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%% Cell type:code id:216f8712 tags:
``` python
import numpy as np
import cvxpy as cp
import matplotlib.pyplot as plt
from scipy.stats import truncnorm
from tqdm import tqdm
from cp_functions import *
from scipy.optimize import minimize
```
%% Cell type:code id:cf0ecd72 tags:
``` python
```
%% Cell type:markdown id:11813f8d tags:
# Comparison of policies
%% Cell type:code id:0337f7bc tags:
``` python
T = 30
init = [1, 1, 1]
W_current = [2, 2, 2]
W_bar = [2, 2, 2]
Q = [0.6, 0.7, 0.5]
C = [6, 4, 3, 4, 6]
D = [100, 100, 100]
alpha = [0.5, 0.5, 0.5]
```
%% Cell type:code id:18039faa tags:
``` python
upper = solve_cp_post(T, init, W_current, W_bar, Q, C, D, alpha)[0]
print("rel is "+str(upper))
```
%% Output
rel is 323.520494439257
%% Cell type:code id:a050be44 tags:
``` python
```
%% Cell type:markdown id:888d8482 tags:
The Myopic Policy
%% Cell type:code id:2f3a0cb1 tags:
``` python
T = 30
my_sigma = [0.1, 0.2, 0.3, 0.4, 0.5, 0.75, 1., 2.]
for sigma in my_sigma:
perfs = []
for _ in tqdm(range(400)):
perf = myopic_policy(T, init, 0., W_bar, Q, C, D, alpha, sigma)
perfs.append(perf)
gap = upper - np.mean(perfs)
std_err = np.std(perfs)/np.sqrt(len(perfs)-1)
print("sigma = " + str(sigma) + ", optimality gap of myopic is: " + str(gap) + " +- " + str(2*std_err))
```
%% Output
100%|██████████| 400/400 [04:19<00:00, 1.54it/s]
sigma = 0.1, optimality gap of myopic is: 11.401668532083704 +- 0.015496018275286056
100%|██████████| 400/400 [04:11<00:00, 1.59it/s]
sigma = 0.2, optimality gap of myopic is: 12.005599689895234 +- 0.05334801905714205
100%|██████████| 400/400 [04:14<00:00, 1.57it/s]
sigma = 0.3, optimality gap of myopic is: 13.92682047821421 +- 0.13651943488775112
100%|██████████| 400/400 [04:07<00:00, 1.61it/s]
sigma = 0.4, optimality gap of myopic is: 16.7393893696094 +- 0.26226986034593697
100%|██████████| 400/400 [04:12<00:00, 1.59it/s]
sigma = 0.5, optimality gap of myopic is: 20.37330959385332 +- 0.37805996400213815
7%|▋ | 27/400 [00:17<03:56, 1.58it/s]C:\Users\cyan\AppData\Roaming\Python\Python39\site-packages\cvxpy\problems\problem.py:1385: UserWarning: Solution may be inaccurate. Try another solver, adjusting the solver settings, or solve with verbose=True for more information.
warnings.warn(
100%|██████████| 400/400 [04:25<00:00, 1.51it/s]
sigma = 0.75, optimality gap of myopic is: 29.162374293247353 +- 0.5828905111648925
100%|██████████| 400/400 [04:26<00:00, 1.50it/s]
sigma = 1.0, optimality gap of myopic is: 34.65782484111173 +- 0.6615687497411535
100%|██████████| 400/400 [04:20<00:00, 1.53it/s]
sigma = 2.0, optimality gap of myopic is: 42.396547307764195 +- 0.8489865804329587
%% Cell type:code id:ba653f71 tags:
``` python
```
%% Cell type:code id:c157ebec tags:
``` python
T = 30
my_sigma = [1e-8]
for sigma in my_sigma:
perfs = []
for _ in tqdm(range(400)):
perf = myopic_policy(T, init, 0., W_bar, Q, C, D, alpha, sigma)
perfs.append(perf)
gap = upper - np.mean(perfs)
std_err = np.std(perfs)/np.sqrt(len(perfs)-1)
print("sigma = " + str(sigma) + ", optimality gap of myopic is: " + str(gap) + " +- " + str(2*std_err))
```
%% Output
100%|██████████| 400/400 [04:05<00:00, 1.63it/s]
sigma = 1e-08, optimality gap of myopic is: 11.357676070885248 +- 1.4061701726222978e-09
%% Cell type:code id:c1be1b95 tags:
``` python
```
%% Cell type:code id:ee48337e tags:
``` python
T = 30
my_sigma = [50.]
for sigma in my_sigma:
perfs = []
for _ in tqdm(range(400)):
perf = myopic_policy(T, init, 0., W_bar, Q, C, D, alpha, sigma)
perfs.append(perf)
gap = upper - np.mean(perfs)
std_err = np.std(perfs)/np.sqrt(len(perfs)-1)
print("sigma = " + str(sigma) + ", optimality gap of myopic is: " + str(gap) + " +- " + str(2*std_err))
```
%% Output
100%|██████████| 400/400 [04:21<00:00, 1.53it/s]
sigma = 50.0, optimality gap of myopic is: 44.835870737540574 +- 0.877526311253225
%% Cell type:code id:ce59bfbf tags:
``` python
```
%% Cell type:code id:8303c0b6 tags:
``` python
```
%% Cell type:markdown id:f288939f tags:
The Update Policy
%% Cell type:code id:086b81ac tags:
``` python
T = 30
my_sigma = [0.1, 0.2, 0.3, 0.4, 0.5, 0.75, 1.]
for sigma in my_sigma:
perfs = []
for _ in tqdm(range(400)):
perf = update_policy(T, init, 0., W_bar, Q, C, D, alpha, sigma)
perfs.append(perf)
gap = upper - np.mean(perfs)
std_err = np.std(perfs)/np.sqrt(len(perfs)-1)
print("sigma = " + str(sigma) + ", optimality gap of update is: " + str(gap) + " +- " + str(2*std_err))
```
%% Output
100%|██████████| 400/400 [1:16:43<00:00, 11.51s/it]
sigma = 0.1, optimality gap of update is: 0.6751724000587274 +- 0.0284472199839743
100%|██████████| 400/400 [1:17:01<00:00, 11.55s/it]
sigma = 0.2, optimality gap of update is: 1.785608100718548 +- 0.05978098879254324
15%|█▍ | 59/400 [11:29<1:06:03, 11.62s/it]C:\Users\cyan\AppData\Roaming\Python\Python39\site-packages\cvxpy\problems\problem.py:1385: UserWarning: Solution may be inaccurate. Try another solver, adjusting the solver settings, or solve with verbose=True for more information.
warnings.warn(
100%|██████████| 400/400 [1:12:19<00:00, 10.85s/it]
sigma = 0.3, optimality gap of update is: 3.5096707400443847 +- 0.11913526304423622
100%|██████████| 400/400 [1:07:11<00:00, 10.08s/it]
sigma = 0.4, optimality gap of update is: 5.459479596568883 +- 0.15754489654769221
100%|██████████| 400/400 [1:09:50<00:00, 10.48s/it]
sigma = 0.5, optimality gap of update is: 7.670634010252172 +- 0.2150031057950384
100%|██████████| 400/400 [1:07:10<00:00, 10.08s/it]
sigma = 0.75, optimality gap of update is: 12.948077942456393 +- 0.32913629277701
100%|██████████| 400/400 [1:05:24<00:00, 9.81s/it]
sigma = 1.0, optimality gap of update is: 16.82817815804907 +- 0.3949186834446812
%% Cell type:code id:d6ae5fdf tags:
``` python
T = 30
my_sigma = [2.]
for sigma in my_sigma:
perfs = []
for _ in tqdm(range(400)):
perf = update_policy(T, init, 0., W_bar, Q, C, D, alpha, sigma)
perfs.append(perf)
gap = upper - np.mean(perfs)
std_err = np.std(perfs)/np.sqrt(len(perfs)-1)
print("sigma = " + str(sigma) + ", optimality gap of update is: " + str(gap) + " +- " + str(2*std_err))
```
%% Output
8%|▊ | 31/400 [05:27<1:04:35, 10.50s/it]C:\Users\cyan\AppData\Roaming\Python\Python39\site-packages\cvxpy\problems\problem.py:1385: UserWarning: Solution may be inaccurate. Try another solver, adjusting the solver settings, or solve with verbose=True for more information.
warnings.warn(
100%|██████████| 400/400 [1:10:11<00:00, 10.53s/it]
sigma = 2.0, optimality gap of update is: 22.198738525815486 +- 0.5169044969707984
%% Cell type:code id:66b3e3f4 tags:
``` python
```
%% Cell type:code id:49780365 tags:
``` python
T = 30
my_sigma = [50.]
for sigma in my_sigma:
perfs = []
for _ in tqdm(range(400)):
perf = update_policy(T, init, 0., W_bar, Q, C, D, alpha, sigma)
perfs.append(perf)
gap = upper - np.mean(perfs)
std_err = np.std(perfs)/np.sqrt(len(perfs)-1)
print("sigma = " + str(sigma) + ", optimality gap of update is: " + str(gap) + " +- " + str(2*std_err))
```
%% Output
9%|▉ | 37/400 [13:24<2:08:46, 21.29s/it]C:\Users\cyan\AppData\Roaming\Python\Python39\site-packages\cvxpy\problems\problem.py:1385: UserWarning: Solution may be inaccurate. Try another solver, adjusting the solver settings, or solve with verbose=True for more information.
warnings.warn(
100%|██████████| 400/400 [2:24:51<00:00, 21.73s/it]
sigma = 50.0, optimality gap of update is: 24.20093157450657 +- 0.5712114760655667
%% Cell type:code id:92b70dbb tags:
``` python
```
%% Cell type:code id:6d872253 tags:
``` python
```
%% Cell type:code id:a6e585b2 tags:
``` python
update = [0.6751724000587274, 1.785608100718548, 3.5096707400443847, 5.459479596568883, 7.670634010252172,
12.948077942456393, 16.82817815804907, 22.198738525815486]
update_ci = [0.0284472199839743, 0.05978098879254324, 0.11913526304423622, 0.15754489654769221,
0.2150031057950384, 0.32913629277701, 0.3949186834446812, 0.5169044969707984]
```
%% Cell type:code id:919e77e5 tags:
``` python
```
%% Cell type:markdown id:87a0dea4 tags:
More on the Hybrid Policy
%% Cell type:code id:dd105e40 tags:
``` python
T = 30
#my_sigma = [0.1, 0.2, 0.3, 0.4, 0.5, 0.75, 1., 2.]
#my_theta = [0.4, 0.8, 1.2, 1.6, 2.0, 2.5, 3., 4.]
my_sigma = [0.5, 0.75, 1., 2.]
my_theta = [2.0, 2.5, 3., 4.]
for i,sigma in enumerate(my_sigma):
perfs = []
counts = []
theta = my_theta[i]
for _ in tqdm(range(400)):
perf,count = hybrid_policy(T, init, 0., W_current, W_bar, Q, C, D, alpha, sigma, count = 0, thres = theta)
perfs.append(perf)
counts.append(count)
gap = upper - np.mean(perfs)
std_err = np.std(perfs)/np.sqrt(len(perfs)-1)
mean_count = np.mean(counts)
std_count = np.std(counts)/np.sqrt(len(counts)-1)
print("sigma = " + str(sigma) + ", optimality gap of hybrid is: " + str(gap) + " +- " + str(2*std_err))
print("sigma = " + str(sigma) + ", resolving counts of hybrid is: " + str(mean_count) + " +- " + str(2*std_count))
```
%% Output
100%|██████████| 400/400 [47:23<00:00, 7.11s/it]
sigma = 0.5, optimality gap of hybrid is: 12.015536928137521 +- 0.23493532374527396
sigma = 0.5, resolving counts of hybrid is: 13.7525 +- 0.26784658291632146
100%|██████████| 400/400 [57:27<00:00, 8.62s/it]
sigma = 0.75, optimality gap of hybrid is: 17.029235091532712 +- 0.32251663156305277
sigma = 0.75, resolving counts of hybrid is: 17.0775 +- 0.2523373194892455
13%|█▎ | 53/400 [08:53<58:13, 10.07s/it]
---------------------------------------------------------------------------
SolverError Traceback (most recent call last)
~\AppData\Local\Temp\ipykernel_16312\3684378760.py in <module>
9 theta = my_theta[i]
10 for _ in tqdm(range(400)):
---> 11 perf,count = hybrid_policy(T, init, 0., W_current, W_bar, Q, C, D, alpha, sigma, count = 0, thres = theta)
12 perfs.append(perf)
13 counts.append(count)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
401 current_state = next_state
402 current_horizon -= 1
--> 403 return hybrid_policy(current_horizon, current_state, current_utility, \
404 W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
~\Downloads\Network numerical examples\cp_functions.py in hybrid_policy(current_horizon, current_state, current_utility, W_current, W_bar, Q, C, D, alpha, sigma, count, thres)
387 for p in range(nb_path):
388 W_current[p] = W_bar[p] + simulate_TN(0., sigma, -W_bar[p], W_bar[p])
--> 389 U_current = U_projection(W_current, current_state, u_star[:,t], Q, C, D)
390 diff = euclidean_distance(current_state,x_star[:,t])+euclidean_distance(W_current,W_bar) \
391 +euclidean_distance(U_current,u_star[:,t])
~\Downloads\Network numerical examples\cp_functions.py in U_projection(W_current, current_state, U_det, Q, C, D)
143 # solve
144 problem = cp.Problem(cp.Minimize(utility), constr)
--> 145 res = problem.solve()
146 u = U.value
147 return u
~\AppData\Roaming\Python\Python39\site-packages\cvxpy\problems\problem.py in solve(self, *args, **kwargs)
491 else:
492 solve_func = Problem._solve
--> 493 return solve_func(self, *args, **kwargs)
494
495 @classmethod
~\AppData\Roaming\Python\Python39\site-packages\cvxpy\problems\problem.py in _solve(self, solver, warm_start, verbose, gp, qcp, requires_grad, enforce_dpp, ignore_dpp, canon_backend, **kwargs)
1066 end = time.time()
1067 self._solve_time = end - start
-> 1068 self.unpack_results(solution, solving_chain, inverse_data)
1069 if verbose:
1070 print(_FOOTER)
~\AppData\Roaming\Python\Python39\site-packages\cvxpy\problems\problem.py in unpack_results(self, solution, chain, inverse_data)
1391 warnings.warn(INF_OR_UNB_MESSAGE)
1392 if solution.status in s.ERROR:
-> 1393 raise error.SolverError(
1394 "Solver '%s' failed. " % chain.solver.name() +
1395 "Try another solver, or solve with verbose=True for more "
SolverError: Solver 'ECOS' failed. Try another solver, or solve with verbose=True for more information.
%% Cell type:code id:98ca1f6e tags:
``` python
```
%% Cell type:code id:326c6228 tags:
``` python
T = 30
#my_sigma = [0.1, 0.2, 0.3, 0.4, 0.5, 0.75, 1., 2.]
#my_theta = [0.4, 0.8, 1.2, 1.6, 2.0, 2.5, 3., 4.]
my_sigma = [1., 2.]
my_theta = [3., 4.]
for i,sigma in enumerate(my_sigma):
perfs = []
counts = []
theta = my_theta[i]
for _ in tqdm(range(400)):
perf,count = hybrid_policy(T, init, 0., W_current, W_bar, Q, C, D, alpha, sigma, count = 0, thres = theta)
perfs.append(perf)
counts.append(count)
gap = upper - np.mean(perfs)
std_err = np.std(perfs)/np.sqrt(len(perfs)-1)
mean_count = np.mean(counts)
std_count = np.std(counts)/np.sqrt(len(counts)-1)
print("sigma = " + str(sigma) + ", optimality gap of hybrid is: " + str(gap) + " +- " + str(2*std_err))
print("sigma = " + str(sigma) + ", resolving counts of hybrid is: " + str(mean_count) + " +- " + str(2*std_count))
```
%% Output
2%|▏ | 6/400 [01:21<1:28:17, 13.44s/it]C:\Users\cyan\AppData\Roaming\Python\Python39\site-packages\cvxpy\problems\problem.py:1385: UserWarning: Solution may be inaccurate. Try another solver, adjusting the solver settings, or solve with verbose=True for more information.
warnings.warn(
100%|██████████| 400/400 [1:43:43<00:00, 15.56s/it]
sigma = 1.0, optimality gap of hybrid is: 21.859185477967003 +- 0.4292526697277563
sigma = 1.0, resolving counts of hybrid is: 16.7475 +- 0.256421171205902
100%|██████████| 400/400 [1:25:52<00:00, 12.88s/it]
sigma = 2.0, optimality gap of hybrid is: 30.39441103886213 +- 0.5523747647466375
sigma = 2.0, resolving counts of hybrid is: 13.465 +- 0.23891515466336488
%% Cell type:code id:bc49647d tags:
``` python
```
%% Cell type:code id:74457027 tags:
``` python
hybrid = [1.6416123472832282, 3.740784098840038, 6.232779010619595, 9.051675187668593, 12.015536928137521, 17.029235091532712,
21.859185477967003, 30.39441103886213]
hybrid_ci = [0.03762840532414709, 0.08864766490269418, 0.12516566921375472, 0.17526187465293427, 0.23493532374527396, 0.32251663156305277,
0.4292526697277563, 0.5523747647466375]
resolve_times = [14.7, 15.1, 14.9, 14.4, 13.8, 17.1, 16.7, 13.5]
```
%% Cell type:code id:aa7bd036 tags:
``` python
```
%% Cell type:code id:4023861f tags:
``` python
```
%% Cell type:code id:9228f02a tags:
``` python
# Data
my_sigma = [0., 0.1, 0.2, 0.3, 0.4, 0.5, 0.75, 1., 2.]
myopic = [11.357676070885248, 11.401668532083704, 12.005599689895234, 13.92682047821421, 16.7393893696094, 20.37330959385332,
29.162374293247353, 34.65782484111173, 42.396547307764195]
myopic_ci = [0., 0.015496018275286056, 0.05334801905714205, 0.13651943488775112, 0.26226986034593697,
0.37805996400213815, 0.5828905111648925, 0.6615687497411535, 0.8489865804329587]
projection = [0., 3.779094662666239, 7.840320754324296, 11.834461835666616, 15.431781204237325, 19.006509927404068, 27.933999009688478, 33.56407740475231, 41.511058266218754]
projection_ci = [0., 0.09219906109427405, 0.17725997975822327, 0.23568836373341567, 0.30743313235919256, 0.38494369354128033, 0.4949934591449486, 0.5607304536386369, 0.7061441744074932]
hybrid = [0., 1.6416123472832282, 3.740784098840038, 6.232779010619595, 9.051675187668593, 12.015536928137521, 17.029235091532712,
21.859185477967003, 30.39441103886213]
hybrid_ci = [0., 0.03762840532414709, 0.08864766490269418, 0.12516566921375472, 0.17526187465293427, 0.23493532374527396, 0.32251663156305277,
0.4292526697277563, 0.5523747647466375]
update = [0., 0.6751724000587274, 1.785608100718548, 3.5096707400443847, 5.459479596568883, 7.670634010252172, 12.948077942456393, 16.82817815804907, 22.198738525815486]
update_ci = [0., 0.0284472199839743, 0.05978098879254324, 0.11913526304423622, 0.15754489654769221, 0.2150031057950384, 0.32913629277701, 0.3949186834446812, 0.5169044969707984]
# Create a new figure
plt.figure()
# Plot the data with error bars
plt.errorbar(my_sigma, myopic, yerr=myopic_ci, fmt='-v', label="Myopic Policy", color = "r")
plt.errorbar(my_sigma, projection, yerr=projection_ci, fmt='-<', label="Projection Policy", color = "purple")
plt.errorbar(my_sigma, hybrid, yerr=hybrid_ci, fmt='->', label="Hybrid Policy", color = "b")
plt.errorbar(my_sigma, update, yerr=update_ci, fmt='-^', label="Update Policy", color = "g")
# Label the axes and create a legend
plt.xlabel("$\sigma$", size=20)
plt.ylabel("Optimality Gap (Smaller is Better)", size=13)
plt.title("$V_{\mathrm{rel-prio}} (\mathbf{x},T) = 323.52...$ with $T=30$",size=13)
plt.legend()
```
%% Output
<matplotlib.legend.Legend at 0x2c62293a280>
%% Cell type:code id:0c4de1dd tags:
``` python
```
%% Cell type:code id:0bd775f2 tags:
``` python
# Create a new figure
plt.figure()
# Plot the data with error bars
plt.errorbar(my_sigma, myopic, yerr=myopic_ci, fmt='-v', label="Myopic Policy", color = "r")
plt.errorbar(my_sigma, projection, yerr=projection_ci, fmt='-<', label="Projection Policy", color = "purple")
plt.errorbar(my_sigma, hybrid, yerr=hybrid_ci, fmt='->', label="Hybrid Policy", color = "b")
plt.errorbar(my_sigma, update, yerr=update_ci, fmt='-^', label="Update Policy", color = "g")
# Label the axes and create a legend
plt.xlabel("$\sigma$", size=20)
plt.ylabel("Optimality Gap (Smaller is Better)", size=13)
plt.title("$V_{\mathrm{rel-prio}} (\mathbf{x},T) = 323.52...$ with $T=30$",size=13)
# Annotate resolve times
resolve_times = [1., 15.7, 16.1, 15.9, 15.4, 14.8, 18.1, 17.7, 14.5]
for i, txt in enumerate(resolve_times):
plt.annotate(txt, (my_sigma[i], hybrid[i]), textcoords="offset points", xytext=(0,8), ha='center', fontsize=8.5, color="b")
# Create an empty plot element for the annotation legend entry
plt.plot([], [], ' ', label="Annotations: Re-solving Counts (Hybrid)")
# Create the legend
plt.legend(fontsize=9.4)
# Display the plot
#plt.show()
plt.savefig("perf-compare-3.pdf", bbox_inches='tight')
```
%% Output
%% Cell type:code id:44813912 tags:
``` python
```
%% Cell type:code id:2da8c60b tags:
``` python
```
%% Cell type:code id:a1871a44 tags:
``` python
```
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