diff --git a/pkg/apis/admissionregistration/fuzzer/fuzzer.go b/pkg/apis/admissionregistration/fuzzer/fuzzer.go
index 111e3494039..ca675e9b19b 100644
--- a/pkg/apis/admissionregistration/fuzzer/fuzzer.go
+++ b/pkg/apis/admissionregistration/fuzzer/fuzzer.go
@@ -98,5 +98,14 @@ var Funcs = func(codecs runtimeserializer.CodecFactory) []interface{} {
 				obj.MatchPolicy = &m
 			}
 		},
+		func(obj *admissionregistration.ParamRef, c fuzz.Continue) {
+			c.FuzzNoCustom(obj) // fuzz self without calling this function again
+
+			// Populate required field
+			if obj.ParameterNotFoundAction == nil {
+				v := admissionregistration.DenyAction
+				obj.ParameterNotFoundAction = &v
+			}
+		},
 	}
 }
diff --git a/pkg/apis/admissionregistration/types.go b/pkg/apis/admissionregistration/types.go
index 2f250653980..578e8d52fe9 100644
--- a/pkg/apis/admissionregistration/types.go
+++ b/pkg/apis/admissionregistration/types.go
@@ -76,6 +76,18 @@ const (
 	AllScopes ScopeType = "*"
 )
 
+// ParameterNotFoundActionType specifies a failure policy that defines how a binding
+// is evaluated when the param referred by its perNamespaceParamRef is not found.
+type ParameterNotFoundActionType string
+
+const (
+	// Allow means all requests will be admitted if no param resources
+	// could be found.
+	AllowAction ParameterNotFoundActionType = "Allow"
+	// Deny means all requests will be denied if no param resources are found.
+	DenyAction ParameterNotFoundActionType = "Deny"
+)
+
 // FailurePolicyType specifies the type of failure policy
 type FailurePolicyType string
 
@@ -401,6 +413,15 @@ type AuditAnnotation struct {
 
 // ValidatingAdmissionPolicyBinding binds the ValidatingAdmissionPolicy with paramerized resources.
 // ValidatingAdmissionPolicyBinding and parameter CRDs together define how cluster administrators configure policies for clusters.
+//
+// For a given admission request, each binding will cause its policy to be
+// evaluated N times, where N is 1 for policies/bindings that don't use
+// params, otherwise N is the number of parameters selected by the binding.
+//
+// The CEL expressions of a policy must have a computed CEL cost below the maximum
+// CEL budget. Each evaluation of the policy is given an independent CEL cost budget.
+// Adding/removing policies, bindings, or params can not affect whether a
+// given (policy, binding, param) combination is within its own CEL budget.
 type ValidatingAdmissionPolicyBinding struct {
 	metav1.TypeMeta
 	// Standard object metadata; More info: https://git.k8s.io/community/contributors/devel/sig-architecture/api-conventions.md#metadata.
@@ -430,9 +451,10 @@ type ValidatingAdmissionPolicyBindingSpec struct {
 	// Required.
 	PolicyName string
 
-	// ParamRef specifies the parameter resource used to configure the admission control policy.
+	// paramRef specifies the parameter resource used to configure the admission control policy.
 	// It should point to a resource of the type specified in ParamKind of the bound ValidatingAdmissionPolicy.
 	// If the policy specifies a ParamKind and the resource referred to by ParamRef does not exist, this binding is considered mis-configured and the FailurePolicy of the ValidatingAdmissionPolicy applied.
+	// If the policy does not specify a ParamKind then this field is ignored, and the rules are evaluated without a param.
 	// +optional
 	ParamRef *ParamRef
 
@@ -486,14 +508,63 @@ type ValidatingAdmissionPolicyBindingSpec struct {
 	ValidationActions []ValidationAction
 }
 
-// ParamRef references a parameter resource
+// ParamRef describes how to locate the params to be used as input to
+// expressions of rules applied by a policy binding.
+// +structType=atomic
 type ParamRef struct {
-	// Name of the resource being referenced.
+	// name is the name of the resource being referenced.
+	//
+	// One of `name` or `selector` must be set, but `name` and `selector` are
+	// mutually exclusive properties. If one is set, the other must be unset.
+	//
+	// A single parameter used for all admission requests can be configured
+	// by setting the `name` field, leaving `selector` blank, and setting namespace
+	// if `paramKind` is namespace-scoped.
+	//
+	// +optional
 	Name string
-	// Namespace of the referenced resource.
-	// Should be empty for the cluster-scoped resources
+
+	// namespace is the namespace of the referenced resource. Allows limiting
+	// the search for params to a specific namespace. Applies to both `name` and
+	// `selector` fields.
+	//
+	// A per-namespace parameter may be used by specifying a namespace-scoped
+	// `paramKind` in the policy and leaving this field empty.
+	//
+	// - If `paramKind` is cluster-scoped, this field MUST be unset. Setting this
+	// field results in a configuration error.
+	//
+	// - If `paramKind` is namespace-scoped, the namespace of the object being
+	// evaluated for admission will be used when this field is left unset. Take
+	// care that if this is left empty the binding must not match any cluster-scoped
+	// resources, which will result in an error.
+	//
 	// +optional
 	Namespace string
+
+	// selector can be used to match multiple param objects based on their labels.
+	// Supply selector: {} to match all resources of the ParamKind.
+	//
+	// If multiple params are found, they are all evaluated with the policy expressions
+	// and the results are ANDed together.
+	//
+	// One of `name` or `selector` must be set, but `name` and `selector` are
+	// mutually exclusive properties. If one is set, the other must be unset.
+	//
+	// +optional
+	Selector *metav1.LabelSelector
+
+	// parameterNotFoundAction controls the behavior of the binding when the resource
+	// exists, and name or selector is valid, but there are no parameters
+	// matched by the binding. If the value is set to `Allow`, then no
+	// matched parameters will be treated as successful validation by the binding.
+	// If set to `Deny`, then no matched parameters will be subject to the
+	// `failurePolicy` of the policy.
+	//
+	// Allowed values are `Allow` or `Deny`
+	//
+	// Required
+	ParameterNotFoundAction *ParameterNotFoundActionType
 }
 
 // MatchResources decides whether to run the admission control policy on an object based
diff --git a/pkg/apis/admissionregistration/v1alpha1/defaults.go b/pkg/apis/admissionregistration/v1alpha1/defaults.go
index 85d12b128f7..1abb61b2c0c 100644
--- a/pkg/apis/admissionregistration/v1alpha1/defaults.go
+++ b/pkg/apis/admissionregistration/v1alpha1/defaults.go
@@ -49,3 +49,11 @@ func SetDefaults_MatchResources(obj *admissionregistrationv1alpha1.MatchResource
 		obj.ObjectSelector = &selector
 	}
 }
+
+// SetDefaults_ParamRef sets defaults for ParamRef
+func SetDefaults_ParamRef(obj *admissionregistrationv1alpha1.ParamRef) {
+	if obj.ParameterNotFoundAction == nil {
+		v := admissionregistrationv1alpha1.DenyAction
+		obj.ParameterNotFoundAction = &v
+	}
+}
diff --git a/pkg/apis/admissionregistration/v1alpha1/defaults_test.go b/pkg/apis/admissionregistration/v1alpha1/defaults_test.go
index 9315118dd8b..3c09d708d5f 100644
--- a/pkg/apis/admissionregistration/v1alpha1/defaults_test.go
+++ b/pkg/apis/admissionregistration/v1alpha1/defaults_test.go
@@ -116,3 +116,58 @@ func TestDefaultAdmissionPolicy(t *testing.T) {
 		})
 	}
 }
+
+func TestDefaultAdmissionPolicyBinding(t *testing.T) {
+	denyAction := v1alpha1.DenyAction
+	equivalent := v1alpha1.Equivalent
+
+	tests := []struct {
+		name     string
+		original runtime.Object
+		expected runtime.Object
+	}{
+		{
+			name: "ValidatingAdmissionPolicyBinding.ParamRef.ParameterNotFoundAction",
+			original: &v1alpha1.ValidatingAdmissionPolicyBinding{
+				Spec: v1alpha1.ValidatingAdmissionPolicyBindingSpec{
+					ParamRef: &v1alpha1.ParamRef{},
+				},
+			},
+			expected: &v1alpha1.ValidatingAdmissionPolicyBinding{
+				Spec: v1alpha1.ValidatingAdmissionPolicyBindingSpec{
+					ParamRef: &v1alpha1.ParamRef{
+						ParameterNotFoundAction: &denyAction,
+					},
+				},
+			},
+		},
+		{
+			name: "ValidatingAdmissionPolicyBinding.MatchResources",
+			original: &v1alpha1.ValidatingAdmissionPolicyBinding{
+				Spec: v1alpha1.ValidatingAdmissionPolicyBindingSpec{
+					MatchResources: &v1alpha1.MatchResources{},
+				},
+			},
+			expected: &v1alpha1.ValidatingAdmissionPolicyBinding{
+				Spec: v1alpha1.ValidatingAdmissionPolicyBindingSpec{
+					MatchResources: &v1alpha1.MatchResources{
+						NamespaceSelector: &metav1.LabelSelector{},
+						ObjectSelector:    &metav1.LabelSelector{},
+						MatchPolicy:       &equivalent,
+					},
+				},
+			},
+		},
+	}
+
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			original := test.original
+			expected := test.expected
+			legacyscheme.Scheme.Default(original)
+			if !apiequality.Semantic.DeepEqual(original, expected) {
+				t.Error(cmp.Diff(expected, original))
+			}
+		})
+	}
+}
diff --git a/pkg/apis/admissionregistration/validation/validation.go b/pkg/apis/admissionregistration/validation/validation.go
index 1f54ab725f2..4ea4ffe78ce 100644
--- a/pkg/apis/admissionregistration/validation/validation.go
+++ b/pkg/apis/admissionregistration/validation/validation.go
@@ -1151,9 +1151,38 @@ func validateParamRef(pr *admissionregistration.ParamRef, fldPath *field.Path) f
 	if pr == nil {
 		return allErrors
 	}
-	for _, msg := range path.ValidatePathSegmentName(pr.Name, false) {
-		allErrors = append(allErrors, field.Invalid(fldPath.Child("name"), pr.Name, msg))
+
+	if len(pr.Name) > 0 {
+		for _, msg := range path.ValidatePathSegmentName(pr.Name, false) {
+			allErrors = append(allErrors, field.Invalid(fldPath.Child("name"), pr.Name, msg))
+		}
+
+		if pr.Selector != nil {
+			allErrors = append(allErrors, field.Forbidden(fldPath.Child("name"), `name and selector are mutually exclusive`))
+		}
 	}
+
+	if pr.Selector != nil {
+		labelSelectorValidationOpts := metav1validation.LabelSelectorValidationOptions{}
+		allErrors = append(allErrors, metav1validation.ValidateLabelSelector(pr.Selector, labelSelectorValidationOpts, fldPath.Child("selector"))...)
+
+		if len(pr.Name) > 0 {
+			allErrors = append(allErrors, field.Forbidden(fldPath.Child("selector"), `name and selector are mutually exclusive`))
+		}
+	}
+
+	if len(pr.Name) == 0 && pr.Selector == nil {
+		allErrors = append(allErrors, field.Required(fldPath, `one of name or selector must be specified`))
+	}
+
+	if pr.ParameterNotFoundAction == nil || len(*pr.ParameterNotFoundAction) == 0 {
+		allErrors = append(allErrors, field.Required(fldPath.Child("parameterNotFoundAction"), ""))
+	} else {
+		if *pr.ParameterNotFoundAction != admissionregistration.DenyAction && *pr.ParameterNotFoundAction != admissionregistration.AllowAction {
+			allErrors = append(allErrors, field.NotSupported(fldPath.Child("parameterNotFoundAction"), pr.ParameterNotFoundAction, []string{string(admissionregistration.DenyAction), string(admissionregistration.AllowAction)}))
+		}
+	}
+
 	return allErrors
 }
 
diff --git a/pkg/apis/admissionregistration/validation/validation_test.go b/pkg/apis/admissionregistration/validation/validation_test.go
index 2c7a13d770f..8b2d50daa95 100644
--- a/pkg/apis/admissionregistration/validation/validation_test.go
+++ b/pkg/apis/admissionregistration/validation/validation_test.go
@@ -32,6 +32,8 @@ import (
 	"k8s.io/kubernetes/pkg/apis/admissionregistration"
 )
 
+func ptr[T any](v T) *T { return &v }
+
 func strPtr(s string) *string { return &s }
 
 func int32Ptr(i int32) *int32 { return &i }
@@ -3517,7 +3519,8 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				MatchResources: &admissionregistration.MatchResources{
 					MatchPolicy: func() *admissionregistration.MatchPolicyType {
@@ -3537,7 +3540,8 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				MatchResources: &admissionregistration.MatchResources{
 					ResourceRules: []admissionregistration.NamedRuleWithOperations{{
@@ -3591,7 +3595,8 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				}, MatchResources: &admissionregistration.MatchResources{
 					ResourceRules: []admissionregistration.NamedRuleWithOperations{{
 						RuleWithOperations: admissionregistration.RuleWithOperations{
@@ -3616,7 +3621,8 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				}, MatchResources: &admissionregistration.MatchResources{
 					ResourceRules: []admissionregistration.NamedRuleWithOperations{{
 						RuleWithOperations: admissionregistration.RuleWithOperations{
@@ -3641,7 +3647,8 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 				MatchResources: &admissionregistration.MatchResources{
@@ -3668,7 +3675,8 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 				MatchResources: &admissionregistration.MatchResources{
@@ -3704,7 +3712,8 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 				MatchResources: &admissionregistration.MatchResources{
@@ -3731,7 +3740,8 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 				MatchResources: &admissionregistration.MatchResources{
@@ -3758,7 +3768,8 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 				MatchResources: &admissionregistration.MatchResources{
@@ -3794,7 +3805,8 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 				MatchResources: &admissionregistration.MatchResources{
@@ -3821,7 +3833,8 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 				MatchResources: &admissionregistration.MatchResources{
@@ -3848,7 +3861,8 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny, admissionregistration.Deny},
 			},
@@ -3863,12 +3877,80 @@ func TestValidateValidatingAdmissionPolicyBinding(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.ValidationAction("illegal")},
 			},
 		},
 		expectedError: `Unsupported value: "illegal": supported values: "Audit", "Deny", "Warn"`,
+	}, {
+		name: "paramRef selector must not be set when name is set",
+		config: &admissionregistration.ValidatingAdmissionPolicyBinding{
+			ObjectMeta: metav1.ObjectMeta{
+				Name: "config",
+			},
+			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
+				PolicyName:        "xyzlimit-scale.example.com",
+				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
+				ParamRef: &admissionregistration.ParamRef{
+					Name: "xyzlimit-scale-setting.example.com",
+					Selector: &metav1.LabelSelector{
+						MatchLabels: map[string]string{
+							"label": "value",
+						},
+					},
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
+				},
+			},
+		},
+		expectedError: `spec.paramRef.name: Forbidden: name and selector are mutually exclusive, spec.paramRef.selector: Forbidden: name and selector are mutually exclusive`,
+	}, {
+		name: "paramRef parameterNotFoundAction must be set",
+		config: &admissionregistration.ValidatingAdmissionPolicyBinding{
+			ObjectMeta: metav1.ObjectMeta{
+				Name: "config",
+			},
+			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
+				PolicyName:        "xyzlimit-scale.example.com",
+				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
+				ParamRef: &admissionregistration.ParamRef{
+					Name: "xyzlimit-scale-setting.example.com",
+				},
+			},
+		},
+		expectedError: "spec.paramRef.parameterNotFoundAction: Required value",
+	}, {
+		name: "paramRef parameterNotFoundAction must be an valid value",
+		config: &admissionregistration.ValidatingAdmissionPolicyBinding{
+			ObjectMeta: metav1.ObjectMeta{
+				Name: "config",
+			},
+			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
+				PolicyName:        "xyzlimit-scale.example.com",
+				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
+				ParamRef: &admissionregistration.ParamRef{
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.ParameterNotFoundActionType("invalid")),
+				},
+			},
+		},
+		expectedError: `spec.paramRef.parameterNotFoundAction: Unsupported value: "invalid": supported values: "Deny", "Allow"`,
+	}, {
+		name: "paramRef one of name or selector",
+		config: &admissionregistration.ValidatingAdmissionPolicyBinding{
+			ObjectMeta: metav1.ObjectMeta{
+				Name: "config",
+			},
+			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
+				PolicyName:        "xyzlimit-scale.example.com",
+				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
+				ParamRef: &admissionregistration.ParamRef{
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
+				},
+			},
+		},
+		expectedError: `one of name or selector must be specified`,
 	}}
 	for _, test := range tests {
 		t.Run(test.name, func(t *testing.T) {
@@ -3903,7 +3985,8 @@ func TestValidateValidatingAdmissionPolicyBindingUpdate(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 				MatchResources: &admissionregistration.MatchResources{
@@ -3937,7 +4020,8 @@ func TestValidateValidatingAdmissionPolicyBindingUpdate(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 				MatchResources: &admissionregistration.MatchResources{
@@ -3973,7 +4057,8 @@ func TestValidateValidatingAdmissionPolicyBindingUpdate(t *testing.T) {
 			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 				PolicyName: "xyzlimit-scale.example.com",
 				ParamRef: &admissionregistration.ParamRef{
-					Name: "xyzlimit-scale-setting.example.com",
+					Name:                    "xyzlimit-scale-setting.example.com",
+					ParameterNotFoundAction: ptr(admissionregistration.DenyAction),
 				},
 				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 				MatchResources: &admissionregistration.MatchResources{
diff --git a/pkg/printers/internalversion/printers.go b/pkg/printers/internalversion/printers.go
index 3d309dce3bb..138e38e025c 100644
--- a/pkg/printers/internalversion/printers.go
+++ b/pkg/printers/internalversion/printers.go
@@ -1673,13 +1673,18 @@ func printValidatingAdmissionPolicyBinding(obj *admissionregistration.Validating
 		Object: runtime.RawExtension{Object: obj},
 	}
 	paramName := "<unset>"
-	if obj.Spec.ParamRef != nil {
-		if obj.Spec.ParamRef.Namespace != "" {
-			paramName = obj.Spec.ParamRef.Namespace + "/" + obj.Spec.ParamRef.Name
-		} else {
-			paramName = obj.Spec.ParamRef.Name
+	if pr := obj.Spec.ParamRef; pr != nil {
+		if len(pr.Name) > 0 {
+			if pr.Namespace != "" {
+				paramName = pr.Namespace + "/" + pr.Name
+			} else {
+				// Can't tell from here if param is cluster-scoped, so all
+				// params without names get * namespace
+				paramName = "*/" + pr.Name
+			}
+		} else if pr.Selector != nil {
+			paramName = pr.Selector.String()
 		}
-
 	}
 	row.Cells = append(row.Cells, obj.Name, obj.Spec.PolicyName, paramName, translateTimestampSince(obj.CreationTimestamp))
 	return []metav1.TableRow{row}, nil
diff --git a/pkg/registry/admissionregistration/validatingadmissionpolicybinding/authz.go b/pkg/registry/admissionregistration/validatingadmissionpolicybinding/authz.go
index a68e6c727e1..49898e694bd 100644
--- a/pkg/registry/admissionregistration/validatingadmissionpolicybinding/authz.go
+++ b/pkg/registry/admissionregistration/validatingadmissionpolicybinding/authz.go
@@ -85,15 +85,21 @@ func (v *validatingAdmissionPolicyBindingStrategy) authorize(ctx context.Context
 		}
 	}
 
-	paramRef := binding.Spec.ParamRef
+	var attrs authorizer.AttributesRecord
 
-	// require that the user can read (verb "get") the referred resource.
-	attrs := authorizer.AttributesRecord{
+	paramRef := binding.Spec.ParamRef
+	verb := "get"
+
+	if len(paramRef.Name) == 0 {
+		verb = "list"
+	}
+
+	attrs = authorizer.AttributesRecord{
 		User:            user,
-		Verb:            "get",
+		Verb:            verb,
 		ResourceRequest: true,
 		Name:            paramRef.Name,
-		Namespace:       paramRef.Namespace,
+		Namespace:       paramRef.Namespace, // if empty, no namespace indicates get across all namespaces
 		APIGroup:        apiGroup,
 		APIVersion:      apiVersion,
 		Resource:        resource,
@@ -104,7 +110,8 @@ func (v *validatingAdmissionPolicyBindingStrategy) authorize(ctx context.Context
 		return err
 	}
 	if d != authorizer.DecisionAllow {
-		return fmt.Errorf(`user %v does not have "get" permission on the object referenced by paramRef`, user)
+		return fmt.Errorf(`user %v does not have "%v" permission on the object referenced by paramRef`, verb, user)
 	}
+
 	return nil
 }
diff --git a/pkg/registry/admissionregistration/validatingadmissionpolicybinding/authz_test.go b/pkg/registry/admissionregistration/validatingadmissionpolicybinding/authz_test.go
index f42fcd380d2..c72e9f92d2a 100644
--- a/pkg/registry/admissionregistration/validatingadmissionpolicybinding/authz_test.go
+++ b/pkg/registry/admissionregistration/validatingadmissionpolicybinding/authz_test.go
@@ -103,19 +103,46 @@ func TestAuthorization(t *testing.T) {
 			strategy := NewStrategy(tc.auth, tc.policyGetter, tc.resourceResolver)
 			t.Run("create", func(t *testing.T) {
 				ctx := request.WithUser(context.Background(), tc.userInfo)
-				errs := strategy.Validate(ctx, validPolicyBinding())
-				if len(errs) > 0 != tc.expectErr {
-					t.Errorf("expected error: %v but got error: %v", tc.expectErr, errs)
+				for _, obj := range validPolicyBindings() {
+					errs := strategy.Validate(ctx, obj)
+					if len(errs) > 0 != tc.expectErr {
+						t.Errorf("expected error: %v but got error: %v", tc.expectErr, errs)
+					}
 				}
 			})
 			t.Run("update", func(t *testing.T) {
 				ctx := request.WithUser(context.Background(), tc.userInfo)
-				obj := validPolicyBinding()
-				objWithChangedParamRef := obj.DeepCopy()
-				objWithChangedParamRef.Spec.ParamRef.Name = "changed"
-				errs := strategy.ValidateUpdate(ctx, obj, objWithChangedParamRef)
-				if len(errs) > 0 != tc.expectErr {
-					t.Errorf("expected error: %v but got error: %v", tc.expectErr, errs)
+				for _, obj := range validPolicyBindings() {
+					objWithChangedParamRef := obj.DeepCopy()
+					if pr := objWithChangedParamRef.Spec.ParamRef; pr != nil {
+						if len(pr.Name) > 0 {
+							pr.Name = "changed"
+						}
+
+						if pr.Selector != nil {
+							pr.Selector = &metav1.LabelSelector{
+								MatchLabels: map[string]string{
+									"changed": "value",
+								},
+							}
+						}
+
+						if len(pr.Namespace) > 0 {
+							pr.Namespace = "othernamespace"
+						}
+
+						if pr.ParameterNotFoundAction == nil || *pr.ParameterNotFoundAction == admissionregistration.AllowAction {
+							v := admissionregistration.DenyAction
+							pr.ParameterNotFoundAction = &v
+						} else {
+							v := admissionregistration.AllowAction
+							pr.ParameterNotFoundAction = &v
+						}
+					}
+					errs := strategy.ValidateUpdate(ctx, obj, objWithChangedParamRef)
+					if len(errs) > 0 != tc.expectErr {
+						t.Errorf("expected error: %v but got error: %v", tc.expectErr, errs)
+					}
 				}
 			})
 		})
diff --git a/pkg/registry/admissionregistration/validatingadmissionpolicybinding/storage/storage_test.go b/pkg/registry/admissionregistration/validatingadmissionpolicybinding/storage/storage_test.go
index db4af525be0..f177f57ea67 100644
--- a/pkg/registry/admissionregistration/validatingadmissionpolicybinding/storage/storage_test.go
+++ b/pkg/registry/admissionregistration/validatingadmissionpolicybinding/storage/storage_test.go
@@ -37,121 +37,175 @@ import (
 )
 
 func TestCreate(t *testing.T) {
-	storage, server := newInsecureStorage(t)
-	defer server.Terminate(t)
-	defer storage.Store.DestroyFunc()
-	test := genericregistrytest.New(t, storage.Store).ClusterScope()
-	configuration := validPolicyBinding()
-	test.TestCreate(
-		// valid
-		configuration,
-		// invalid
-		newPolicyBinding(""),
-	)
+	for _, configuration := range validPolicyBindings() {
+		t.Run(configuration.Name, func(t *testing.T) {
+			storage, server := newInsecureStorage(t)
+			defer server.Terminate(t)
+			defer storage.Store.DestroyFunc()
+			test := genericregistrytest.New(t, storage.Store).ClusterScope()
+
+			test.TestCreate(
+				// valid
+				configuration,
+				// invalid
+				newPolicyBinding(""),
+			)
+		})
+	}
 }
 
 func TestUpdate(t *testing.T) {
-	storage, server := newInsecureStorage(t)
-	defer server.Terminate(t)
-	defer storage.Store.DestroyFunc()
-	test := genericregistrytest.New(t, storage.Store).ClusterScope()
-
-	test.TestUpdate(
-		// valid
-		validPolicyBinding(),
-		// updateFunc
-		func(obj runtime.Object) runtime.Object {
-			object := obj.(*admissionregistration.ValidatingAdmissionPolicyBinding)
-			object.Labels = map[string]string{"c": "d"}
-			return object
-		},
-		// invalid updateFunc
-		func(obj runtime.Object) runtime.Object {
-			object := obj.(*admissionregistration.ValidatingAdmissionPolicyBinding)
-			object.Name = ""
-			return object
-		},
-	)
+	for _, b := range validPolicyBindings() {
+		storage, server := newInsecureStorage(t)
+		defer server.Terminate(t)
+		defer storage.Store.DestroyFunc()
+		t.Run(b.Name, func(t *testing.T) {
+			test := genericregistrytest.New(t, storage.Store).ClusterScope()
+			test.TestUpdate(
+				// valid
+				b,
+				// updateFunc
+				func(obj runtime.Object) runtime.Object {
+					object := obj.(*admissionregistration.ValidatingAdmissionPolicyBinding)
+					object.Labels = map[string]string{"c": "d"}
+					return object
+				},
+				// invalid updateFunc
+				func(obj runtime.Object) runtime.Object {
+					object := obj.(*admissionregistration.ValidatingAdmissionPolicyBinding)
+					object.Name = ""
+					return object
+				},
+			)
+		})
+	}
 }
 
 func TestGet(t *testing.T) {
-	storage, server := newInsecureStorage(t)
-	defer server.Terminate(t)
-	defer storage.Store.DestroyFunc()
-	test := genericregistrytest.New(t, storage.Store).ClusterScope()
-	test.TestGet(validPolicyBinding())
+	for _, b := range validPolicyBindings() {
+		t.Run(b.Name, func(t *testing.T) {
+			storage, server := newInsecureStorage(t)
+			defer server.Terminate(t)
+			defer storage.Store.DestroyFunc()
+
+			test := genericregistrytest.New(t, storage.Store).ClusterScope()
+			test.TestGet(b)
+		})
+	}
 }
 
 func TestList(t *testing.T) {
-	storage, server := newInsecureStorage(t)
-	defer server.Terminate(t)
-	defer storage.Store.DestroyFunc()
-	test := genericregistrytest.New(t, storage.Store).ClusterScope()
-	test.TestList(validPolicyBinding())
+	for _, b := range validPolicyBindings() {
+		t.Run(b.Name, func(t *testing.T) {
+			storage, server := newInsecureStorage(t)
+			defer server.Terminate(t)
+			defer storage.Store.DestroyFunc()
+			test := genericregistrytest.New(t, storage.Store).ClusterScope()
+			test.TestList(b)
+		})
+	}
 }
 
 func TestDelete(t *testing.T) {
-	storage, server := newInsecureStorage(t)
-	defer server.Terminate(t)
-	defer storage.Store.DestroyFunc()
-	test := genericregistrytest.New(t, storage.Store).ClusterScope()
-	test.TestDelete(validPolicyBinding())
+	for _, b := range validPolicyBindings() {
+		t.Run(b.Name, func(t *testing.T) {
+			storage, server := newInsecureStorage(t)
+			defer server.Terminate(t)
+			defer storage.Store.DestroyFunc()
+
+			test := genericregistrytest.New(t, storage.Store).ClusterScope()
+			test.TestDelete(b)
+		})
+	}
 }
 
 func TestWatch(t *testing.T) {
-	storage, server := newInsecureStorage(t)
-	defer server.Terminate(t)
-	defer storage.Store.DestroyFunc()
-	test := genericregistrytest.New(t, storage.Store).ClusterScope()
-	test.TestWatch(
-		validPolicyBinding(),
-		[]labels.Set{},
-		[]labels.Set{
-			{"hoo": "bar"},
-		},
-		[]fields.Set{
-			{"metadata.name": "foo"},
-		},
-		[]fields.Set{
-			{"metadata.name": "nomatch"},
-		},
-	)
+	for _, b := range validPolicyBindings() {
+		t.Run(b.Name, func(t *testing.T) {
+			storage, server := newInsecureStorage(t)
+			defer server.Terminate(t)
+			defer storage.Store.DestroyFunc()
+			test := genericregistrytest.New(t, storage.Store).ClusterScope()
+			test.TestWatch(
+				b,
+				[]labels.Set{},
+				[]labels.Set{
+					{"hoo": "bar"},
+				},
+				[]fields.Set{
+					{"metadata.name": b.Name},
+				},
+				[]fields.Set{
+					{"metadata.name": "nomatch"},
+				},
+			)
+		})
+	}
 }
 
-func validPolicyBinding() *admissionregistration.ValidatingAdmissionPolicyBinding {
-	return &admissionregistration.ValidatingAdmissionPolicyBinding{
-		ObjectMeta: metav1.ObjectMeta{
-			Name: "foo",
-		},
-		Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
-			PolicyName: "replicalimit-policy.example.com",
-			ParamRef: &admissionregistration.ParamRef{
-				Name: "param-test",
+func validPolicyBindings() []*admissionregistration.ValidatingAdmissionPolicyBinding {
+	denyAction := admissionregistration.DenyAction
+	return []*admissionregistration.ValidatingAdmissionPolicyBinding{
+		{
+			ObjectMeta: metav1.ObjectMeta{
+				Name: "foo",
 			},
-			ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
-			MatchResources: &admissionregistration.MatchResources{
-				MatchPolicy: func() *admissionregistration.MatchPolicyType {
-					r := admissionregistration.MatchPolicyType("Exact")
-					return &r
-				}(),
-				ObjectSelector: &metav1.LabelSelector{
-					MatchLabels: map[string]string{"a": "b"},
+			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
+				PolicyName: "replicalimit-policy.example.com",
+				ParamRef: &admissionregistration.ParamRef{
+					Name:                    "replica-limit-test.example.com",
+					ParameterNotFoundAction: &denyAction,
 				},
-				NamespaceSelector: &metav1.LabelSelector{
-					MatchLabels: map[string]string{"a": "b"},
+				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
+			},
+		},
+		{
+			ObjectMeta: metav1.ObjectMeta{
+				Name: "foo-clusterwide",
+			},
+			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
+				PolicyName: "replicalimit-policy.example.com",
+				ParamRef: &admissionregistration.ParamRef{
+					Name:                    "replica-limit-test.example.com",
+					Namespace:               "default",
+					ParameterNotFoundAction: &denyAction,
 				},
-				ResourceRules: []admissionregistration.NamedRuleWithOperations{
-					{
-						RuleWithOperations: admissionregistration.RuleWithOperations{
-							Operations: []admissionregistration.OperationType{"CREATE"},
-							Rule: admissionregistration.Rule{
-								APIGroups:   []string{"a"},
-								APIVersions: []string{"a"},
-								Resources:   []string{"a"},
-							},
+				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
+			},
+		},
+		{
+			ObjectMeta: metav1.ObjectMeta{
+				Name: "foo-selector",
+			},
+			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
+				PolicyName: "replicalimit-policy.example.com",
+				ParamRef: &admissionregistration.ParamRef{
+					Selector: &metav1.LabelSelector{
+						MatchLabels: map[string]string{
+							"label": "value",
 						},
 					},
+					ParameterNotFoundAction: &denyAction,
 				},
+				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
+			},
+		},
+		{
+			ObjectMeta: metav1.ObjectMeta{
+				Name: "foo-selector-clusterwide",
+			},
+			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
+				PolicyName: "replicalimit-policy.example.com",
+				ParamRef: &admissionregistration.ParamRef{
+					Namespace: "mynamespace",
+					Selector: &metav1.LabelSelector{
+						MatchLabels: map[string]string{
+							"label": "value",
+						},
+					},
+					ParameterNotFoundAction: &denyAction,
+				},
+				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 			},
 		},
 	}
@@ -166,7 +220,8 @@ func newPolicyBinding(name string) *admissionregistration.ValidatingAdmissionPol
 		Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
 			PolicyName: "replicalimit-policy.example.com",
 			ParamRef: &admissionregistration.ParamRef{
-				Name: "param-test",
+				Name:      "param-test",
+				Namespace: "default",
 			},
 			ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 			MatchResources:    &admissionregistration.MatchResources{},
diff --git a/pkg/registry/admissionregistration/validatingadmissionpolicybinding/strategy_test.go b/pkg/registry/admissionregistration/validatingadmissionpolicybinding/strategy_test.go
index 57d4cedd2c0..55b310db31a 100644
--- a/pkg/registry/admissionregistration/validatingadmissionpolicybinding/strategy_test.go
+++ b/pkg/registry/admissionregistration/validatingadmissionpolicybinding/strategy_test.go
@@ -35,32 +35,87 @@ func TestPolicyBindingStrategy(t *testing.T) {
 		t.Errorf("PolicyBinding should not allow create on update")
 	}
 
-	configuration := validPolicyBinding()
-	strategy.PrepareForCreate(ctx, configuration)
-	errs := strategy.Validate(ctx, configuration)
-	if len(errs) != 0 {
-		t.Errorf("Unexpected error validating %v", errs)
-	}
-	invalidConfiguration := &admissionregistration.ValidatingAdmissionPolicyBinding{
-		ObjectMeta: metav1.ObjectMeta{Name: ""},
-	}
-	strategy.PrepareForUpdate(ctx, invalidConfiguration, configuration)
-	errs = strategy.ValidateUpdate(ctx, invalidConfiguration, configuration)
-	if len(errs) == 0 {
-		t.Errorf("Expected a validation error")
+	for _, configuration := range validPolicyBindings() {
+		strategy.PrepareForCreate(ctx, configuration)
+		errs := strategy.Validate(ctx, configuration)
+		if len(errs) != 0 {
+			t.Errorf("Unexpected error validating %v", errs)
+		}
+		invalidConfiguration := &admissionregistration.ValidatingAdmissionPolicyBinding{
+			ObjectMeta: metav1.ObjectMeta{Name: ""},
+		}
+		strategy.PrepareForUpdate(ctx, invalidConfiguration, configuration)
+		errs = strategy.ValidateUpdate(ctx, invalidConfiguration, configuration)
+		if len(errs) == 0 {
+			t.Errorf("Expected a validation error")
+		}
 	}
 }
-func validPolicyBinding() *admissionregistration.ValidatingAdmissionPolicyBinding {
-	return &admissionregistration.ValidatingAdmissionPolicyBinding{
-		ObjectMeta: metav1.ObjectMeta{
-			Name: "foo",
-		},
-		Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
-			PolicyName: "replicalimit-policy.example.com",
-			ParamRef: &admissionregistration.ParamRef{
-				Name: "replica-limit-test.example.com",
+
+func validPolicyBindings() []*admissionregistration.ValidatingAdmissionPolicyBinding {
+	denyAction := admissionregistration.DenyAction
+	return []*admissionregistration.ValidatingAdmissionPolicyBinding{
+		{
+			ObjectMeta: metav1.ObjectMeta{
+				Name: "foo",
+			},
+			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
+				PolicyName: "replicalimit-policy.example.com",
+				ParamRef: &admissionregistration.ParamRef{
+					Name:                    "replica-limit-test.example.com",
+					ParameterNotFoundAction: &denyAction,
+				},
+				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
+			},
+		},
+		{
+			ObjectMeta: metav1.ObjectMeta{
+				Name: "foo-clusterwide",
+			},
+			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
+				PolicyName: "replicalimit-policy.example.com",
+				ParamRef: &admissionregistration.ParamRef{
+					Name:                    "replica-limit-test.example.com",
+					Namespace:               "default",
+					ParameterNotFoundAction: &denyAction,
+				},
+				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
+			},
+		},
+		{
+			ObjectMeta: metav1.ObjectMeta{
+				Name: "foo-selector",
+			},
+			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
+				PolicyName: "replicalimit-policy.example.com",
+				ParamRef: &admissionregistration.ParamRef{
+					Selector: &metav1.LabelSelector{
+						MatchLabels: map[string]string{
+							"label": "value",
+						},
+					},
+					ParameterNotFoundAction: &denyAction,
+				},
+				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
+			},
+		},
+		{
+			ObjectMeta: metav1.ObjectMeta{
+				Name: "foo-selector-clusterwide",
+			},
+			Spec: admissionregistration.ValidatingAdmissionPolicyBindingSpec{
+				PolicyName: "replicalimit-policy.example.com",
+				ParamRef: &admissionregistration.ParamRef{
+					Namespace: "mynamespace",
+					Selector: &metav1.LabelSelector{
+						MatchLabels: map[string]string{
+							"label": "value",
+						},
+					},
+					ParameterNotFoundAction: &denyAction,
+				},
+				ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 			},
-			ValidationActions: []admissionregistration.ValidationAction{admissionregistration.Deny},
 		},
 	}
 }
diff --git a/staging/src/k8s.io/api/admissionregistration/v1alpha1/types.go b/staging/src/k8s.io/api/admissionregistration/v1alpha1/types.go
index 3b0745cc6d5..575456c8386 100644
--- a/staging/src/k8s.io/api/admissionregistration/v1alpha1/types.go
+++ b/staging/src/k8s.io/api/admissionregistration/v1alpha1/types.go
@@ -39,6 +39,18 @@ const (
 	AllScopes ScopeType = v1.AllScopes
 )
 
+// ParameterNotFoundActionType specifies a failure policy that defines how a binding
+// is evaluated when the param referred by its perNamespaceParamRef is not found.
+// +enum
+type ParameterNotFoundActionType string
+
+const (
+	// Ignore means that an error finding params for a binding is ignored
+	AllowAction ParameterNotFoundActionType = "Allow"
+	// Fail means that an error finding params for a binding is ignored
+	DenyAction ParameterNotFoundActionType = "Deny"
+)
+
 // FailurePolicyType specifies a failure policy that defines how unrecognized errors from the admission endpoint are handled.
 // +enum
 type FailurePolicyType string
@@ -363,6 +375,15 @@ type AuditAnnotation struct {
 
 // ValidatingAdmissionPolicyBinding binds the ValidatingAdmissionPolicy with paramerized resources.
 // ValidatingAdmissionPolicyBinding and parameter CRDs together define how cluster administrators configure policies for clusters.
+//
+// For a given admission request, each binding will cause its policy to be
+// evaluated N times, where N is 1 for policies/bindings that don't use
+// params, otherwise N is the number of parameters selected by the binding.
+//
+// The CEL expressions of a policy must have a computed CEL cost below the maximum
+// CEL budget. Each evaluation of the policy is given an independent CEL cost budget.
+// Adding/removing policies, bindings, or params can not affect whether a
+// given (policy, binding, param) combination is within its own CEL budget.
 type ValidatingAdmissionPolicyBinding struct {
 	metav1.TypeMeta `json:",inline"`
 	// Standard object metadata; More info: https://git.k8s.io/community/contributors/devel/sig-architecture/api-conventions.md#metadata.
@@ -393,9 +414,10 @@ type ValidatingAdmissionPolicyBindingSpec struct {
 	// Required.
 	PolicyName string `json:"policyName,omitempty" protobuf:"bytes,1,rep,name=policyName"`
 
-	// ParamRef specifies the parameter resource used to configure the admission control policy.
+	// paramRef specifies the parameter resource used to configure the admission control policy.
 	// It should point to a resource of the type specified in ParamKind of the bound ValidatingAdmissionPolicy.
 	// If the policy specifies a ParamKind and the resource referred to by ParamRef does not exist, this binding is considered mis-configured and the FailurePolicy of the ValidatingAdmissionPolicy applied.
+	// If the policy does not specify a ParamKind then this field is ignored, and the rules are evaluated without a param.
 	// +optional
 	ParamRef *ParamRef `json:"paramRef,omitempty" protobuf:"bytes,2,rep,name=paramRef"`
 
@@ -450,15 +472,59 @@ type ValidatingAdmissionPolicyBindingSpec struct {
 	ValidationActions []ValidationAction `json:"validationActions,omitempty" protobuf:"bytes,4,rep,name=validationActions"`
 }
 
-// ParamRef references a parameter resource
+// ParamRef describes how to locate the params to be used as input to
+// expressions of rules applied by a policy binding.
 // +structType=atomic
 type ParamRef struct {
-	// Name of the resource being referenced.
+	// `name` is the name of the resource being referenced.
+	//
+	// `name` and `selector` are mutually exclusive properties. If one is set,
+	// the other must be unset.
+	//
+	// +optional
 	Name string `json:"name,omitempty" protobuf:"bytes,1,rep,name=name"`
-	// Namespace of the referenced resource.
-	// Should be empty for the cluster-scoped resources
+
+	// namespace is the namespace of the referenced resource. Allows limiting
+	// the search for params to a specific namespace. Applies to both `name` and
+	// `selector` fields.
+	//
+	// A per-namespace parameter may be used by specifying a namespace-scoped
+	// `paramKind` in the policy and leaving this field empty.
+	//
+	// - If `paramKind` is cluster-scoped, this field MUST be unset. Setting this
+	// field results in a configuration error.
+	//
+	// - If `paramKind` is namespace-scoped, the namespace of the object being
+	// evaluated for admission will be used when this field is left unset. Take
+	// care that if this is left empty the binding must not match any cluster-scoped
+	// resources, which will result in an error.
+	//
 	// +optional
 	Namespace string `json:"namespace,omitempty" protobuf:"bytes,2,rep,name=namespace"`
+
+	// selector can be used to match multiple param objects based on their labels.
+	// Supply selector: {} to match all resources of the ParamKind.
+	//
+	// If multiple params are found, they are all evaluated with the policy expressions
+	// and the results are ANDed together.
+	//
+	// One of `name` or `selector` must be set, but `name` and `selector` are
+	// mutually exclusive properties. If one is set, the other must be unset.
+	//
+	// +optional
+	Selector *metav1.LabelSelector `json:"selector,omitempty" protobuf:"bytes,3,rep,name=selector"`
+
+	// `parameterNotFoundAction` controls the behavior of the binding when the resource
+	// exists, and name or selector is valid, but there are no parameters
+	// matched by the binding. If the value is set to `Allow`, then no
+	// matched parameters will be treated as successful validation by the binding.
+	// If set to `Deny`, then no matched parameters will be subject to the
+	// `failurePolicy` of the policy.
+	//
+	// Allowed values are `Allow` or `Deny`
+	// Default to `Deny`
+	// +optional
+	ParameterNotFoundAction *ParameterNotFoundActionType `json:"parameterNotFoundAction,omitempty" protobuf:"bytes,4,rep,name=parameterNotFoundAction"`
 }
 
 // MatchResources decides whether to run the admission control policy on an object based