diff --git a/java/api/src/main/java/org/ray/api/options/BaseTaskOptions.java b/java/api/src/main/java/org/ray/api/options/BaseTaskOptions.java
index 501ad151e..65494d532 100644
--- a/java/api/src/main/java/org/ray/api/options/BaseTaskOptions.java
+++ b/java/api/src/main/java/org/ray/api/options/BaseTaskOptions.java
@@ -7,19 +7,13 @@ import java.util.Map;
  * The options class for RayCall or ActorCreation.
  */
 public abstract class BaseTaskOptions {
-  public final Map<String, Double> resources;
+  public Map<String, Double> resources;
 
   public BaseTaskOptions() {
     resources = new HashMap<>();
   }
 
   public BaseTaskOptions(Map<String, Double> resources) {
-    for (Map.Entry<String, Double> entry : resources.entrySet()) {
-      if (entry.getValue().compareTo(0.0) <= 0) {
-        throw new IllegalArgumentException(String.format("Resource capacity should be " +
-            "positive, but got resource %s = %f.", entry.getKey(), entry.getValue()));
-      }
-    }
     this.resources = resources;
   }
 
diff --git a/java/example.conf b/java/example.conf
index cbdaf781d..e6aaa37ea 100644
--- a/java/example.conf
+++ b/java/example.conf
@@ -14,7 +14,7 @@ ray {
   run-mode = CLUSTER
 
   // Available resources on this node.
-  resources: "CPU:4"
+  resources: "CPU:4,GPU:0"
 
   // The address of the redis server to connect, in format `ip:port`.
   // If not provided, Ray processes will be started locally, including
diff --git a/java/runtime/src/main/java/org/ray/runtime/AbstractRayRuntime.java b/java/runtime/src/main/java/org/ray/runtime/AbstractRayRuntime.java
index 0cd6ee4f6..00d24714f 100644
--- a/java/runtime/src/main/java/org/ray/runtime/AbstractRayRuntime.java
+++ b/java/runtime/src/main/java/org/ray/runtime/AbstractRayRuntime.java
@@ -32,6 +32,7 @@ import org.ray.runtime.raylet.RayletClient;
 import org.ray.runtime.task.ArgumentsBuilder;
 import org.ray.runtime.task.TaskLanguage;
 import org.ray.runtime.task.TaskSpec;
+import org.ray.runtime.util.ResourceUtil;
 import org.ray.runtime.util.UniqueIdUtil;
 import org.slf4j.Logger;
 import org.slf4j.LoggerFactory;
@@ -356,6 +357,11 @@ public abstract class AbstractRayRuntime implements RayRuntime {
       resources = new HashMap<>(taskOptions.resources);
     }
 
+    if (!resources.containsKey(ResourceUtil.CPU_LITERAL)
+        && !resources.containsKey(ResourceUtil.CPU_LITERAL.toLowerCase())) {
+      resources.put(ResourceUtil.CPU_LITERAL, 0.0);
+    }
+
     int maxActorReconstruction = 0;
     if (taskOptions instanceof ActorCreationOptions) {
       maxActorReconstruction = ((ActorCreationOptions) taskOptions).maxReconstructions;
diff --git a/java/runtime/src/main/java/org/ray/runtime/config/RayConfig.java b/java/runtime/src/main/java/org/ray/runtime/config/RayConfig.java
index 99e67288d..78bfda089 100644
--- a/java/runtime/src/main/java/org/ray/runtime/config/RayConfig.java
+++ b/java/runtime/src/main/java/org/ray/runtime/config/RayConfig.java
@@ -104,6 +104,10 @@ public class RayConfig {
             + "setting it to the number of CPU cores: {}", numCpu);
         resources.put("CPU", numCpu * 1.0);
       }
+      if (!resources.containsKey("GPU")) {
+        LOGGER.warn("No GPU resource is set in configuration, setting it to 0");
+        resources.put("GPU", 0.0);
+      }
     }
     // Driver id.
     String driverId = config.getString("ray.driver.id");
diff --git a/java/streaming/src/main/resources/ray.conf b/java/streaming/src/main/resources/ray.conf
index faf1ca9aa..4494cff06 100644
--- a/java/streaming/src/main/resources/ray.conf
+++ b/java/streaming/src/main/resources/ray.conf
@@ -1,5 +1,5 @@
 ray {
   run-mode = SINGLE_PROCESS
-  resources = "CPU:4"
+  resources = "CPU:4,GPU:0"
   redis.address = ""
 }
diff --git a/java/test/src/main/java/org/ray/api/test/ResourcesManagementTest.java b/java/test/src/main/java/org/ray/api/test/ResourcesManagementTest.java
index c3d0e4152..6ca9d7c9d 100644
--- a/java/test/src/main/java/org/ray/api/test/ResourcesManagementTest.java
+++ b/java/test/src/main/java/org/ray/api/test/ResourcesManagementTest.java
@@ -46,30 +46,22 @@ public class ResourcesManagementTest extends BaseTest {
   @Test
   public void testMethods() {
     TestUtils.skipTestUnderSingleProcess();
-    CallOptions callOptions1 = new CallOptions(ImmutableMap.of("CPU", 4.0));
+    CallOptions callOptions1 = new CallOptions(ImmutableMap.of("CPU", 4.0, "GPU", 0.0));
 
     // This is a case that can satisfy required resources.
     // The static resources for test are "CPU:4,RES-A:4".
     RayObject<Integer> result1 = Ray.call(ResourcesManagementTest::echo, 100, callOptions1);
     Assert.assertEquals(100, (int) result1.get());
 
-    CallOptions callOptions2 = new CallOptions(ImmutableMap.of("CPU", 4.0));
+    CallOptions callOptions2 = new CallOptions(ImmutableMap.of("CPU", 4.0, "GPU", 2.0));
 
     // This is a case that can't satisfy required resources.
     // The static resources for test are "CPU:4,RES-A:4".
     final RayObject<Integer> result2 = Ray.call(ResourcesManagementTest::echo, 200, callOptions2);
     WaitResult<Integer> waitResult = Ray.wait(ImmutableList.of(result2), 1, 1000);
 
-    Assert.assertEquals(1, waitResult.getReady().size());
-    Assert.assertEquals(0, waitResult.getUnready().size());
-
-    try {
-      CallOptions callOptions3 = new CallOptions(ImmutableMap.of("CPU", 0.0));
-      Assert.fail();
-    } catch (RuntimeException e) {
-      // We should receive a RuntimeException indicates that we should not
-      // pass a zero capacity resource.
-    }
+    Assert.assertEquals(0, waitResult.getReady().size());
+    Assert.assertEquals(1, waitResult.getUnready().size());
   }
 
   @Test
@@ -77,7 +69,7 @@ public class ResourcesManagementTest extends BaseTest {
     TestUtils.skipTestUnderSingleProcess();
 
     ActorCreationOptions actorCreationOptions1 =
-        new ActorCreationOptions(ImmutableMap.of("CPU", 2.0));
+        new ActorCreationOptions(ImmutableMap.of("CPU", 2.0, "GPU", 0.0));
 
     // This is a case that can satisfy required resources.
     // The static resources for test are "CPU:4,RES-A:4".
@@ -88,7 +80,7 @@ public class ResourcesManagementTest extends BaseTest {
     // This is a case that can't satisfy required resources.
     // The static resources for test are "CPU:4,RES-A:4".
     ActorCreationOptions actorCreationOptions2 =
-        new ActorCreationOptions(ImmutableMap.of("CPU", 8.0));
+        new ActorCreationOptions(ImmutableMap.of("CPU", 8.0, "GPU", 0.0));
 
     RayActor<ResourcesManagementTest.Echo> echo2 =
         Ray.createActor(Echo::new, actorCreationOptions2);
diff --git a/python/ray/includes/task.pxi b/python/ray/includes/task.pxi
index 70e7e584d..872b93d22 100644
--- a/python/ray/includes/task.pxi
+++ b/python/ray/includes/task.pxi
@@ -44,6 +44,8 @@ cdef class Task:
         # Parse the resource map.
         if resource_map is not None:
             required_resources = resource_map_from_dict(resource_map)
+        if required_resources.count(b"CPU") == 0:
+            required_resources[b"CPU"] = 1.0
         if placement_resource_map is not None:
             required_placement_resources = (
                 resource_map_from_dict(placement_resource_map))
diff --git a/python/ray/services.py b/python/ray/services.py
index 4a6fd30f3..0fc7f4e73 100644
--- a/python/ray/services.py
+++ b/python/ray/services.py
@@ -1029,25 +1029,14 @@ def check_and_update_resources(num_cpus, num_gpus, resources):
         if gpu_ids is not None:
             resources["GPU"] = min(resources["GPU"], len(gpu_ids))
 
-    resources = {
-        resource_label: resource_quantity
-        for resource_label, resource_quantity in resources.items()
-        if resource_quantity != 0
-    }
-
     # Check types.
     for _, resource_quantity in resources.items():
         assert (isinstance(resource_quantity, int)
                 or isinstance(resource_quantity, float))
         if (isinstance(resource_quantity, float)
                 and not resource_quantity.is_integer()):
-            raise ValueError(
-                "Resource quantities must all be whole numbers. Received {}.".
-                format(resources))
-        if resource_quantity < 0:
-            raise ValueError(
-                "Resource quantities must be nonnegative. Received {}.".format(
-                    resources))
+            raise ValueError("Resource quantities must all be whole numbers.")
+
         if resource_quantity > ray_constants.MAX_RESOURCE_QUANTITY:
             raise ValueError("Resource quantities must be at most {}.".format(
                 ray_constants.MAX_RESOURCE_QUANTITY))
@@ -1124,9 +1113,8 @@ def start_raylet(redis_address,
 
     # Limit the number of workers that can be started in parallel by the
     # raylet. However, make sure it is at least 1.
-    num_cpus_static = static_resources.get("CPU", 0)
     maximum_startup_concurrency = max(
-        1, min(multiprocessing.cpu_count(), num_cpus_static))
+        1, min(multiprocessing.cpu_count(), static_resources["CPU"]))
 
     # Format the resource argument in a form like 'CPU,1.0,GPU,0,Custom,3'.
     resource_argument = ",".join(
diff --git a/python/ray/tests/test_basic.py b/python/ray/tests/test_basic.py
index c24c90e0d..d535fa593 100644
--- a/python/ray/tests/test_basic.py
+++ b/python/ray/tests/test_basic.py
@@ -1948,15 +1948,15 @@ def test_multiple_raylets(ray_start_cluster):
     store_names = []
     store_names += [
         client["ObjectStoreSocketName"] for client in client_table
-        if client["Resources"].get("GPU", 0) == 0
+        if client["Resources"]["GPU"] == 0
     ]
     store_names += [
         client["ObjectStoreSocketName"] for client in client_table
-        if client["Resources"].get("GPU", 0) == 5
+        if client["Resources"]["GPU"] == 5
     ]
     store_names += [
         client["ObjectStoreSocketName"] for client in client_table
-        if client["Resources"].get("GPU", 0) == 1
+        if client["Resources"]["GPU"] == 1
     ]
     assert len(store_names) == 3
 
@@ -2126,32 +2126,6 @@ def test_many_custom_resources(shutdown_only):
     ray.get(results)
 
 
-def test_zero_capacity_deletion_semantics(shutdown_only):
-    ray.init(num_cpus=2, num_gpus=1, resources={"test_resource": 1})
-
-    def test():
-        resources = ray.global_state.available_resources()
-        retry_count = 0
-
-        while resources and retry_count < 5:
-            time.sleep(0.1)
-            resources = ray.global_state.available_resources()
-            retry_count += 1
-
-        if retry_count >= 5:
-            raise RuntimeError("Resources were available even after retries.")
-
-        return resources
-
-    function = ray.remote(
-        num_cpus=2, num_gpus=1, resources={"test_resource": 1})(test)
-    cluster_resources = ray.get(function.remote())
-
-    # All cluster resources should be utilized and
-    # cluster_resources must be empty
-    assert cluster_resources == {}
-
-
 @pytest.fixture
 def save_gpu_ids_shutdown_only():
     # Record the curent value of this environment variable so that we can
diff --git a/python/ray/tests/test_global_state.py b/python/ray/tests/test_global_state.py
index bc82eb859..ee3d304c2 100644
--- a/python/ray/tests/test_global_state.py
+++ b/python/ray/tests/test_global_state.py
@@ -51,8 +51,8 @@ def test_uses_resources(ray_start_regular):
 
     while not resource_used:
         available_resources = ray.global_state.available_resources()
-        resource_used = available_resources.get(
-            "CPU", 0) == cluster_resources.get("CPU", 0) - 1
+        resource_used = available_resources[
+            "CPU"] == cluster_resources["CPU"] - 1
 
     assert resource_used
 
diff --git a/python/ray/tune/ray_trial_executor.py b/python/ray/tune/ray_trial_executor.py
index 27fea5694..7f10a9ee1 100644
--- a/python/ray/tune/ray_trial_executor.py
+++ b/python/ray/tune/ray_trial_executor.py
@@ -11,7 +11,7 @@ import time
 import traceback
 
 import ray
-from ray.tune.error import AbortTrialExecution
+from ray.tune.error import TuneError, AbortTrialExecution
 from ray.tune.logger import NoopLogger
 from ray.tune.trial import Trial, Resources, Checkpoint
 from ray.tune.trial_executor import TrialExecutor
@@ -363,22 +363,17 @@ class RayTrialExecutor(TrialExecutor):
                 resources = ray.services.check_and_update_resources(
                     None, None, None)
             if not resources:
-                logger.warning(
-                    "Cluster resources not detected or are 0. Retrying...")
+                logger.warning("Cluster resources not detected. Retrying...")
                 time.sleep(0.5)
 
-        if not resources:
-            # NOTE: This hides the possibility that Ray may be waiting for
-            # clients to connect.
-            resources.setdefault("CPU", 0)
-            resources.setdefault("GPU", 0)
-            logger.warning("Cluster resources cannot be detected or are 0. "
-                           "You can resume this experiment by passing in "
-                           "`resume=True` to `run`.")
+        if not resources or "CPU" not in resources:
+            raise TuneError("Cluster resources cannot be detected. "
+                            "You can resume this experiment by passing in "
+                            "`resume=True` to `run`.")
 
         resources = resources.copy()
-        num_cpus = resources.pop("CPU", 0)
-        num_gpus = resources.pop("GPU", 0)
+        num_cpus = resources.pop("CPU")
+        num_gpus = resources.pop("GPU")
         custom_resources = resources
 
         self._avail_resources = Resources(
diff --git a/python/ray/worker.py b/python/ray/worker.py
index 3f4072087..f3c17601f 100644
--- a/python/ray/worker.py
+++ b/python/ray/worker.py
@@ -653,13 +653,6 @@ class Worker(object):
                     raise ValueError(
                         "Resource quantities must all be whole numbers.")
 
-            # Remove any resources with zero quantity requirements
-            resources = {
-                resource_label: resource_quantity
-                for resource_label, resource_quantity in resources.items()
-                if resource_quantity > 0
-            }
-
             if placement_resources is None:
                 placement_resources = {}
 
@@ -1877,7 +1870,7 @@ def connect(node,
             nil_actor_counter,  # actor_counter.
             [],  # new_actor_handles.
             [],  # execution_dependencies.
-            {},  # resource_map.
+            {"CPU": 0},  # resource_map.
             {},  # placement_resource_map.
         )
 
diff --git a/src/ray/raylet/node_manager.cc b/src/ray/raylet/node_manager.cc
index b8daec203..7e68eafa1 100644
--- a/src/ray/raylet/node_manager.cc
+++ b/src/ray/raylet/node_manager.cc
@@ -1469,16 +1469,15 @@ void NodeManager::HandleTaskBlocked(const std::shared_ptr<LocalClientConnection>
       // Get the CPU resources required by the running task.
       const auto required_resources = task.GetTaskSpecification().GetRequiredResources();
       double required_cpus = required_resources.GetNumCpus();
-      std::unordered_map<std::string, double> cpu_resources;
-      if (required_cpus > 0) {
-        cpu_resources[kCPU_ResourceLabel] = required_cpus;
-      }
+      const std::unordered_map<std::string, double> cpu_resources = {
+          {kCPU_ResourceLabel, required_cpus}};
 
       // Release the CPU resources.
       auto const cpu_resource_ids = worker->ReleaseTaskCpuResources();
       local_available_resources_.Release(cpu_resource_ids);
-      cluster_resource_map_[gcs_client_->client_table().GetLocalClientId()].Release(
-          ResourceSet(cpu_resources));
+      RAY_CHECK(
+          cluster_resource_map_[gcs_client_->client_table().GetLocalClientId()].Release(
+              ResourceSet(cpu_resources)));
       worker->MarkBlocked();
 
       // Try dispatching tasks since we may have released some resources.
@@ -1522,11 +1521,9 @@ void NodeManager::HandleTaskUnblocked(
       // Get the CPU resources required by the running task.
       const auto required_resources = task.GetTaskSpecification().GetRequiredResources();
       double required_cpus = required_resources.GetNumCpus();
-      std::unordered_map<std::string, double> cpu_resources_map;
-      if (required_cpus > 0) {
-        cpu_resources_map[kCPU_ResourceLabel] = required_cpus;
-      }
-      const ResourceSet cpu_resources(cpu_resources_map);
+      const ResourceSet cpu_resources(
+          std::unordered_map<std::string, double>({{kCPU_ResourceLabel, required_cpus}}));
+
       // Check if we can reacquire the CPU resources.
       bool oversubscribed = !local_available_resources_.Contains(cpu_resources);
 
@@ -1536,8 +1533,9 @@ void NodeManager::HandleTaskUnblocked(
         // reacquire here may be different from the ones that the task started with.
         auto const resource_ids = local_available_resources_.Acquire(cpu_resources);
         worker->AcquireTaskCpuResources(resource_ids);
-        cluster_resource_map_[gcs_client_->client_table().GetLocalClientId()].Acquire(
-            cpu_resources);
+        RAY_CHECK(
+            cluster_resource_map_[gcs_client_->client_table().GetLocalClientId()].Acquire(
+                cpu_resources));
       } else {
         // In this case, we simply don't reacquire the CPU resources for the worker.
         // The worker can keep running and when the task finishes, it will simply
@@ -1629,7 +1627,7 @@ bool NodeManager::AssignTask(const Task &task) {
   auto acquired_resources =
       local_available_resources_.Acquire(spec.GetRequiredResources());
   const auto &my_client_id = gcs_client_->client_table().GetLocalClientId();
-  cluster_resource_map_[my_client_id].Acquire(spec.GetRequiredResources());
+  RAY_CHECK(cluster_resource_map_[my_client_id].Acquire(spec.GetRequiredResources()));
 
   if (spec.IsActorCreationTask()) {
     // Check that we are not placing an actor creation task on a node with 0 CPUs.
@@ -1743,8 +1741,8 @@ void NodeManager::FinishAssignedTask(Worker &worker) {
   // Release task's resources. The worker's lifetime resources are still held.
   auto const &task_resources = worker.GetTaskResourceIds();
   local_available_resources_.Release(task_resources);
-  cluster_resource_map_[gcs_client_->client_table().GetLocalClientId()].Release(
-      task_resources.ToResourceSet());
+  RAY_CHECK(cluster_resource_map_[gcs_client_->client_table().GetLocalClientId()].Release(
+      task_resources.ToResourceSet()));
   worker.ResetTaskResourceIds();
 
   // If this was an actor or actor creation task, handle the actor's new state.
@@ -2036,9 +2034,6 @@ void NodeManager::ForwardTaskOrResubmit(const Task &task,
 
     RAY_LOG(INFO) << "Failed to forward task " << task_id << " to node manager "
                   << node_manager_id;
-
-    // TODO(romilb): We should probably revert the load subtraction from
-    // SchedulingPolicy::Schedule()
     // Mark the failed task as pending to let other raylets know that we still
     // have the task. TaskDependencyManager::TaskPending() is assumed to be
     // idempotent.
diff --git a/src/ray/raylet/scheduling_policy.cc b/src/ray/raylet/scheduling_policy.cc
index a8c1db4b1..01a3cde57 100644
--- a/src/ray/raylet/scheduling_policy.cc
+++ b/src/ray/raylet/scheduling_policy.cc
@@ -49,13 +49,11 @@ std::unordered_map<TaskID, ClientID> SchedulingPolicy::Schedule(
       const auto &node_resources = client_resource_pair.second;
       ResourceSet available_node_resources =
           ResourceSet(node_resources.GetAvailableResources());
-      // TODO(romilb): Why do we need to subtract load from available resources?
-      // Even if we don't the code path below for choosing a dst_client_id would be
-      // similar.
-      available_node_resources.SubtractResources(node_resources.GetLoadResources());
+      available_node_resources.SubtractResourcesStrict(node_resources.GetLoadResources());
       RAY_LOG(DEBUG) << "client_id " << node_client_id
                      << " avail: " << node_resources.GetAvailableResources().ToString()
-                     << " load: " << node_resources.GetLoadResources().ToString();
+                     << " load: " << node_resources.GetLoadResources().ToString()
+                     << " avail-load: " << available_node_resources.ToString();
 
       if (resource_demand.IsSubset(available_node_resources)) {
         // This node is a feasible candidate.
diff --git a/src/ray/raylet/scheduling_resources.cc b/src/ray/raylet/scheduling_resources.cc
index 17a9aba16..cd4a80cd0 100644
--- a/src/ray/raylet/scheduling_resources.cc
+++ b/src/ray/raylet/scheduling_resources.cc
@@ -9,39 +9,16 @@ namespace ray {
 
 namespace raylet {
 
-bool EqualsZeroEpsilon(double quantity) {
-  if ((quantity <= EPSILON) && (quantity >= -1 * EPSILON)) {
-    return true;
-  }
-  return false;
-}
-
-bool EqualsOneEpsilon(double quantity) {
-  if ((quantity <= 1 + EPSILON) && (quantity >= 1 - EPSILON)) {
-    return true;
-  }
-  return false;
-}
-
 ResourceSet::ResourceSet() {}
 
 ResourceSet::ResourceSet(const std::unordered_map<std::string, double> &resource_map)
-    : resource_capacity_(resource_map) {
-  for (auto const &resource_pair : resource_capacity_) {
-    RAY_CHECK(resource_pair.second > 0 + EPSILON)
-        << "Resource " << resource_pair.first << " capacity is " << resource_pair.second
-        << ". Should have been greater than zero.";
-  }
-}
+    : resource_capacity_(resource_map) {}
 
 ResourceSet::ResourceSet(const std::vector<std::string> &resource_labels,
                          const std::vector<double> resource_capacity) {
   RAY_CHECK(resource_labels.size() == resource_capacity.size());
   for (uint i = 0; i < resource_labels.size(); i++) {
-    RAY_CHECK(resource_capacity[i] > 0 + EPSILON)
-        << "Resource " << resource_labels[i] << " capacity is " << resource_capacity[i]
-        << ". Should have been greater than zero.";
-    resource_capacity_[resource_labels[i]] = resource_capacity[i];
+    RAY_CHECK(AddResource(resource_labels[i], resource_capacity[i]));
   }
 }
 
@@ -53,7 +30,13 @@ bool ResourceSet::operator==(const ResourceSet &rhs) const {
 
 bool ResourceSet::IsEmpty() const {
   // Check whether the capacity of each resource type is zero. Exit early if not.
-  return resource_capacity_.empty();
+  if (resource_capacity_.empty()) return true;
+  for (const auto &resource_pair : resource_capacity_) {
+    if (resource_pair.second > 0) {
+      return false;
+    }
+  }
+  return true;
 }
 
 bool ResourceSet::IsSubset(const ResourceSet &other) const {
@@ -61,7 +44,11 @@ bool ResourceSet::IsSubset(const ResourceSet &other) const {
   for (const auto &resource_pair : resource_capacity_) {
     const auto &resource_name = resource_pair.first;
     const double lhs_quantity = resource_pair.second;
-    double rhs_quantity = other.GetResource(resource_name);
+    double rhs_quantity = 0;
+    if (!other.GetResource(resource_name, &rhs_quantity)) {
+      // Resource not found in rhs, therefore lhs is not a subset of rhs.
+      return false;
+    }
     if (lhs_quantity > rhs_quantity) {
       // Resource found in rhs, but lhs capacity exceeds rhs capacity.
       return false;
@@ -80,42 +67,41 @@ bool ResourceSet::IsEqual(const ResourceSet &rhs) const {
   return (this->IsSubset(rhs) && rhs.IsSubset(*this));
 }
 
+bool ResourceSet::AddResource(const std::string &resource_name, double capacity) {
+  resource_capacity_[resource_name] = capacity;
+  return true;
+}
+
 bool ResourceSet::RemoveResource(const std::string &resource_name) {
   throw std::runtime_error("Method not implemented");
 }
-void ResourceSet::SubtractResources(const ResourceSet &other) {
-  // Subtract the resources and delete any if new capacity is zero.
-  for (const auto &resource_pair : other.GetResourceMap()) {
-    const std::string &resource_label = resource_pair.first;
-    const double &resource_capacity = resource_pair.second;
-    if (resource_capacity_.count(resource_label) == 1) {
-      resource_capacity_[resource_label] -= resource_capacity;
-      if (resource_capacity_[resource_label] < 0 + EPSILON) {
-        resource_capacity_.erase(resource_label);
-      }
-    }
-  }
-}
 
-void ResourceSet::SubtractResourcesStrict(const ResourceSet &other) {
-  // Subtract the resources, make sure none goes below zero and delete any if new capacity
-  // is zero.
+bool ResourceSet::SubtractResourcesStrict(const ResourceSet &other) {
+  // Subtract the resources and track whether a resource goes below zero.
+  bool oversubscribed = false;
   for (const auto &resource_pair : other.GetResourceMap()) {
     const std::string &resource_label = resource_pair.first;
     const double &resource_capacity = resource_pair.second;
     RAY_CHECK(resource_capacity_.count(resource_label) == 1)
         << "Attempt to acquire unknown resource: " << resource_label;
     resource_capacity_[resource_label] -= resource_capacity;
-    // TODO(romilb): Double precision subtraction may sometimes be less than zero by a
-    // small epsilon - need to fix.
-    RAY_CHECK(resource_capacity_[resource_label] >= 0 - EPSILON)
-        << "Capacity of resource " << resource_label << " after subtraction is negative ("
-        << resource_capacity_[resource_label] << ")."
-        << " Debug: resource_capacity_:" << ToString() << ", other: " << other.ToString();
-    if (EqualsZeroEpsilon(resource_capacity_[resource_label])) {
-      resource_capacity_.erase(resource_label);
+    if (resource_capacity_[resource_label] < 0) {
+      oversubscribed = true;
     }
   }
+  return !oversubscribed;
+}
+
+// Perform a left join.
+bool ResourceSet::AddResourcesStrict(const ResourceSet &other) {
+  // Return failure if attempting to perform vector addition with unknown labels.
+  for (const auto &resource_pair : other.GetResourceMap()) {
+    const std::string &resource_label = resource_pair.first;
+    const double &resource_capacity = resource_pair.second;
+    RAY_CHECK(resource_capacity_.count(resource_label) != 0);
+    resource_capacity_[resource_label] += resource_capacity;
+  }
+  return true;
 }
 
 // Perform an outer join.
@@ -123,22 +109,33 @@ void ResourceSet::AddResources(const ResourceSet &other) {
   for (const auto &resource_pair : other.GetResourceMap()) {
     const std::string &resource_label = resource_pair.first;
     const double &resource_capacity = resource_pair.second;
-    resource_capacity_[resource_label] += resource_capacity;
+    if (resource_capacity_.count(resource_label) == 0) {
+      // Add the new label if not found.
+      RAY_CHECK(AddResource(resource_label, resource_capacity));
+    } else {
+      // Increment the resource by its capacity.
+      resource_capacity_[resource_label] += resource_capacity;
+    }
   }
 }
 
-double ResourceSet::GetResource(const std::string &resource_name) const {
-  if (EqualsZeroEpsilon(resource_capacity_.count(resource_name))) {
-    return 0;
+bool ResourceSet::GetResource(const std::string &resource_name, double *value) const {
+  if (!value) {
+    return false;
   }
-  double capacity = resource_capacity_.at(resource_name);
-  RAY_CHECK(capacity > 0 + EPSILON) << "Resource " << resource_name << " capacity is "
-                                    << capacity
-                                    << ". Should have been greater than zero.";
-  return capacity;
+  if (resource_capacity_.count(resource_name) == 0) {
+    *value = std::nan("");
+    return false;
+  }
+  *value = resource_capacity_.at(resource_name);
+  return true;
 }
 
-double ResourceSet::GetNumCpus() const { return GetResource(kCPU_ResourceLabel); }
+double ResourceSet::GetNumCpus() const {
+  double num_cpus;
+  RAY_CHECK(GetResource(kCPU_ResourceLabel, &num_cpus));
+  return num_cpus;
+}
 
 const std::string ResourceSet::ToString() const {
   std::string return_string = "";
@@ -225,12 +222,6 @@ ResourceIds ResourceIds::Acquire(double resource_quantity) {
       if (fractional_pair.second >= resource_quantity) {
         auto return_pair = std::make_pair(fractional_pair.first, resource_quantity);
         fractional_pair.second -= resource_quantity;
-
-        // Remove the fractional pair if the new capacity is 0
-        if (EqualsZeroEpsilon(fractional_pair.second)) {
-          std::swap(fractional_pair, fractional_ids_[fractional_ids_.size() - 1]);
-          fractional_ids_.pop_back();
-        }
         return ResourceIds({return_pair});
       }
     }
@@ -266,18 +257,15 @@ void ResourceIds::Release(const ResourceIds &resource_ids) {
     if (fractional_pair_it == fractional_ids_.end()) {
       fractional_ids_.push_back(fractional_pair_to_return);
     } else {
+      RAY_CHECK(fractional_pair_it->second < 1);
       fractional_pair_it->second += fractional_pair_to_return.second;
-      // TODO(romilb): Double precision addition may sometimes exceed 1 by a small epsilon
-      // - need to fix this.
-      RAY_CHECK(fractional_pair_it->second <= 1 + EPSILON)
-          << "Fractional Resource Id " << fractional_pair_it->first << " capacity is "
-          << fractional_pair_it->second << ". Should have been less than one.";
       // If this makes the ID whole, then return it to the list of whole IDs.
-      // TODO(romilb): Double precision addition may sometimes exceed 1 by a small epsilon
-      // - need to fix this.
-      if (EqualsOneEpsilon(fractional_pair_it->second)) {
+      if (fractional_pair_it->second >= 1) {
         whole_ids_.push_back(resource_id);
-        fractional_ids_.erase(fractional_pair_it);
+        fractional_pair_it->second -= 1;
+        if (fractional_pair_it->second < 1e-6) {
+          fractional_ids_.erase(fractional_pair_it);
+        }
       }
     }
   }
@@ -295,10 +283,6 @@ const std::vector<std::pair<int64_t, double>> &ResourceIds::FractionalIds() cons
   return fractional_ids_;
 }
 
-bool ResourceIds::TotalQuantityIsZero() const {
-  return whole_ids_.empty() && fractional_ids_.empty();
-}
-
 double ResourceIds::TotalQuantity() const {
   double total_quantity = whole_ids_.size();
   for (auto const &fractional_pair : fractional_ids_) {
@@ -346,9 +330,9 @@ bool ResourceIdSet::Contains(const ResourceSet &resource_set) const {
   for (auto const &resource_pair : resource_set.GetResourceMap()) {
     auto const &resource_name = resource_pair.first;
     double resource_quantity = resource_pair.second;
-    RAY_CHECK(resource_quantity > 0 + EPSILON) << "Resource " << resource_name
-                                               << " capacity is " << resource_quantity
-                                               << ". Should have been greater than zero.";
+    if (resource_quantity == 0) {
+      continue;
+    }
 
     auto it = available_resources_.find(resource_name);
     if (it == available_resources_.end()) {
@@ -368,16 +352,14 @@ ResourceIdSet ResourceIdSet::Acquire(const ResourceSet &resource_set) {
   for (auto const &resource_pair : resource_set.GetResourceMap()) {
     auto const &resource_name = resource_pair.first;
     double resource_quantity = resource_pair.second;
-    RAY_CHECK(resource_quantity > 0 + EPSILON) << "Resource " << resource_name
-                                               << " capacity is " << resource_quantity
-                                               << ". Should have been greater than zero.";
+
+    if (resource_quantity == 0) {
+      continue;
+    }
 
     auto it = available_resources_.find(resource_name);
     RAY_CHECK(it != available_resources_.end());
     acquired_resources[resource_name] = it->second.Acquire(resource_quantity);
-    if (it->second.TotalQuantityIsZero()) {
-      available_resources_.erase(it);
-    }
   }
   return ResourceIdSet(acquired_resources);
 }
@@ -386,10 +368,15 @@ void ResourceIdSet::Release(const ResourceIdSet &resource_id_set) {
   for (auto const &resource_pair : resource_id_set.AvailableResources()) {
     auto const &resource_name = resource_pair.first;
     auto const &resource_ids = resource_pair.second;
-    RAY_CHECK(!resource_ids.TotalQuantityIsZero());
+
+    if (resource_ids.TotalQuantity() == 0) {
+      continue;
+    }
 
     auto it = available_resources_.find(resource_name);
     if (it == available_resources_.end()) {
+      // This should not happen when Release is called on resources that were obtained
+      // through a corresponding call to Acquire.
       available_resources_[resource_name] = resource_ids;
     } else {
       it->second.Release(resource_ids);
@@ -487,6 +474,18 @@ SchedulingResources::SchedulingResources(const ResourceSet &total)
 
 SchedulingResources::~SchedulingResources() {}
 
+ResourceAvailabilityStatus SchedulingResources::CheckResourcesSatisfied(
+    ResourceSet &resources) const {
+  if (!resources.IsSubset(resources_total_)) {
+    return ResourceAvailabilityStatus::kInfeasible;
+  }
+  // Resource demand specified is feasible. Check if it's available.
+  if (!resources.IsSubset(resources_available_)) {
+    return ResourceAvailabilityStatus::kResourcesUnavailable;
+  }
+  return ResourceAvailabilityStatus::kFeasible;
+}
+
 const ResourceSet &SchedulingResources::GetAvailableResources() const {
   return resources_available_;
 }
@@ -508,13 +507,13 @@ const ResourceSet &SchedulingResources::GetLoadResources() const {
 }
 
 // Return specified resources back to SchedulingResources.
-void SchedulingResources::Release(const ResourceSet &resources) {
-  resources_available_.AddResources(resources);
+bool SchedulingResources::Release(const ResourceSet &resources) {
+  return resources_available_.AddResourcesStrict(resources);
 }
 
 // Take specified resources from SchedulingResources.
-void SchedulingResources::Acquire(const ResourceSet &resources) {
-  resources_available_.SubtractResourcesStrict(resources);
+bool SchedulingResources::Acquire(const ResourceSet &resources) {
+  return resources_available_.SubtractResourcesStrict(resources);
 }
 
 std::string SchedulingResources::DebugString() const {
diff --git a/src/ray/raylet/scheduling_resources.h b/src/ray/raylet/scheduling_resources.h
index df1a53779..daf6372c4 100644
--- a/src/ray/raylet/scheduling_resources.h
+++ b/src/ray/raylet/scheduling_resources.h
@@ -8,25 +8,19 @@
 
 #include "ray/raylet/format/node_manager_generated.h"
 
-#define EPSILON 0.00001
-
 namespace ray {
 
 namespace raylet {
 
 const std::string kCPU_ResourceLabel = "CPU";
 
-/// \brief Test if the quantity is within epsilon bounds of 0.
-///
-/// \param quantity: Quantity to check
-/// \return True if  -epsilon <= Quantity <= epsilon, False otherwise.
-bool EqualsZeroEpsilon(double quantity);
-
-/// \brief Test if the quantity is within epsilon bounds of 1.
-///
-/// \param quantity: Quantity to check
-/// \return True if  1 - epsilon <= Quantity <= 1 + epsilon, False otherwise.
-bool EqualsOneEpsilon(double quantity);
+/// Resource availability status reports whether the resource requirement is
+/// (1) infeasible, (2) feasible but currently unavailable, or (3) available.
+enum class ResourceAvailabilityStatus : int {
+  kInfeasible,            ///< Cannot ever satisfy resource requirements.
+  kResourcesUnavailable,  ///< Feasible, but not currently available.
+  kFeasible               ///< Feasible and currently available.
+};
 
 /// \class ResourceSet
 /// \brief Encapsulates and operates on a set of resources, including CPUs,
@@ -73,12 +67,26 @@ class ResourceSet {
   /// False otherwise.
   bool IsSuperset(const ResourceSet &other) const;
 
+  /// \brief Add a new resource to the resource set.
+  ///
+  /// \param resource_name: name/label of the resource to add.
+  /// \param capacity: numeric capacity value for the resource to add.
+  /// \return True, if the resource was successfully added. False otherwise.
+  bool AddResource(const std::string &resource_name, double capacity);
+
   /// \brief Remove the specified resource from the resource set.
   ///
   /// \param resource_name: name/label of the resource to remove.
   /// \return True, if the resource was successfully removed. False otherwise.
   bool RemoveResource(const std::string &resource_name);
 
+  /// \brief Add a set of resources to the current set of resources only if the resource
+  /// labels match.
+  ///
+  /// \param other: The other resource set to add.
+  /// \return True if the resource set was added successfully. False otherwise.
+  bool AddResourcesStrict(const ResourceSet &other);
+
   /// \brief Aggregate resources from the other set into this set, adding any missing
   /// resource labels to this set.
   ///
@@ -86,28 +94,21 @@ class ResourceSet {
   /// \return Void.
   void AddResources(const ResourceSet &other);
 
-  /// \brief Subtract a set of resources from the current set of resources.
-  /// Deletes any resource if the capacity after subtraction is zero or negative.
+  /// \brief Subtract a set of resources from the current set of resources, only if
+  /// resource labels match.
   ///
   /// \param other: The resource set to subtract from the current resource set.
-  /// \return Void.
-  void SubtractResources(const ResourceSet &other);
-
-  /// \brief Subtract a set of resources from the current set of resources and
-  /// check that the post-subtraction result nonnegative. Assumes other
-  /// is a subset of the ResourceSet. Deletes any resource if the capacity after
-  /// subtraction is zero.
-  ///
-  /// \param other: The resource set to subtract from the current resource set.
-  /// \return Void.
-  void SubtractResourcesStrict(const ResourceSet &other);
+  /// \return True if the resource set was subtracted successfully.
+  /// False otherwise.
+  bool SubtractResourcesStrict(const ResourceSet &other);
 
   /// Return the capacity value associated with the specified resource.
   ///
   /// \param resource_name: Resource name for which capacity is requested.
-  /// \return The capacity value associated with the specified resource, zero if resource
-  /// does not exist.
-  double GetResource(const std::string &resource_name) const;
+  /// \param[out] value: Resource capacity value.
+  /// \return True if the resource capacity value was successfully retrieved.
+  /// False otherwise.
+  bool GetResource(const std::string &resource_name, double *value) const;
 
   /// Return the number of CPUs.
   ///
@@ -125,7 +126,7 @@ class ResourceSet {
   const std::string ToString() const;
 
  private:
-  /// Resource capacity map. The capacities (double) are always positive.
+  /// Resource capacity map.
   std::unordered_map<std::string, double> resource_capacity_;
 };
 
@@ -204,11 +205,6 @@ class ResourceIds {
   /// \return The fractional IDs.
   const std::vector<std::pair<int64_t, double>> &FractionalIds() const;
 
-  /// \brief Check if ResourceIds has any resources.
-  ///
-  /// \return True if there are no whole or fractional resources. False otherwise.
-  bool TotalQuantityIsZero() const;
-
   /// \brief Return the total quantity of resources, ignoring the specific IDs.
   ///
   /// \return The total quantity of the resource.
@@ -333,6 +329,13 @@ class SchedulingResources {
   /// \brief SchedulingResources destructor.
   ~SchedulingResources();
 
+  /// \brief Check if the specified resource request can be satisfied.
+  ///
+  /// \param set: The set of resources representing the resource request.
+  /// \return Availability status that specifies if the requested resource set
+  /// is feasible, infeasible, or feasible but unavailable.
+  ResourceAvailabilityStatus CheckResourcesSatisfied(ResourceSet &set) const;
+
   /// \brief Request the set and capacity of resources currently available.
   ///
   /// \return Immutable set of resources with currently available capacity.
@@ -360,14 +363,16 @@ class SchedulingResources {
   /// \brief Release the amount of resources specified.
   ///
   /// \param resources: the amount of resources to be released.
-  /// \return Void.
-  void Release(const ResourceSet &resources);
+  /// \return True if resources were successfully released. False otherwise.
+  bool Release(const ResourceSet &resources);
 
   /// \brief Acquire the amount of resources specified.
   ///
   /// \param resources: the amount of resources to be acquired.
-  /// \return Void.
-  void Acquire(const ResourceSet &resources);
+  /// \return True if resources were acquired without oversubscription. If this
+  /// returns false, then the resources were still acquired, but we are now at
+  /// negative resources.
+  bool Acquire(const ResourceSet &resources);
 
   /// Returns debug string for class.
   ///
diff --git a/src/ray/raylet/worker_pool_test.cc b/src/ray/raylet/worker_pool_test.cc
index 9799dfb80..c548fc924 100644
--- a/src/ray/raylet/worker_pool_test.cc
+++ b/src/ray/raylet/worker_pool_test.cc
@@ -77,7 +77,7 @@ static inline TaskSpecification ExampleTaskSpec(
   std::vector<std::string> function_descriptor(3);
   return TaskSpecification(DriverID::nil(), TaskID::nil(), 0, ActorID::nil(),
                            ObjectID::nil(), 0, actor_id, ActorHandleID::nil(), 0, {}, {},
-                           0, {}, {}, language, function_descriptor);
+                           0, {{}}, {{}}, language, function_descriptor);
 }
 
 TEST_F(WorkerPoolTest, HandleWorkerRegistration) {