objective function with known lipschitz constant

README.md

@@ -34,31 +34,3 @@ cd lipo-python
 docker build . -t lipo-python
 docker run -v <path-to-cloned-repo>/:/home/ -it lipo-python
 ```
-
-## Resources
-
-[Global optimization of Lipschitz functions](https://arxiv.org/abs/1703.02628).
-
-* C. Malherbe and N. Vayatis. "Global optimization of Lipschitz functions". ICML. 2314 - 2323. (2017)
-
-[BayesOpt](https://arxiv.org/abs/1405.7430)
-
-* R. Martinez-Cantin. BayesOpt: {A} Bayesian Optimization Library for Nonlinear Optimization, Experimental Design and Bandits. CoRR. 1405.7430. (2014)
-
-[CMA-ES - Covariance Matrix Adaptation Evolution Strategy](https://www.researchgate.net/publication/227050324_The_CMA_Evolution_Strategy_A_Comparing_Review)
-
-* N. Hansen. The CMA Evolution Strategy: A Comparing Review. In J.A. Lozano, P. Larrañaga, I. Inza and E. Bengoetxea (Eds.). Towards a new evolutionary computation. Advances in estimation of distribution algorithms. Springer, pp. 75-102 (2006).
-
-**IS ABOVE POINTING AT THE CORRECT PAPER?**
-
-[CRS - Controlled Random Search with Local Mutation](https://link.springer.com/article/10.1007/s10957-006-9101-0)
-
-* P. Kaelo and M. M. Ali, "Some variants of the controlled random search algorithm for global optimization," J. Optim. Theory Appl. 130 (2), 253-264 (2006).
-
-[DIRECT](https://link.springer.com/article/10.1007/BF00941892)
-
-* D. R. Jones, C. D. Perttunen, and B. E. Stuckmann, "Lipschitzian optimization without the lipschitz constant," J. Optimization Theory and Applications, vol. 79, p. 157 (1993).
-
-[MLSL - Multi-Level Single-Linkage](https://link.springer.com/article/10.1007/BF02592071)  
-
-* A. H. G. Rinnooy Kan and G. T. Timmer, "Stochastic global optimization methods," Mathematical Programming, vol. 39, p. 27-78 (1987). (Actually 2 papers — part I: clustering methods, p. 27, then part II: multilevel methods, p. 57.)

requirements.txt

@@ -2,4 +2,6 @@ numpy == 1.14.2
 scipy == 0.19.1
 scikit-learn == 0.19.1
 pandas == 0.23.1
+matplotlib == 2.1.2
 tqdm == 4.23.4
+

resources.md

@@ -0,0 +1,27 @@
+## Resources
+
+[Global optimization of Lipschitz functions](https://arxiv.org/abs/1703.02628).
+
+* C. Malherbe and N. Vayatis. "Global optimization of Lipschitz functions". ICML. 2314 - 2323. (2017)
+
+[BayesOpt](https://arxiv.org/abs/1405.7430)
+
+* R. Martinez-Cantin. BayesOpt: {A} Bayesian Optimization Library for Nonlinear Optimization, Experimental Design and Bandits. CoRR. 1405.7430. (2014)
+
+[CMA-ES - Covariance Matrix Adaptation Evolution Strategy](https://www.researchgate.net/publication/227050324_The_CMA_Evolution_Strategy_A_Comparing_Review)
+
+* N. Hansen. The CMA Evolution Strategy: A Comparing Review. In J.A. Lozano, P. Larrañaga, I. Inza and E. Bengoetxea (Eds.). Towards a new evolutionary computation. Advances in estimation of distribution algorithms. Springer, pp. 75-102 (2006).
+
+**IS ABOVE POINTING AT THE CORRECT PAPER?**
+
+[CRS - Controlled Random Search with Local Mutation](https://link.springer.com/article/10.1007/s10957-006-9101-0)
+
+* P. Kaelo and M. M. Ali, "Some variants of the controlled random search algorithm for global optimization," J. Optim. Theory Appl. 130 (2), 253-264 (2006).
+
+[DIRECT](https://link.springer.com/article/10.1007/BF00941892)
+
+* D. R. Jones, C. D. Perttunen, and B. E. Stuckmann, "Lipschitzian optimization without the lipschitz constant," J. Optimization Theory and Applications, vol. 79, p. 157 (1993).
+
+[MLSL - Multi-Level Single-Linkage](https://link.springer.com/article/10.1007/BF02592071)  
+
+* A. H. G. Rinnooy Kan and G. T. Timmer, "Stochastic global optimization methods," Mathematical Programming, vol. 39, p. 27-78 (1987). (Actually 2 papers — part I: clustering methods, p. 27, then part II: multilevel methods, p. 57.)

src/objective_functions.py

@@ -47,12 +47,28 @@ def deb_one(x):
 
 deb_one_bounds = [(-5,5)]*5
 
+def parabola(x):
+    if x.shape[0] != 1:
+        raise ValueError('Input array first dimension should be of size 1')
+    return - x**2
+
+parabola_bounds = [(-1,1)]
+
+def paraboloid2d(x):
+    if x.shape[0] != 2:
+        raise ValueError('Input array first dimension should be of size 2')
+    return -(x[0]**2 + x[1]**2)
+
+paraboloid2d_bounds = [(-1,1)]*2
+
 synthetic_functions = {
     'Holder Table' : {'func': holder_table, 'bnds': holder_bounds},
     'Rosenbrock': {'func': rosenbrock, 'bnds': rosenbrock_bounds},
     'Linear Slope': {'func': linear_slope, 'bnds': linear_slope_bounds},
     'Sphere': {'func': sphere, 'bnds': sphere_bounds},
-    'Deb N.1': {'func': deb_one, 'bnds': deb_one_bounds}
+    'Deb N.1': {'func': deb_one, 'bnds': deb_one_bounds},
+    'Parabola': {'func': parabola, 'bnds': parabola_bounds},
+    'Paraboloid2d': {'func': paraboloid2d, 'bnds': paraboloid2d_bounds}
 }
 
 def get_data(path):

src/optimize.py

@@ -49,7 +49,8 @@ def main(num_sim, num_iter, optimizers, objectives):
     parser.add_argument('--objective', type=str, 
                         help='type of objective functions to optimize',
                         choices=['Holder Table', 'Rosenbrock', 'Sphere', 
-                                 'Linear Slope', 'Deb N.1', 'Housing', 'Yacht'])
+                                 'Linear Slope', 'Deb N.1', 'Housing', 'Yacht',
+                                 'Parabola', 'Paraboloid2d'])
     parser.add_argument('--synthetic', default=False, action='store_true')
     args = parser.parse_args()
 

src/plot_k.py

@@ -0,0 +1,70 @@
+#!usr/bin/env python
+
+# Script to plot the lipschitz estimates
+# Usage:
+#    - python plot_k.py inputfile 1 myplot
+
+import argparse
+import pickle
+import numpy as np
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+
+def main(results, lipschitz_constant, filename, 
+         optimizer='AdaLIPO', q=(5,95), figsize=(10,5)):
+
+    if len(results.keys()) > 1:
+        raise RuntimeError('Inputfile must be simulation using single objective function!')
+
+    func_name = list(results.keys())[0] 
+    d = results[func_name][optimizer][0]['x'].shape[1]
+    num_sim = len(results[func_name][optimizer])
+    num_iter = len(results[func_name][optimizer][0]['k'])
+
+    k_results = np.zeros((num_sim, num_iter))
+
+    for sim in range(num_sim):
+        k_results[sim,:] = results[func_name][optimizer][sim]['k']
+
+    median_loss = np.median(a=k_results, axis=0)
+    upper_loss = np.percentile(a=k_results, q=q[1], axis=0)
+    lower_loss = np.percentile(a=k_results, q=q[0], axis=0)
+    yerr = np.abs(np.vstack((lower_loss,  upper_loss)) - median_loss)
+
+    fig, ax = plt.subplots()
+    fig.set_size_inches(figsize[0], figsize[1])
+
+    ax.plot(range(1,num_iter+1), [lipschitz_constant]*num_iter, color='red')
+
+    ax.plot(range(1,num_iter+1), median_loss)
+    ax.errorbar(
+        x=range(1,num_iter+1), 
+        y=median_loss,
+        yerr=yerr, 
+        linestyle='None',
+        alpha=0.5, 
+        capsize=200/num_iter
+    )
+    ax.set(xlabel='Iteration Number', ylabel='Lipschitz Constant')
+
+    plt.legend(['True', 'Estimated', '90 % Error bars'])
+    plt.title('Convergence of Lipschitz Constant Estimate of {}-d Paraboloid'.format(d))
+    if filename:
+        fig = ax.get_figure()
+        fig.savefig(filename)
+    else:
+        plt.show()
+
+if __name__ == '__main__':
+
+    parser = argparse.ArgumentParser()
+    parser.add_argument('inputfile', type=str)
+    parser.add_argument('--K', type=float, default=None)
+    parser.add_argument('--filename', type=str, default=None)
+    args = parser.parse_args()
+
+    with open(args.inputfile, 'rb') as f:
+        results = pickle.load(f)
+
+    main(results, args.K, args.filename)

src/sequential.py

@@ -71,6 +71,7 @@ def adaptive_lipo(func,
     y = np.zeros(n) - np.Inf
     x = np.zeros((n, d))
     loss = np.zeros(n)
+    k_arr = np.zeros(n)
 
     # preallocate the distance arrays
     # x_dist = np.zeros((n * (n - 1)) // 2)
@@ -87,10 +88,12 @@ def adaptive_lipo(func,
     x_prop = u * (bound_maxs - bound_mins) + bound_mins
     x[0] = x_prop
     y[0] = func(x_prop)
+    k_arr[0] = k
 
     upper_bound = lambda x_prop, y, x, k: np.min(y+k*np.linalg.norm(x_prop-x,axis=1))
 
     for t in np.arange(1, n):
+        print('Iteration {}'.format(t))
 
         # draw a uniformly distributed random variable
         u = np.random.rand(d)
@@ -99,6 +102,7 @@ def adaptive_lipo(func,
         # check if we are exploring or exploiting
         if np.random.rand() > p: # enter to exploit w/ prob (1-p)
             # exploiting - ensure we're drawing from potential maximizers
+            print('Into the while...')
             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 
@@ -108,7 +112,7 @@ def adaptive_lipo(func,
                 # print(upper_bound(x_prop, y[:t], x[:t], k))
             #     print(np.max(y[:t]))
                 # print('------')
-            # print("BREAK")
+            print('Out of the while')
         else:
             pass 
             # we keep the randomly drawn point as our next iterate
@@ -147,10 +151,14 @@ def adaptive_lipo(func,
         # print(k)
         i_t = np.ceil(np.log(k_est)/np.log(1+alpha))
         k = (1+alpha)**i_t
+        print('Lipschitz Constant Estimate: {}'.format(k))
+        print('\n')
         # print(k)
         # print("----")
+        k_arr[t] = k
+
 
-    output = {'loss': loss, 'x': x, 'y': y}
+    output = {'loss': loss, 'x': x, 'y': y, 'k': k_arr}
     return output
 
 optimizers = {