diff --git a/miplearn/__init__.py b/miplearn/__init__.py
index 2a83ff8..ba8d728 100644
--- a/miplearn/__init__.py
+++ b/miplearn/__init__.py
@@ -13,6 +13,7 @@ from .components.lazy_dynamic import DynamicLazyConstraintsComponent
 from .components.lazy_static import StaticLazyConstraintsComponent
 from .components.cuts import UserCutsComponent
 from .components.primal import PrimalSolutionComponent
+from .components.relaxation import RelaxationComponent
 
 from .classifiers.adaptive import AdaptiveClassifier
 from .classifiers.threshold import MinPrecisionThreshold
diff --git a/miplearn/components/__init__.py b/miplearn/components/__init__.py
index 8e1c524..b5dde38 100644
--- a/miplearn/components/__init__.py
+++ b/miplearn/components/__init__.py
@@ -29,7 +29,6 @@ def classifier_evaluation_dict(tp, tn, fp, fn):
     else:
         d["Precision"] = 1.0
 
-
     t = (p + n) / 100.0
     d["Predicted positive (%)"] = d["Predicted positive"] / t
     d["Predicted negative (%)"] = d["Predicted negative"] / t
diff --git a/miplearn/components/lazy_static.py b/miplearn/components/lazy_static.py
index d223eaf..b685fd4 100644
--- a/miplearn/components/lazy_static.py
+++ b/miplearn/components/lazy_static.py
@@ -25,7 +25,7 @@ class StaticLazyConstraintsComponent(Component):
                  use_two_phase_gap=True,
                  large_gap=1e-2,
                  violation_tolerance=-0.5,
-                ):
+                 ):
         self.threshold = threshold
         self.classifier_prototype = classifier
         self.classifiers = {}
@@ -116,11 +116,11 @@ class StaticLazyConstraintsComponent(Component):
         logger.info("Extracting lazy constraints...")
         for cid in solver.internal_solver.get_constraint_ids():
             if instance.is_constraint_lazy(cid):
-                category = instance.get_lazy_constraint_category(cid)
+                category = instance.get_constraint_category(cid)
                 if category not in x:
                     x[category] = []
                     constraints[category] = []
-                x[category] += [instance.get_lazy_constraint_features(cid)]
+                x[category] += [instance.get_constraint_features(cid)]
                 c = LazyConstraint(cid=cid,
                                    obj=solver.internal_solver.extract_constraint(cid))
                 constraints[category] += [c]
@@ -147,7 +147,7 @@ class StaticLazyConstraintsComponent(Component):
         constraints = {}
         for instance in train_instances:
             for cid in instance.found_violated_lazy_constraints:
-                category = instance.get_lazy_constraint_category(cid)
+                category = instance.get_constraint_category(cid)
                 if category not in constraints:
                     constraints[category] = set()
                 constraints[category].add(cid)
@@ -162,7 +162,7 @@ class StaticLazyConstraintsComponent(Component):
             result[category] = []
             for instance in train_instances:
                 for cid in cids:
-                    result[category].append(instance.get_lazy_constraint_features(cid))
+                    result[category].append(instance.get_constraint_features(cid))
         return result
 
     def y(self, train_instances):
diff --git a/miplearn/components/relaxation.py b/miplearn/components/relaxation.py
new file mode 100644
index 0000000..9320ad2
--- /dev/null
+++ b/miplearn/components/relaxation.py
@@ -0,0 +1,151 @@
+#  MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
+#  Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
+#  Released under the modified BSD license. See COPYING.md for more details.
+
+import logging
+import sys
+from copy import deepcopy
+
+import numpy as np
+from miplearn.components import classifier_evaluation_dict
+from tqdm import tqdm
+
+from miplearn import Component
+from miplearn.classifiers.counting import CountingClassifier
+
+logger = logging.getLogger(__name__)
+
+
+class RelaxationComponent(Component):
+    """
+    A Component which builds a relaxation of the problem by dropping constraints.
+
+    Currently, this component drops all integrality constraints, as well as
+    all inequality constraints which are not likely binding in the LP relaxation.
+    In a future version of MIPLearn, this component may decide to keep some
+    integrality constraints it it determines that they have small impact on
+    running time, but large impact on dual bound.
+    """
+
+    def __init__(self,
+                 classifier=CountingClassifier(),
+                 threshold=0.95,
+                 slack_tolerance=1e-5,
+                 ):
+        self.classifiers = {}
+        self.classifier_prototype = classifier
+        self.threshold = threshold
+        self.slack_tolerance = slack_tolerance
+
+    def before_solve(self, solver, instance, _):
+        logger.info("Relaxing integrality...")
+        solver.internal_solver.relax()
+
+        logger.info("Predicting redundant LP constraints...")
+        cids = solver.internal_solver.get_constraint_ids()
+        x, constraints = self.x([instance],
+                                constraint_ids=cids,
+                                return_constraints=True)
+        y = self.predict(x)
+        n_removed = 0
+        for category in y.keys():
+            for i in range(len(y[category])):
+                if y[category][i][0] == 1:
+                    cid = constraints[category][i]
+                    solver.internal_solver.extract_constraint(cid)
+                    n_removed += 1
+        logger.info("Removed %d predicted redundant LP constraints" % n_removed)
+
+    def after_solve(self, solver, instance, model, results):
+        instance.slacks = solver.internal_solver.get_constraint_slacks()
+
+    def fit(self, training_instances):
+        training_instances = [instance
+                              for instance in training_instances
+                              if hasattr(instance, "slacks")]
+        logger.debug("Extracting x and y...")
+        x = self.x(training_instances)
+        y = self.y(training_instances)
+        logger.debug("Fitting...")
+        for category in tqdm(x.keys(),
+                             desc="Fit (relaxation)",
+                             disable=not sys.stdout.isatty()):
+            if category not in self.classifiers:
+                self.classifiers[category] = deepcopy(self.classifier_prototype)
+            self.classifiers[category].fit(x[category], y[category])
+
+    def x(self,
+          instances,
+          constraint_ids=None,
+          return_constraints=False):
+        x = {}
+        constraints = {}
+        for instance in instances:
+            if constraint_ids is not None:
+                cids = constraint_ids
+            else:
+                cids = instance.slacks.keys()
+            for cid in cids:
+                category = instance.get_constraint_category(cid)
+                if category is None:
+                    continue
+                if category not in x:
+                    x[category] = []
+                    constraints[category] = []
+                x[category] += [instance.get_constraint_features(cid)]
+                constraints[category] += [cid]
+        if return_constraints:
+            return x, constraints
+        else:
+            return x
+
+    def y(self, instances):
+        y = {}
+        for instance in instances:
+            for (cid, slack) in instance.slacks.items():
+                category = instance.get_constraint_category(cid)
+                if category is None:
+                    continue
+                if category not in y:
+                    y[category] = []
+                if slack > self.slack_tolerance:
+                    y[category] += [[1]]
+                else:
+                    y[category] += [[0]]
+        return y
+
+    def predict(self, x):
+        y = {}
+        for (category, x_cat) in x.items():
+            if category not in self.classifiers:
+                continue
+            y[category] = []
+            #x_cat = np.array(x_cat)
+            proba = self.classifiers[category].predict_proba(x_cat)
+            for i in range(len(proba)):
+                if proba[i][1] >= self.threshold:
+                    y[category] += [[1]]
+                else:
+                    y[category] += [[0]]
+        return y
+
+    def evaluate(self, instance):
+        x = self.x([instance])
+        y_true = self.y([instance])
+        y_pred = self.predict(x)
+        tp, tn, fp, fn = 0, 0, 0, 0
+        for category in y_true.keys():
+            for i in range(len(y_true[category])):
+                if y_pred[category][i][0] == 1:
+                    if y_true[category][i][0] == 1:
+                        tp += 1
+                    else:
+                        fp += 1
+                else:
+                    if y_true[category][i][0] == 1:
+                        fn += 1
+                    else:
+                        tn += 1
+        return classifier_evaluation_dict(tp, tn, fp, fn)
+
+
diff --git a/miplearn/components/tests/test_lazy_static.py b/miplearn/components/tests/test_lazy_static.py
index 56a0014..5bfa76e 100644
--- a/miplearn/components/tests/test_lazy_static.py
+++ b/miplearn/components/tests/test_lazy_static.py
@@ -29,12 +29,12 @@ def test_usage_with_solver():
         "c3": True,
         "c4": True,
     }[cid])
-    instance.get_lazy_constraint_features = Mock(side_effect=lambda cid: {
+    instance.get_constraint_features = Mock(side_effect=lambda cid: {
         "c2": [1.0, 0.0],
         "c3": [0.5, 0.5],
         "c4": [1.0],
     }[cid])
-    instance.get_lazy_constraint_category = Mock(side_effect=lambda cid: {
+    instance.get_constraint_category = Mock(side_effect=lambda cid: {
         "c2": "type-a",
         "c3": "type-a",
         "c4": "type-b",
@@ -72,13 +72,13 @@ def test_usage_with_solver():
     ])
 
     # For the lazy ones, should ask for features
-    instance.get_lazy_constraint_features.assert_has_calls([
+    instance.get_constraint_features.assert_has_calls([
         call("c2"), call("c3"), call("c4"),
     ])
 
     # Should also ask for categories
-    assert instance.get_lazy_constraint_category.call_count == 3
-    instance.get_lazy_constraint_category.assert_has_calls([
+    assert instance.get_constraint_category.call_count == 3
+    instance.get_constraint_category.assert_has_calls([
         call("c2"), call("c3"), call("c4"),
     ])
 
@@ -126,14 +126,14 @@ def test_usage_with_solver():
 def test_fit():
     instance_1 = Mock(spec=Instance)
     instance_1.found_violated_lazy_constraints = ["c1", "c2", "c4", "c5"]
-    instance_1.get_lazy_constraint_category = Mock(side_effect=lambda cid: {
+    instance_1.get_constraint_category = Mock(side_effect=lambda cid: {
         "c1": "type-a",
         "c2": "type-a",
         "c3": "type-a",
         "c4": "type-b",
         "c5": "type-b",
     }[cid])
-    instance_1.get_lazy_constraint_features = Mock(side_effect=lambda cid: {
+    instance_1.get_constraint_features = Mock(side_effect=lambda cid: {
         "c1": [1, 1],
         "c2": [1, 2],
         "c3": [1, 3],
@@ -143,14 +143,14 @@ def test_fit():
 
     instance_2 = Mock(spec=Instance)
     instance_2.found_violated_lazy_constraints = ["c2", "c3", "c4"]
-    instance_2.get_lazy_constraint_category = Mock(side_effect=lambda cid: {
+    instance_2.get_constraint_category = Mock(side_effect=lambda cid: {
         "c1": "type-a",
         "c2": "type-a",
         "c3": "type-a",
         "c4": "type-b",
         "c5": "type-b",
     }[cid])
-    instance_2.get_lazy_constraint_features = Mock(side_effect=lambda cid: {
+    instance_2.get_constraint_features = Mock(side_effect=lambda cid: {
         "c1": [2, 1],
         "c2": [2, 2],
         "c3": [2, 3],
diff --git a/miplearn/components/tests/test_relaxation.py b/miplearn/components/tests/test_relaxation.py
new file mode 100644
index 0000000..f75bc68
--- /dev/null
+++ b/miplearn/components/tests/test_relaxation.py
@@ -0,0 +1,188 @@
+#  MIPLearn: Extensible Framework for Learning-Enhanced Mixed-Integer Optimization
+#  Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
+#  Released under the modified BSD license. See COPYING.md for more details.
+
+from unittest.mock import Mock, call
+
+from miplearn import (RelaxationComponent,
+                      LearningSolver,
+                      Instance,
+                      InternalSolver)
+from miplearn.classifiers import Classifier
+
+
+def test_usage_with_solver():
+    solver = Mock(spec=LearningSolver)
+
+    internal = solver.internal_solver = Mock(spec=InternalSolver)
+    internal.get_constraint_ids = Mock(return_value=["c1", "c2", "c3", "c4"])
+    internal.get_constraint_slacks = Mock(side_effect=lambda: {
+        "c1": 0.5,
+        "c2": 0.0,
+        "c3": 0.0,
+        "c4": 1.4,
+    })
+
+    instance = Mock(spec=Instance)
+    instance.get_constraint_features = Mock(side_effect=lambda cid: {
+        "c2": [1.0, 0.0],
+        "c3": [0.5, 0.5],
+        "c4": [1.0],
+    }[cid])
+    instance.get_constraint_category = Mock(side_effect=lambda cid: {
+        "c1": None,
+        "c2": "type-a",
+        "c3": "type-a",
+        "c4": "type-b",
+    }[cid])
+
+    component = RelaxationComponent()
+    component.classifiers = {
+        "type-a": Mock(spec=Classifier),
+        "type-b": Mock(spec=Classifier),
+    }
+    component.classifiers["type-a"].predict_proba = \
+        Mock(return_value=[
+            [0.20, 0.80],
+            [0.05, 0.95],
+        ])
+    component.classifiers["type-b"].predict_proba = \
+        Mock(return_value=[
+            [0.02, 0.98],
+        ])
+
+    # LearningSolver calls before_solve
+    component.before_solve(solver, instance, None)
+
+    # Should relax integrality of the problem
+    internal.relax.assert_called_once()
+
+    # Should query list of constraints
+    internal.get_constraint_ids.assert_called_once()
+
+    # Should query category and features for each constraint in the model
+    assert instance.get_constraint_category.call_count == 4
+    instance.get_constraint_category.assert_has_calls([
+        call("c1"), call("c2"), call("c3"), call("c4"),
+    ])
+
+    # For constraint with non-null categories, should ask for features
+    assert instance.get_constraint_features.call_count == 3
+    instance.get_constraint_features.assert_has_calls([
+        call("c2"), call("c3"), call("c4"),
+    ])
+
+    # Should ask ML to predict whether constraint should be removed
+    component.classifiers["type-a"].predict_proba.assert_called_once_with([[1.0, 0.0], [0.5, 0.5]])
+    component.classifiers["type-b"].predict_proba.assert_called_once_with([[1.0]])
+
+    # Should ask internal solver to remove constraints predicted as redundant
+    assert internal.extract_constraint.call_count == 2
+    internal.extract_constraint.assert_has_calls([
+        call("c3"), call("c4"),
+    ])
+
+    # LearningSolver calls after_solve
+    component.after_solve(solver, instance, None, None)
+
+    # Should query slack for all constraints
+    internal.get_constraint_slacks.assert_called_once()
+
+    # Should store constraint slacks in instance object
+    assert hasattr(instance, "slacks")
+    assert instance.slacks == {
+        "c1": 0.5,
+        "c2": 0.0,
+        "c3": 0.0,
+        "c4": 1.4,
+    }
+
+
+def test_x_y_fit_predict_evaluate():
+    instances = [Mock(spec=Instance), Mock(spec=Instance)]
+    component = RelaxationComponent(slack_tolerance=0.05,
+                                    threshold=0.80)
+    component.classifiers = {
+        "type-a": Mock(spec=Classifier),
+        "type-b": Mock(spec=Classifier),
+    }
+    component.classifiers["type-a"].predict_proba = \
+        Mock(return_value=[
+            [0.20, 0.80],
+        ])
+    component.classifiers["type-b"].predict_proba = \
+        Mock(return_value=[
+            [0.50, 0.50],
+            [0.05, 0.95],
+        ])
+
+    # First mock instance
+    instances[0].slacks = {
+        "c1": 0.00,
+        "c2": 0.05,
+        "c3": 0.00,
+        "c4": 30.0,
+    }
+    instances[0].get_constraint_category = Mock(side_effect=lambda cid: {
+        "c1": None,
+        "c2": "type-a",
+        "c3": "type-a",
+        "c4": "type-b",
+    }[cid])
+    instances[0].get_constraint_features = Mock(side_effect=lambda cid: {
+        "c2": [1.0, 0.0],
+        "c3": [0.5, 0.5],
+        "c4": [1.0],
+    }[cid])
+
+    # Second mock instance
+    instances[1].slacks = {
+        "c1": 0.00,
+        "c3": 0.30,
+        "c4": 0.00,
+        "c5": 0.00,
+    }
+    instances[1].get_constraint_category = Mock(side_effect=lambda cid: {
+        "c1": None,
+        "c3": "type-a",
+        "c4": "type-b",
+        "c5": "type-b",
+    }[cid])
+    instances[1].get_constraint_features = Mock(side_effect=lambda cid: {
+        "c3": [0.3, 0.4],
+        "c4": [0.7],
+        "c5": [0.8],
+    }[cid])
+
+    expected_x = {
+        "type-a": [[1.0, 0.0], [0.5, 0.5], [0.3, 0.4]],
+        "type-b": [[1.0], [0.7], [0.8]],
+    }
+    expected_y = {
+        "type-a": [[0], [0], [1]],
+        "type-b": [[1], [0], [0]]
+    }
+
+    # Should build X and Y matrices correctly
+    assert component.x(instances) == expected_x
+    assert component.y(instances) == expected_y
+
+    # Should pass along X and Y matrices to classifiers
+    component.fit(instances)
+    component.classifiers["type-a"].fit.assert_called_with(expected_x["type-a"], expected_y["type-a"])
+    component.classifiers["type-b"].fit.assert_called_with(expected_x["type-b"], expected_y["type-b"])
+
+    assert component.predict(expected_x) == {
+        "type-a": [[1]],
+        "type-b": [[0], [1]]
+    }
+
+    ev = component.evaluate(instances[1])
+    assert ev["True positive"] == 1
+    assert ev["True negative"] == 1
+    assert ev["False positive"] == 1
+    assert ev["False negative"] == 0
+
+
+
+
diff --git a/miplearn/instance.py b/miplearn/instance.py
index 10157b3..c37b751 100644
--- a/miplearn/instance.py
+++ b/miplearn/instance.py
@@ -82,6 +82,12 @@ class Instance(ABC):
         """
         return "default"
 
+    def get_constraint_features(self, cid):
+        return np.zeros(1)
+
+    def get_constraint_category(self, cid):
+        return cid
+
     def has_static_lazy_constraints(self):
         return False
 
@@ -91,12 +97,6 @@ class Instance(ABC):
     def is_constraint_lazy(self, cid):
         return False
 
-    def get_lazy_constraint_features(self, cid):
-        return np.zeros(1)
-
-    def get_lazy_constraint_category(self, cid):
-        return cid
-
     def find_violated_lazy_constraints(self, model):
         """
         Returns lazy constraint violations found for the current solution.
diff --git a/miplearn/solvers/gurobi.py b/miplearn/solvers/gurobi.py
index 822ae7a..21c6921 100644
--- a/miplearn/solvers/gurobi.py
+++ b/miplearn/solvers/gurobi.py
@@ -274,6 +274,13 @@ class GurobiSolver(InternalSolver):
         else:
             raise Exception("Unknown sense: %s" % sense)
 
+    def get_constraint_slacks(self):
+        return {c.ConstrName: c.Slack for c in self.model.getConstrs()}
+
+    def relax(self):
+        self.model = self.model.relax()
+        self._update_vars()
+
     def set_branching_priorities(self, priorities):
         self._raise_if_callback()
         logger.warning("set_branching_priorities not implemented")
diff --git a/miplearn/solvers/internal.py b/miplearn/solvers/internal.py
index 9c9ee4a..c42d524 100644
--- a/miplearn/solvers/internal.py
+++ b/miplearn/solvers/internal.py
@@ -176,6 +176,21 @@ class InternalSolver(ABC):
         """
         pass
 
+    @abstractmethod
+    def relax(self):
+        """
+        Drops all integrality constraints from the model.
+        """
+        pass
+
+    @abstractmethod
+    def get_constraint_slacks(self):
+        """
+        Returns a dictionary mapping constraint name to the constraint slack
+        in the current solution.
+        """
+        pass
+
     @abstractmethod
     def is_constraint_satisfied(self, cobj):
         pass
diff --git a/miplearn/solvers/learning.py b/miplearn/solvers/learning.py
index 958699e..98bbac9 100644
--- a/miplearn/solvers/learning.py
+++ b/miplearn/solvers/learning.py
@@ -25,13 +25,20 @@ INSTANCES = [None]  # type: List[Optional[dict]]
 def _parallel_solve(instance_idx):
     solver = deepcopy(SOLVER[0])
     instance = INSTANCES[0][instance_idx]
-    results = solver.solve(instance)
+    if not hasattr(instance, "found_violated_lazy_constraints"):
+        instance.found_violated_lazy_constraints = []
+    if not hasattr(instance, "found_violated_user_cuts"):
+        instance.found_violated_user_cuts = []
+    if not hasattr(instance, "slacks"):
+        instance.slacks = {}
+    solver_results = solver.solve(instance)
     return {
-        "Results": results,
-        "Solution": instance.solution,
-        "LP solution": instance.lp_solution,
-        "Violated lazy constraints": instance.found_violated_lazy_constraints,
-        #"Violated user cuts": instance.found_violated_user_cuts,
+        "solver_results": solver_results,
+        "solution": instance.solution,
+        "lp_solution": instance.lp_solution,
+        "found_violated_lazy_constraints": instance.found_violated_lazy_constraints,
+        "found_violated_user_cuts": instance.found_violated_user_cuts,
+        "slacks": instance.slacks
     }
 
 
@@ -245,16 +252,17 @@ class LearningSolver:
                               list(range(len(instances))),
                               num_cpus=n_jobs,
                               desc=label)
-        results = [p["Results"] for p in p_map_results]
+        results = [p["solver_results"] for p in p_map_results]
         for (idx, r) in enumerate(p_map_results):
-            instances[idx].solution = r["Solution"]
-            instances[idx].lp_solution = r["LP solution"]
-            instances[idx].lp_value = r["Results"]["LP value"]
-            instances[idx].lower_bound = r["Results"]["Lower bound"]
-            instances[idx].upper_bound = r["Results"]["Upper bound"]
-            instances[idx].found_violated_lazy_constraints = r["Violated lazy constraints"]
-            #instances[idx].found_violated_user_cuts = r["Violated user cuts"]
-            instances[idx].solver_log = r["Results"]["Log"]
+            instances[idx].solution = r["solution"]
+            instances[idx].lp_solution = r["lp_solution"]
+            instances[idx].lp_value = r["solver_results"]["LP value"]
+            instances[idx].lower_bound = r["solver_results"]["Lower bound"]
+            instances[idx].upper_bound = r["solver_results"]["Upper bound"]
+            instances[idx].found_violated_lazy_constraints = r["found_violated_lazy_constraints"]
+            instances[idx].found_violated_user_cuts = r["found_violated_user_cuts"]
+            instances[idx].slacks = r["slacks"]
+            instances[idx].solver_log = r["solver_results"]["Log"]
         self._restore_miplearn_logger()
         return results
 
diff --git a/miplearn/solvers/pyomo/base.py b/miplearn/solvers/pyomo/base.py
index b509985..472019c 100644
--- a/miplearn/solvers/pyomo/base.py
+++ b/miplearn/solvers/pyomo/base.py
@@ -244,3 +244,9 @@ class BasePyomoSolver(InternalSolver):
     @abstractmethod
     def _get_gap_tolerance_option_name(self):
         pass
+
+    def relax(self):
+        raise Exception("not implemented")
+
+    def get_constraint_slacks(self):
+        raise Exception("not implemented")
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