diff --git a/jax/experimental/optimizers.py b/jax/experimental/optimizers.py
index 7970825fe750..08dc2c98c465 100644
--- a/jax/experimental/optimizers.py
+++ b/jax/experimental/optimizers.py
@@ -382,6 +382,41 @@ def get_params(state):
     return x
   return init, update, get_params
 
+
+@optimizer
+def adamax(step_size, b1=0.9, b2=0.999, eps=1e-8):
+  """Construct optimizer triple for AdaMax (a variant of Adam based on infinity norm).
+
+  Args:
+    step_size: positive scalar, or a callable representing a step size schedule
+      that maps the iteration index to positive scalar.
+    b1: optional, a positive scalar value for beta_1, the exponential decay rate
+      for the first moment estimates (default 0.9).
+    b2: optional, a positive scalar value for beta_2, the exponential decay rate
+      for the second moment estimates (default 0.999).
+    eps: optional, a positive scalar value for epsilon, a small constant for
+      numerical stability (default 1e-8).
+
+  Returns:
+    An (init_fun, update_fun, get_params) triple.
+  """
+  step_size = make_schedule(step_size)
+  def init(x0):
+    m0 = np.zeros_like(x0)
+    u0 = np.zeros_like(x0)
+    return x0, m0, u0
+  def update(i, g, state):
+    x, m, u = state
+    m = (1 - b1) * g + b1 * m  # First  moment estimate.
+    u = np.maximum(b2 * u, np.abs(g))  # Update exponentially weighted infinity norm.
+    x = x - (step_size(i) / (1 - b1 ** (i + 1))) * m / (u + eps)
+    return x, m, u
+  def get_params(state):
+    x, m, u = state
+    return x
+  return init, update, get_params
+
+
 @optimizer
 def sm3(step_size, momentum=0.9):
   """Construct optimizer triple for SM3.
diff --git a/tests/optimizers_test.py b/tests/optimizers_test.py
index 6a994e90ca5c..0df6ade29d1d 100644
--- a/tests/optimizers_test.py
+++ b/tests/optimizers_test.py
@@ -149,6 +149,13 @@ def loss(xs):
     x0 = (np.ones(2), np.ones((2, 2)))
     self._CheckOptimizer(optimizers.sm3, loss, x0, num_iters, step_size)
 
+  def testAdaMaxVector(self):
+    def loss(x): return np.dot(x, x)
+    x0 = np.ones(2)
+    num_iters = 100
+    step_size = 0.1
+    self._CheckOptimizer(optimizers.adamax, loss, x0, num_iters, step_size)
+
   def testSgdVectorExponentialDecaySchedule(self):
     def loss(x): return np.dot(x, x)
     x0 = np.ones(2)