diff --git a/src/sequential.py b/src/sequential.py
index 2a2fbee..daf02a2 100644
--- a/src/sequential.py
+++ b/src/sequential.py
@@ -64,7 +64,8 @@ def adaptive_lipo(func,
     # dimension of the domain
     d = len(bounds)
 
-    k_seq=(1+0.01/d)**np.arange(-10000,10000) # Page 16
+    alpha = 0.01/d
+    k_seq=(1+alpha)**np.arange(-10000,10000) # Page 16
 
     # preallocate the output arrays
     y = np.zeros(n) - np.Inf
@@ -72,8 +73,8 @@ def adaptive_lipo(func,
     loss = np.zeros(n)
 
     # preallocate the distance arrays
-    x_dist = np.zeros((n * (n - 1)) // 2)
-    y_dist = np.zeros((n * (n - 1)) // 2)
+    # x_dist = np.zeros((n * (n - 1)) // 2)
+    # y_dist = np.zeros((n * (n - 1)) // 2)
     
     # the lower/upper bounds on each dimension
     bound_mins = np.array([bnd[0] for bnd in bounds])
@@ -81,6 +82,7 @@ def adaptive_lipo(func,
     
     # initialization with randomly drawn point in domain and k = 0
     k = 0
+    k_est = -np.inf
     u = np.random.rand(d)
     x_prop = u * (bound_maxs - bound_mins) + bound_mins
     x[0] = x_prop
@@ -95,12 +97,22 @@ def adaptive_lipo(func,
         x_prop = u * (bound_maxs - bound_mins) + bound_mins
 
         # check if we are exploring or exploiting
-        if np.random.rand() > p: # enter w/ prob (1-p)
+        if np.random.rand() > p: # enter to exploit w/ prob (1-p)
             # exploiting - ensure we're drawing from potential maximizers
-            while upper_bound(x_prop, y[:t], x[:t], k) < np.max(y):
+            while upper_bound(x_prop, y[:t], x[:t], k) < np.max(y[:t]):
                 u = np.random.rand(d)
                 x_prop = u * (bound_maxs - bound_mins) + bound_mins 
-
+                # import pdb
+                # pdb.set_trace()
+
+                # print(upper_bound(x_prop, y[:t], x[:t], k))
+            #     print(np.max(y[:t]))
+                # print('------')
+            # print("BREAK")
+        else:
+            pass 
+            # we keep the randomly drawn point as our next iterate
+            # this is "exploration"
         # add proposal to array of visited points
         x[t] = x_prop
         y[t] = func(x_prop)
@@ -108,27 +120,35 @@ def adaptive_lipo(func,
 
         # compute current number of tracked distances
         old_num_dist = (t * (t - 1)) // 2
+        new_num_dist = old_num_dist + t
 
         # compute distance between newl values and all 
         # previously seen points - should be of shape (t,)
         # then insert new distances into x_dist, y_dist resp.
-        new_x_dist = np.sqrt(np.sum((x[:t] - x_prop)**2, axis=1))
-        x_dist[old_num_dist:(old_num_dist + t)] = new_x_dist 
+        # new_x_dist = np.linalg.norm(x[:t]-x[t],axis=1)
+        new_x_dist = np.sqrt(np.sum((x[:t] - x[t])**2, axis=1))
+        # x_dist[old_num_dist:new_num_dist] = new_x_dist 
 
         new_y_dist = np.abs(y[:t] - y[t])
-        y_dist[old_num_dist:(old_num_dist + t)] = new_y_dist
+        # y_dist[old_num_dist:new_num_dist] = new_y_dist
 
         # compute new number of of tracked distances
         # and update estimate of lipschitz constant
-        new_num_dist = old_num_dist + t
-        k_est = np.max(y_dist[:new_num_dist] / x_dist[:new_num_dist]) 
+        k_est = max(k_est, np.max(new_y_dist/new_x_dist))  # faster
+        # k_est = np.max(y_dist[:new_num_dist] / x_dist[:new_num_dist])  # slow because num_dist gets large
+        
+
         # get the smallest element of k_seq that is bigger than k_est
         # note: we're using argmax to get the first occurrence
         # note: this relies on k_seq being sorted in nondecreasing order
         k = k_seq[np.argmax(k_seq >= k_est)]
         # note: in the paper, k_seq is called k_i 
         #       and k is called \hat{k}_t
-
+        # print(k)
+        i_t = np.ceil(np.log(k_est)/np.log(1+alpha))
+        k = (1+alpha)**i_t
+        # print(k)
+        # print("----")
 
     output = {'loss': loss, 'x': x, 'y': y}
     return output