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plot_policy_improvement.py
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plot_policy_improvement.py
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import deepdish as dd
import matplotlib
matplotlib.use('TkAgg')
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import matplotlib.lines as mlines
from matplotlib.legend import Legend
import seaborn as sns; sns.set(color_codes=True)
import os
import scipy.signal as signal
# Colors
alpha = 0.15
sns.set(style="whitegrid", palette="Paired")
colorSet = sns.color_palette("Paired", 10);
def discounted_sum(costs, discount):
'''
Calculate discounted sum of costs
'''
y = signal.lfilter([1], [1, -discount], x=costs[::-1])
return y[::-1][0]
def color_gen():
colors = [ "dusty purple", "windows blue", "faded green", "dark pink", "amber"]
colors = sns.xkcd_palette(colors)
idx = -1
while 1:
idx = (idx + 1) % len(colors)
yield colors[idx]
# Data setup
dones = dd.io.load(os.path.join('seed_2_data', 'car_data_is_done_seed_2.h5'))
costs = dd.io.load(os.path.join('seed_2_data', 'car_data_rewards_seed_2.h5'))
dones = np.hstack([0,1+np.where(dones)[0]])
episodes = []
for low_, high_ in zip(dones[:-1], dones[1:]):
new_episode ={
'c': costs[low_:high_, 0].reshape(-1),
'brake': costs[low_:high_, -1].reshape(-1),
'lane': costs[low_:high_, 3].reshape(-1),
}
episodes.append(new_episode)
discounted_costs = np.array([[discounted_sum(x['c'],.95),discounted_sum(x['brake'],.95),discounted_sum(x['lane'],.95)] for x in episodes])
data = dd.io.load('car_policy_improvement.h5')
DQN = [-39.61397106365249, 7.703194041056963, 115.62071639160499]
LSPI = pd.read_csv('lspi_results.csv')
plt.rc('text', usetex=True)
lines, fill_betweens= [], []
plt.rc_context({'axes.edgecolor':'k'})
fig, ax1 = plt.subplots()
ax1.grid(alpha=.35)
max_iterations = 27
iterations = range(len(data['g_eval'][0][:max_iterations]))
colors = color_gen()
constraint_names = ['Braking', 'Center of Lane']
constraint_upper_bound = [5.8, 85.]#[1.5, 5.]
locations = ['lower left', 'lower center', 'lower right']
fontsize = 16
legend_fontsize = 16
legend_title_fontsize = 16
major_tick_mark_size = 14
def derandomize(data, constraints, min_iteration):
fqe_c = np.array(data['c_eval'][0])[:,-1]
fqe_g_0 = np.array(data['g_eval'][0])[:,-1]
fqe_g_1 = np.array(data['g_eval'][1])[:,-1]
out = []
for iteration in range(min_iteration, len(fqe_c)):
df_tmp = pd.DataFrame(np.hstack([np.arange(min_iteration,iteration+1).reshape(1,-1).T, fqe_c[min_iteration:(iteration+1)].reshape(1,-1).T, fqe_g_0[min_iteration:(iteration+1)].reshape(1,-1).T, fqe_g_1[min_iteration:(iteration+1)].reshape(1,-1).T ]), columns=['iteration', 'fqe_c', 'fqe_g_0', 'fqe_g_1'])
df_tmp = df_tmp[(df_tmp['fqe_g_0'] < constraints[0]) & (df_tmp['fqe_g_1'] < constraints[1]) ]
try:
argmin = np.argmin(np.array(df_tmp['fqe_c']))
it = int(df_tmp.iloc[argmin]['iteration'])
except:
argmin = 0
it = 0
out.append(np.hstack([iteration, np.hstack([data['c_exacts'][it], np.array(data['g_exacts'])[it,:-1]]) ]))
return pd.DataFrame(out, columns=['iterations', 'c_derandomized', 'g_0_derandomized', 'g_1_derandomized'])
df_derandom = derandomize(data, np.array(constraint_upper_bound)*.8, 0)
legend = []
car_color = colors.next()
derandom_color = colors.next()
c_values = np.array(data['c_eval_actuals'])[:max_iterations,-10:,:] # shape = (iteration #, k, performance)
last = np.cumsum(c_values[:,-1,0])/np.arange(1,1+len(c_values[:,-1,0]))#*100
evaluation = np.array(pd.DataFrame(c_values[:,-1,0]).expanding().mean()).reshape(-1)
std = np.array(pd.DataFrame(c_values[:,-1,0]).expanding().std()).reshape(-1)
#evaluation = np.mean(c_values, axis=1)[:,0]#*100
#std = np.std(c_values, axis=1)[:,0]#*100
lines.append( ax1.plot(iterations, last, color = car_color,linestyle='-',markersize=7, label='Exact') )
lines.append( ax1.plot(df_derandom['iterations'], df_derandom['c_derandomized'], color = derandom_color,linestyle='-',markersize=7, label='Exact') )
# lines.append( ax1.plot(iterations, evaluation, color = car_color,marker='s',markersize=7, label='Mean of last 10') )
# fill_betweens.append( ax1.fill_between(iterations,evaluation-std, evaluation+std, alpha = alpha, color = car_color, zorder = 10) )
y_err_lower = last - np.min(c_values, axis=1)[:,0]
y_err_higher = last - np.max(c_values, axis=1)[:,0]
legend.append( mlines.Line2D([], [], color=car_color, linestyle='-',
markersize=7, label='Percent of Track Covered') )
legend.append( mlines.Line2D([], [], color=derandom_color, linestyle='-',
markersize=7, label='Percent of Track Covered') )
# legend.append( mlines.Line2D([], [], color=car_color, marker='s',
# markersize=7, label='Percent of Track Covered') )
## Baselines
# LSPI
lspi_color = colors.next()
lspi = np.array(LSPI.iloc[:,0])
evaluation = np.array(pd.DataFrame(lspi).expanding().mean()).reshape(-1)
lines.append( ax1.plot(iterations, evaluation, color = lspi_color,markersize=7,linestyle='-' , label='Exact') )
legend.append( mlines.Line2D([], [], color=lspi_color, linestyle='-' ,
markersize=7, label='Percent of Track Covered') )
# DQN
dqn_color = colors.next()
dqn = np.array([DQN[0]]*len(last))
evaluation = np.array(pd.DataFrame(dqn).expanding().mean()).reshape(-1)
lines.append( ax1.plot(iterations, evaluation, color = dqn_color,markersize=7,linestyle='-' , label='Exact') )
legend.append( mlines.Line2D([], [], color=dqn_color, linestyle='-' ,
markersize=7, label='Percent of Track Covered') )
# Pi_D
pi_d_color = colors.next()
evaluation = np.mean(discounted_costs[:,0]).reshape(-1)
lines.append( ax1.plot(iterations, [evaluation]*len(iterations), color = pi_d_color,markersize=7,linestyle='-' , label='Exact') )
legend.append( mlines.Line2D([], [], color=pi_d_color, linestyle='-' ,
markersize=7, label='Percent of Track Covered') )
legend.append( mlines.Line2D([], [], color='k', linestyle='--' ,
markersize=7, label='Percent of Track Covered') )
ax1.set_xlabel('Iteration (t)', fontsize=fontsize)
ax1.set_ylabel('Value (Main Objective)', color='k', fontsize=fontsize+2)
ax1.tick_params(axis='y', labelcolor='k')
ax1.set_ylim(bottom=-55, top=-15)
# ax1.set_ylim(bottom=20, top=55)
ax1.set_xlim(-.5, 25)
labels = np.array(['FQE', 'Algo 2', 'Mean', 'Regularized LSPI', 'Online-RL \n(no constraint)', 'Algo 2 \n(Derandomized)', r'$\pi_D$', 'Constraint Threshold'])
leg = Legend(ax1,
np.array(legend)[[0,1,2,3,4,5]],
labels[[1,5,3,4,6,7]],
loc='center right', #loc='lower center',
bbox_to_anchor=(1.01,.5), #bbox_to_anchor=(.5,0),
bbox_transform=fig.transFigure,
ncol = 1,#ncol = 2,
frameon=True,
fontsize = legend_fontsize-1)
ax1.add_artist(leg)
plt.tick_params(axis='both', which='major', labelsize=major_tick_mark_size)
plt.tick_params(axis='both', which='minor', labelsize=8)
ax1.set_title('Main Objective - Accumulated Cost', fontsize=fontsize+2)
# plt.subplots_adjust(right=0.7)
# plt.tight_layout()#rect=[0,.2,1,1])
plt.tight_layout(rect=[-.025,-.025,.675,1.025])
# plt.savefig('car_main_value_wo_band.png', format='png', dpi=300)
# plt.show()
# import pdb; pdb.set_trace()
# car_color = colors.next()
# c_values = np.array(data['c_eval'][0])[:,-10:] # shape = (iteration #, k)
# last = np.mean(c_values, axis=1)#c_values[:,-1,0]#*100
# evaluation = np.mean(c_values, axis=1)#*100
# std = np.std(c_values, axis=1)#*100
# lines.append( ax1.plot(iterations, last, color = car_color,marker='o',markersize=7, label='Percent of Track Covered') )
# fill_betweens.append( ax1.fill_between(iterations,evaluation-std, evaluation+std, alpha = alpha, color = car_color, zorder = 10) )
# legend.append( mlines.Line2D([], [], color=car_color, marker='o',
# markersize=7, label='Percent of Track Covered') )
#labels = np.array([r"$FQE: \;\; \frac{1}{10}\sum_{i=40}^{50}\widehat{C^{i}}(\pi_{Q_{50}})$", r"$Exact: \;\; C(\pi_{Q_{50}})$", r'$Mean: \;\; \frac{1}{10}\sum_{i=40}^{50} C(\pi_{Q_i})$'])
# labels = np.array(['FQE', r'$Our \; C$', 'Mean', r'$DQN \; C$', r'$LSPI \; C$'])
# leg = Legend(ax1, np.array(legend)[[0,1,2]], labels[[1,3,4]], title='Main Objective', loc=locations[0], frameon=False, fontsize = legend_fontsize) #shadow=True, fancybox=True,
# ax1.add_artist(leg)
# ax = ax1.twinx()
# tex_labels = [[r'$FQE: \;\; \frac{1}{10}\sum_{i=40}^{50} \widehat{G^{i}_0}(\pi_{Q_{50}})$', r'$Exact: \;\; G_0(\pi_{Q_{50}})$'],
# [r'$FQE: \;\; \frac{1}{10}\sum_{i=40}^{50} \widehat{G^{i}_1}(\pi_{Q_{50}})$', r'$Exact: \;\; G_1(\pi_{Q_{50}})$']]
# tex_labels = [[r'$FQE \; G_0$', r'$Our \; G_0$'], [r'$FQE \; G_1$', r'$Our \; G_1$']]
# baseline_labels = [[r'$DQN \; G_0$', r'$LSPI \; G_0$'], [r'$DQN \; G_1$', r'$LSPI \; G_1$']]
tex_labels = [[r'$FQE \; G_0$', 'Algo 2', 'Algo 2 (Derandomized)'], [r'$FQE \; G_1$', 'Algo 2', 'Algo 2 (Derandomized)']]
# baseline_labels = [['DDQN', 'LSPI'], ['DDQN', 'LSPI']]
baseline_labels = [['Online-RL (no constraint)', 'Regularized LSPI', r'$\pi_D$'], ['Online-RL (no constraint)', 'Regularized LSPI', r'$\pi_D$']]
# plt.clf()
fig, axs = plt.subplots(2, sharex=True)
for idx in data['g_eval'].keys():
colors = color_gen()
ax = axs[idx]
ax.grid(alpha=.35)
legend = []
# FQE
constraint = np.array(data['g_eval'][idx]) # shape = (iteration #, k) referring to Q_k
constraint = constraint[:max_iterations,-10:]
# evaluation = np.array(pd.DataFrame(np.mean(constraint, axis = 1)/constraint_upper_bound[idx]).expanding().mean()).reshape(-1)
# std = np.array(pd.DataFrame(np.mean(constraint, axis = 1)/constraint_upper_bound[idx]).expanding().std()).reshape(-1)
# evaluation = np.mean(constraint, axis = 1)/constraint_upper_bound[idx]
# std = np.std(constraint, axis=1)/constraint_upper_bound[idx]
label = constraint_names[idx]
# lines.append( ax.plot(iterations, evaluation, color = color,marker='o',markersize=7, label=tex_labels[idx][0]) )
# fill_betweens.append( ax.fill_between(iterations,evaluation-std, evaluation+std, alpha = alpha, color = color, zorder = 11+2*idx) )
#legend.append( mlines.Line2D([], [], color=color, marker='o',
# markersize=7, label=tex_labels[idx][0]) )
# EXACT
g_exacts = np.array(data['g_exacts'])[:max_iterations,idx]#/constraint_upper_bound[idx]
evaluation = np.array(pd.DataFrame(g_exacts).expanding().mean()).reshape(-1)
std = np.array(pd.DataFrame(g_exacts).expanding().std()).reshape(-1)
lines.append( ax.plot(iterations, evaluation, color = car_color ,linestyle='-' ,linewidth=2.0, label=tex_labels[idx][1]) )
legend.append( mlines.Line2D([], [], color=car_color, linestyle='-' ,linewidth=2.0,
markersize=7, label=tex_labels[idx][1]) )
# Derandomized
lines.append( ax.plot(df_derandom['iterations'], df_derandom['g_%s_derandomized' % idx], linewidth=2.0,color = derandom_color,linestyle='-',markersize=7, label='Exact') )
legend.append( mlines.Line2D([], [], color=derandom_color, linestyle='-' ,linewidth=2.0,
markersize=7, label=tex_labels[idx][2]) )
# fill_betweens.append( ax.fill_between(iterations,evaluation-std, evaluation+std, alpha = alpha, color = color, zorder = 11+2*idx+1) )
## BASELINES
# fill_betweens.append( ax.fill_between(iterations,evaluation-std, evaluation+std, alpha = alpha, color = color, zorder = 11+2*idx+1) )
# LSPI
baseline = np.array(LSPI.iloc[:,idx+1])*constraint_upper_bound[idx]
evaluation = np.array(pd.DataFrame(baseline).expanding().mean()).reshape(-1)
std = np.array(pd.DataFrame(baseline).expanding().std()).reshape(-1)
lines.append( ax.plot(iterations, evaluation, color = lspi_color , linestyle='-', linewidth=2.0,label=baseline_labels[idx][1]) )
legend.append( mlines.Line2D([], [], color=lspi_color, linestyle='-', linewidth=2.0,
markersize=7, label=baseline_labels[idx][1]) )
# fill_betweens.append( ax.fill_between(iterations,evaluation-std, evaluation+std, alpha = alpha, color = color, zorder = 11+2*idx+1) )
# DQN
baseline = np.array([DQN[idx+1]]*len(evaluation))#/constraint_upper_bound[idx]
evaluation = np.array(pd.DataFrame(baseline).expanding().mean()).reshape(-1)
std = np.array(pd.DataFrame(baseline).expanding().std()).reshape(-1)
lines.append( ax.plot(iterations, evaluation, color = dqn_color , linestyle='-' ,linewidth=2.0, label=baseline_labels[idx][0]) )
legend.append( mlines.Line2D([], [], color=dqn_color, linestyle='-',linewidth=2.0,
markersize=7, label=baseline_labels[idx][0]) )
# Pi_D
evaluation = np.mean(discounted_costs[:,idx+1]).reshape(-1)
lines.append( ax.plot(iterations, [evaluation]*len(iterations), color = pi_d_color,markersize=7,linewidth=2.0,linestyle='-' , label=baseline_labels[idx][2]) )
legend.append( mlines.Line2D([], [], color=pi_d_color, linestyle='-' ,linewidth=2.0,
markersize=7, label=baseline_labels[idx][2]) )
# THRESHOLD
constraint_violation = [constraint_upper_bound[idx]]*len(iterations)
lines.append( ax.plot(iterations, constraint_violation, color = 'k', linestyle=':', linewidth=2.0, marker=None) )
legend.append( mlines.Line2D([], [], color='k', linestyle=':', marker=None, linewidth=2.0, label='Constraint Threshold') )
labels = []
for i in range(len(legend)):
line = legend[i]
try:
labels += [line.label]
except:
labels += [line.get_label()]
if idx == 1:
# leg = Legend(ax,
# legend,
# labels,
# title=label,
# # loc='center left',
# bbox_to_anchor=(0.5, -0.05),
# ncol = 3,
# frameon=False,
# # bbox_to_anchor=(1, 0.5),
# fontsize = legend_fontsize-3)
leg = Legend(ax,
legend,
labels,
loc='lower center',
bbox_to_anchor=(.5,0),
bbox_transform=fig.transFigure,
ncol = 2,
frameon=True,
fontsize = legend_fontsize-2)
plt.setp(leg.get_title(),fontsize='%s' % legend_title_fontsize)
# ax.add_artist(leg)
if idx == 1:
ax.set_xlabel('Iteration (t)', fontsize=fontsize)
lab = ['Value (Braking)', 'Value (Lane Center)'][idx]
ax.set_ylabel(lab, color='k', fontsize=fontsize+2)
# ax.set_ylim(bottom=-1, top=3)
ax.tick_params(axis='y', labelcolor='k')
if idx == 0: ax.set_ylim(bottom=-2, top=15)
ax.set_xlim(-.5, 25)
axs[0].tick_params(axis='both', which='major', labelsize=major_tick_mark_size)
axs[1].tick_params(axis='both', which='major', labelsize=major_tick_mark_size)
axs[0].set_title('Constraints - Accumulated Cost', fontsize=fontsize+2)
plt.tight_layout(rect=[-.025,-.025,1.025,1.025])#rect=[0,.2,1,1])
# plt.savefig('car_constraint_values_wo_band.png', format='png', dpi=300)
# plt.show()
import pdb; pdb.set_trace()
############################################
# W/ Band
# plt.clf()
fig, ax1 = plt.subplots()
legend = []
c_values = np.array(data['c_eval_actuals'])[:max_iterations,-10:,:] # shape = (iteration #, k, performance)
last = np.cumsum(c_values[:,-1,0])/np.arange(1,1+len(c_values[:,-1,0]))#*100
evaluation = np.array(pd.DataFrame(c_values[:,-1,0]).expanding().mean()).reshape(-1)
std = np.array(pd.DataFrame(c_values[:,-1,0]).expanding().std()).reshape(-1)
#evaluation = np.mean(c_values, axis=1)[:,0]#*100
#std = np.std(c_values, axis=1)[:,0]#*100
lines.append( ax1.plot(iterations, last, color = car_color,linestyle='-',markersize=7, label='Exact') )
lines.append( ax1.plot(df_derandom['iterations'], df_derandom['c_derandomized'], color = derandom_color,linestyle='-',markersize=7, label='Exact') )
# lines.append( ax1.plot(iterations, evaluation, color = car_color,marker='s',markersize=7, label='Mean of last 10') )
fill_betweens.append( ax1.fill_between(iterations,evaluation-std, evaluation+std, alpha = alpha, color = car_color, zorder = 10) )
legend.append( mlines.Line2D([], [], color=car_color, linestyle='-',
markersize=7, label='Percent of Track Covered') )
legend.append( mlines.Line2D([], [], color=derandom_color, linestyle='-',
markersize=7, label='Percent of Track Covered') )
# Pi_D
evaluation = np.mean(discounted_costs[:,0])
std = np.std(discounted_costs[:,0])
lines.append( ax1.plot(iterations, [evaluation]*len(iterations), color = pi_d_color,markersize=7,linestyle='-' , label='Exact') )
legend.append( mlines.Line2D([], [], color=pi_d_color, linestyle='-' ,
markersize=7, label='Percent of Track Covered') )
fill_betweens.append( ax1.fill_between(iterations,evaluation-std, evaluation+std, alpha = alpha, color = pi_d_color, zorder = 10) )
ax1.set_xlabel('Iteration (t)', fontsize=fontsize)
ax1.set_ylabel('Main Objective Value', color='k', fontsize=fontsize)
ax1.tick_params(axis='y', labelcolor='k')
ax1.set_ylim(bottom=-55, top=-15)
# ax1.set_ylim(bottom=20, top=55)
ax1.set_xlim(-.5, 25)
labels = np.array(['FQE', 'Algo 2', 'Mean', 'Regularized LSPI', 'Online-RL (no constraint)', 'Algo 2 (Derandomized)', r'$\pi_D$'])
# leg = Legend(ax1, np.array(legend), labels[[1,6]], loc='upper right', frameon=True, fontsize = legend_fontsize)
leg = Legend(ax1,
np.array(legend),
labels[[1,5,6]],
loc='lower center',
bbox_to_anchor=(.5,0),
bbox_transform=fig.transFigure,
ncol = 2,
frameon=True,
fontsize = legend_fontsize)
ax1.add_artist(leg)
plt.tick_params(axis='both', which='major', labelsize=major_tick_mark_size)
plt.tick_params(axis='both', which='minor', labelsize=8)
ax1.set_title('Main Objective - Accumulated Cost', fontsize=fontsize)
# plt.tight_layout()
plt.tight_layout(rect=[0,.15,1,1])
plt.savefig('car_main_value.png', format='png', dpi=300)
plt.show()
plt.clf()
fig, axs = plt.subplots(2, sharex=True)
for idx in data['g_eval'].keys():
ax = axs[idx]
ax.grid(alpha=.35)
legend = []
# FQE
constraint = np.array(data['g_eval'][idx]) # shape = (iteration #, k) referring to Q_k
constraint = constraint[:max_iterations,-10:]
# evaluation = np.array(pd.DataFrame(np.mean(constraint, axis = 1)/constraint_upper_bound[idx]).expanding().mean()).reshape(-1)
# std = np.array(pd.DataFrame(np.mean(constraint, axis = 1)/constraint_upper_bound[idx]).expanding().std()).reshape(-1)
# evaluation = np.mean(constraint, axis = 1)/constraint_upper_bound[idx]
# std = np.std(constraint, axis=1)/constraint_upper_bound[idx]
label = constraint_names[idx]
# lines.append( ax.plot(iterations, evaluation, color = color,marker='o',markersize=7, label=tex_labels[idx][0]) )
# fill_betweens.append( ax.fill_between(iterations,evaluation-std, evaluation+std, alpha = alpha, color = color, zorder = 11+2*idx) )
#legend.append( mlines.Line2D([], [], color=color, marker='o',
# markersize=7, label=tex_labels[idx][0]) )
# EXACT
g_exacts = np.array(data['g_exacts'])[:max_iterations,idx]#/constraint_upper_bound[idx]
evaluation = np.array(pd.DataFrame(g_exacts).expanding().mean()).reshape(-1)
std = np.array(pd.DataFrame(g_exacts).expanding().std()).reshape(-1)
fill_betweens.append( ax.fill_between(iterations,evaluation-std, evaluation+std, alpha = alpha, color = car_color, zorder = 10) )
lines.append( ax.plot(iterations, evaluation, color = car_color ,linestyle='-' , label=tex_labels[idx][1]) )
legend.append( mlines.Line2D([], [], color=car_color, linestyle='-' ,
markersize=7, label=tex_labels[idx][1]) )
# Derandomized
lines.append( ax.plot(df_derandom['iterations'], df_derandom['g_%s_derandomized' % idx],color = derandom_color,linestyle='-',markersize=7, label='Exact') )
legend.append( mlines.Line2D([], [], color=derandom_color, linestyle='-',
markersize=7, label=tex_labels[idx][2]) )
# Pi_D
evaluation = np.mean(discounted_costs[:,idx+1])
std = np.std(discounted_costs[:,idx+1])
lines.append( ax.plot(iterations, [evaluation]*len(iterations), color = pi_d_color,markersize=7,linestyle='-' , label=baseline_labels[idx][2]) )
legend.append( mlines.Line2D([], [], color=pi_d_color, linestyle='-' ,
markersize=7, label=baseline_labels[idx][2]) )
fill_betweens.append( ax.fill_between(iterations,evaluation-std, evaluation+std, alpha = alpha, color = pi_d_color, zorder = 10) )
# THRESHOLD
constraint_violation = [constraint_upper_bound[idx]]*len(iterations)
lines.append( ax.plot(iterations, constraint_violation, color = 'k', linestyle=':', linewidth=2.0, marker=None) )
legend.append( mlines.Line2D([], [], color='k', linestyle=':', marker=None, linewidth=2.0, label='Constraint Threshold') )
labels = []
for i in range(len(legend)):
line = legend[i]
try:
labels += [line.label]
except:
labels += [line.get_label()]
if idx == 1:
leg = Legend(ax,
legend,
labels,
loc='lower center',
bbox_to_anchor=(.5,0),
bbox_transform=fig.transFigure,
ncol = 2,
frameon=True,
fontsize = legend_fontsize)
# leg = Legend(ax, legend, labels, title=label, loc='center left', frameon=False, bbox_to_anchor=(1, 0.5), fontsize = legend_fontsize-3)
plt.setp(leg.get_title(),fontsize='%s' % legend_title_fontsize)
ax.add_artist(leg)
if idx == 1:
ax.set_xlabel('Iteration (t)', fontsize=fontsize)
lab = ['Value (Braking)', 'Value (Lane Center)'][idx]
ax.set_ylabel(lab, color='k', fontsize=fontsize-2)
# ax.set_ylim(bottom=-1, top=3)
ax.tick_params(axis='y', labelcolor='k')
if idx == 0: ax.set_ylim(bottom=-2, top=15)
ax.set_xlim(-.5, 25)
axs[0].tick_params(axis='both', which='major', labelsize=major_tick_mark_size)
axs[1].tick_params(axis='both', which='major', labelsize=major_tick_mark_size)
axs[0].set_title('Constraints - Accumulated Cost', fontsize=fontsize)
# plt.tight_layout()
plt.tight_layout(rect=[0,.15,1,1])
plt.savefig('car_constraint_values.png', format='png', dpi=300)
plt.show()