diff --git a/lib/irt_ruby.rb b/lib/irt_ruby.rb
index 8fb5314..6479b61 100644
--- a/lib/irt_ruby.rb
+++ b/lib/irt_ruby.rb
@@ -2,6 +2,7 @@
 
 require "irt_ruby/version"
 require "matrix"
+require "irt_ruby/model_options_validator"
 require "irt_ruby/response_data_validator"
 require "irt_ruby/rasch_model"
 require "irt_ruby/two_parameter_model"
diff --git a/lib/irt_ruby/model_options_validator.rb b/lib/irt_ruby/model_options_validator.rb
new file mode 100644
index 0000000..56973b2
--- /dev/null
+++ b/lib/irt_ruby/model_options_validator.rb
@@ -0,0 +1,38 @@
+# frozen_string_literal: true
+
+module IrtRuby
+  # Validates optimization hyperparameters shared by IRT model implementations.
+  module ModelOptionsValidator
+    module_function
+
+    def validate!(max_iter:, tolerance:, param_tolerance:, learning_rate:, decay_factor:)
+      validate_positive_integer!(:max_iter, max_iter)
+      validate_positive_finite_numeric!(:tolerance, tolerance)
+      validate_positive_finite_numeric!(:param_tolerance, param_tolerance)
+      validate_positive_finite_numeric!(:learning_rate, learning_rate)
+      validate_decay_factor!(decay_factor)
+    end
+
+    def validate_positive_integer!(name, value)
+      return if value.is_a?(Integer) && value.positive?
+
+      raise ArgumentError, "#{name} must be a positive Integer"
+    end
+
+    def validate_positive_finite_numeric!(name, value)
+      return if finite_numeric?(value) && value.positive?
+
+      raise ArgumentError, "#{name} must be a positive finite Numeric"
+    end
+
+    def validate_decay_factor!(value)
+      return if finite_numeric?(value) && value.positive? && value < 1
+
+      raise ArgumentError, "decay_factor must be a finite Numeric strictly between 0 and 1"
+    end
+
+    def finite_numeric?(value)
+      value.is_a?(Numeric) && !value.is_a?(Complex) && value.finite?
+    end
+  end
+end
diff --git a/lib/irt_ruby/rasch_model.rb b/lib/irt_ruby/rasch_model.rb
index 086e70e..a499092 100644
--- a/lib/irt_ruby/rasch_model.rb
+++ b/lib/irt_ruby/rasch_model.rb
@@ -1,5 +1,6 @@
 # frozen_string_literal: true
 
+require "irt_ruby/model_options_validator"
 require "irt_ruby/response_data_validator"
 
 module IrtRuby
@@ -21,6 +22,12 @@ def initialize(data,
       # data: A Matrix or array-of-arrays of responses (0/1 or nil for missing).
       # missing_strategy: :ignore (skip), :treat_as_incorrect, :treat_as_correct
 
+      ModelOptionsValidator.validate!(max_iter: max_iter,
+                                      tolerance: tolerance,
+                                      param_tolerance: param_tolerance,
+                                      learning_rate: learning_rate,
+                                      decay_factor: decay_factor)
+
       @data = data
       @data_array = ResponseDataValidator.validate!(data)
       num_rows = @data_array.size
diff --git a/lib/irt_ruby/three_parameter_model.rb b/lib/irt_ruby/three_parameter_model.rb
index f172de2..9b3410b 100644
--- a/lib/irt_ruby/three_parameter_model.rb
+++ b/lib/irt_ruby/three_parameter_model.rb
@@ -1,5 +1,6 @@
 # frozen_string_literal: true
 
+require "irt_ruby/model_options_validator"
 require "irt_ruby/response_data_validator"
 
 module IrtRuby
@@ -20,6 +21,12 @@ def initialize(data,
                    learning_rate: 0.01,
                    decay_factor: 0.5,
                    missing_strategy: :ignore)
+      ModelOptionsValidator.validate!(max_iter: max_iter,
+                                      tolerance: tolerance,
+                                      param_tolerance: param_tolerance,
+                                      learning_rate: learning_rate,
+                                      decay_factor: decay_factor)
+
       @data = data
       @data_array = ResponseDataValidator.validate!(data)
       num_rows = @data_array.size
diff --git a/lib/irt_ruby/two_parameter_model.rb b/lib/irt_ruby/two_parameter_model.rb
index e9a5a98..04e1c6f 100644
--- a/lib/irt_ruby/two_parameter_model.rb
+++ b/lib/irt_ruby/two_parameter_model.rb
@@ -1,5 +1,6 @@
 # frozen_string_literal: true
 
+require "irt_ruby/model_options_validator"
 require "irt_ruby/response_data_validator"
 
 module IrtRuby
@@ -16,6 +17,12 @@ class TwoParameterModel
     def initialize(data, max_iter: 1000, tolerance: 1e-6, param_tolerance: 1e-6,
                    learning_rate: 0.01, decay_factor: 0.5,
                    missing_strategy: :ignore)
+      ModelOptionsValidator.validate!(max_iter: max_iter,
+                                      tolerance: tolerance,
+                                      param_tolerance: param_tolerance,
+                                      learning_rate: learning_rate,
+                                      decay_factor: decay_factor)
+
       @data = data
       @data_array = ResponseDataValidator.validate!(data)
       num_rows = @data_array.size
diff --git a/spec/irt_ruby/rasch_model_spec.rb b/spec/irt_ruby/rasch_model_spec.rb
index b4fa443..aa468e4 100644
--- a/spec/irt_ruby/rasch_model_spec.rb
+++ b/spec/irt_ruby/rasch_model_spec.rb
@@ -4,6 +4,7 @@
 
 RSpec.describe IrtRuby::RaschModel do
   it_behaves_like "response data validation"
+  it_behaves_like "model optimization option validation"
 
   let(:data_array) do
     [
diff --git a/spec/irt_ruby/three_parameter_model_spec.rb b/spec/irt_ruby/three_parameter_model_spec.rb
index e120ea6..38fcab8 100644
--- a/spec/irt_ruby/three_parameter_model_spec.rb
+++ b/spec/irt_ruby/three_parameter_model_spec.rb
@@ -4,6 +4,7 @@
 
 RSpec.describe IrtRuby::ThreeParameterModel do
   it_behaves_like "response data validation"
+  it_behaves_like "model optimization option validation"
 
   let(:data_array) do
     [
diff --git a/spec/irt_ruby/two_parameter_model_spec.rb b/spec/irt_ruby/two_parameter_model_spec.rb
index 4c9e906..11ef270 100644
--- a/spec/irt_ruby/two_parameter_model_spec.rb
+++ b/spec/irt_ruby/two_parameter_model_spec.rb
@@ -4,6 +4,7 @@
 
 RSpec.describe IrtRuby::TwoParameterModel do
   it_behaves_like "response data validation"
+  it_behaves_like "model optimization option validation"
 
   let(:data_array) do
     [
diff --git a/spec/spec_helper.rb b/spec/spec_helper.rb
index 0ddcf0c..c1ec94a 100644
--- a/spec/spec_helper.rb
+++ b/spec/spec_helper.rb
@@ -41,6 +41,24 @@
   end
 end
 
+RSpec.shared_examples "model optimization option validation" do
+  let(:valid_data) { [[1, 0], [0, 1]] }
+
+  {
+    max_iter: [0, -1, 1.5, "100", nil],
+    tolerance: [0, -1e-6, Float::INFINITY, -Float::INFINITY, Float::NAN, Complex(1, 0), "1e-6", nil],
+    param_tolerance: [0, -1e-6, Float::INFINITY, -Float::INFINITY, Float::NAN, Complex(1, 0), "1e-6", nil],
+    learning_rate: [0, -0.01, Float::INFINITY, -Float::INFINITY, Float::NAN, Complex(0.01, 0), "0.01", nil],
+    decay_factor: [0, 1, -0.1, 1.1, Float::INFINITY, -Float::INFINITY, Float::NAN, Complex(0.5, 0), "0.5", nil]
+  }.each do |option, invalid_values|
+    invalid_values.each do |value|
+      it "rejects #{option}=#{value.inspect}" do
+        expect { described_class.new(valid_data, option => value) }.to raise_error(ArgumentError, /\A#{option} /)
+      end
+    end
+  end
+end
+
 RSpec.configure do |config|
   # Enable flags like --only-failures and --next-failure
   config.example_status_persistence_file_path = ".rspec_status"