
-        self._tags = tuple([str(index) for index in range(len(init_subspaces))])
+        # If init_subspaces are not provided, leave it to the subclasses to create them.
+        self._init_subspaces = None
+        self._tags = None
+        if init_subspaces is not None:
+            if not isinstance(init_subspaces, Sequence):
+                init_subspaces = [init_subspaces]
+            self._init_subspaces = tuple(init_subspaces)
+            self._tags = tuple([str(index) for index in range(len(init_subspaces))])
+
         self._rule = rule
 
     def __repr__(self) -> str:
@@ -1202,6 +1213,11 @@ def state_func(
 
             Use the rule to acquire points from the acquisition space.
             """
+
+            # Subspaces should be set by the time we call `acquire`.
+            assert self._tags is not None
+            assert self._init_subspaces is not None
+
             # If state is set, the tags should be the same as the tags of the acquisition space
             # in the state.
             if state is not None:
@@ -1399,6 +1415,28 @@ class BatchTrustRegionBox(BatchTrustRegion[ProbabilisticModelType, SingleObjecti
     This is intended to be used for single-objective optimization with batching.
     """
 
+    def acquire(
+        self,
+        search_space: SearchSpace,
+        models: Mapping[Tag, ProbabilisticModelType],
+        datasets: Optional[Mapping[Tag, Dataset]] = None,
+    ) -> types.State[BatchTrustRegion.State | None, TensorType]:
+        if self._init_subspaces is None:
+            # If no initial subspaces were provided, create N default subspaces, where N is the
+            # number of query points in the base-rule.
+            # Currently the detection for N is only implemented for EGO.
+            if isinstance(self._rule, EfficientGlobalOptimization):
+                num_query_points = self._rule._num_query_points
+            else:
+                num_query_points = 1
+
+            self._init_subspaces = tuple(
+                [SingleObjectiveTrustRegionBox(search_space) for _ in range(num_query_points)]
+            )
+            self._tags = tuple([str(index) for index in range(len(self._init_subspaces))])
+
+        return super().acquire(search_space, models, datasets)
+
     @inherit_check_shapes
     def get_initialize_subspaces_mask(
         self,