IIT-M RL-ASSIGNMENT-2-TAXI
Solution for submission 132266
A detailed solution for submission 132266 submitted for challenge IIT-M RL-ASSIGNMENT-2-TAXI
rohan_jagdish_vashodia_cs17b025
What is the notebook about?¶
Problem - Taxi Environment Algorithms¶
This problem deals with a taxi environment and stochastic actions. The tasks you have to do are:
- Implement Policy Iteration
- Implement Modified Policy Iteration
- Implement Value Iteration
- Implement Gauss Seidel Value Iteration
- Visualize the results
- Explain the results
How to use this notebook? 📝¶
This is a shared template and any edits you make here will not be saved.You should make a copy in your own drive. Click the "File" menu (top-left), then "Save a Copy in Drive". You will be working in your copy however you like.
Update the config parameters. You can define the common variables here
| Variable | Description |
|---|---|
AICROWD_DATASET_PATH |
Path to the file containing test data. This should be an absolute path. |
AICROWD_RESULTS_DIR |
Path to write the output to. |
AICROWD_ASSETS_DIR |
In case your notebook needs additional files (like model weights, etc.,), you can add them to a directory and specify the path to the directory here (please specify relative path). The contents of this directory will be sent to AIcrowd for evaluation. |
AICROWD_API_KEY |
In order to submit your code to AIcrowd, you need to provide your account's API key. This key is available at https://www.aicrowd.com/participants/me |
- Installing packages. Please use the Install packages 🗃 section to install the packages
Setup AIcrowd Utilities 🛠¶
We use this to bundle the files for submission and create a submission on AIcrowd. Do not edit this block.
In [5]:
!pip install aicrowd-cli > /dev/null
AIcrowd Runtime Configuration 🧷¶
Get login API key from https://www.aicrowd.com/participants/me
In [8]:
import os
AICROWD_DATASET_PATH = os.getenv("DATASET_PATH", os.getcwd()+"/13d77bb0-b325-4e95-a03b-833eb6694acd_a2_taxi_inputs.zip")
AICROWD_RESULTS_DIR = os.getenv("OUTPUTS_DIR", "results")
In [9]:
In [10]:
!unzip $AICROWD_DATASET_PATH
In [11]:
DATASET_DIR = 'inputs/'
Taxi Environment¶
Read the environment to understand the functions, but do not edit anything
In [12]:
import numpy as np
class TaxiEnv_HW2:
def __init__(self, states, actions, probabilities, rewards, initial_policy):
self.possible_states = states
self._possible_actions = {st: ac for st, ac in zip(states, actions)}
self._ride_probabilities = {st: pr for st, pr in zip(states, probabilities)}
self._ride_rewards = {st: rw for st, rw in zip(states, rewards)}
self.initial_policy = initial_policy
self._verify()
def _check_state(self, state):
assert state in self.possible_states, "State %s is not a valid state" % state
def _verify(self):
"""
Verify that data conditions are met:
Number of actions matches shape of next state and actions
Every probability distribution adds up to 1
"""
ns = len(self.possible_states)
for state in self.possible_states:
ac = self._possible_actions[state]
na = len(ac)
rp = self._ride_probabilities[state]
assert np.all(rp.shape == (na, ns)), "Probabilities shape mismatch"
rr = self._ride_rewards[state]
assert np.all(rr.shape == (na, ns)), "Rewards shape mismatch"
assert np.allclose(rp.sum(axis=1), 1), "Probabilities don't add up to 1"
def possible_actions(self, state):
""" Return all possible actions from a given state """
self._check_state(state)
return self._possible_actions[state]
def ride_probabilities(self, state, action):
"""
Returns all possible ride probabilities from a state for a given action
For every action a list with the returned with values in the same order as self.possible_states
"""
actions = self.possible_actions(state)
ac_idx = actions.index(action)
return self._ride_probabilities[state][ac_idx]
def ride_rewards(self, state, action):
actions = self.possible_actions(state)
ac_idx = actions.index(action)
return self._ride_rewards[state][ac_idx]
Example of Environment usage¶
In [13]:
def check_taxienv():
# These are the values as used in the pdf, but they may be changed during submission, so do not hardcode anything
states = ['A', 'B', 'C']
actions = [['1','2','3'], ['1','2'], ['1','2','3']]
probs = [np.array([[1/2, 1/4, 1/4],
[1/16, 3/4, 3/16],
[1/4, 1/8, 5/8]]),
np.array([[1/2, 0, 1/2],
[1/16, 7/8, 1/16]]),
np.array([[1/4, 1/4, 1/2],
[1/8, 3/4, 1/8],
[3/4, 1/16, 3/16]]),]
rewards = [np.array([[10, 4, 8],
[ 8, 2, 4],
[ 4, 6, 4]]),
np.array([[14, 0, 18],
[ 8, 16, 8]]),
np.array([[10, 2, 8],
[6, 4, 2],
[4, 0, 8]]),]
initial_policy = {'A': '1', 'B': '1', 'C': '1'}
env = TaxiEnv_HW2(states, actions, probs, rewards, initial_policy)
print("All possible states", env.possible_states)
print("All possible actions from state B", env.possible_actions('B'))
print("Ride probabilities from state A with action 2", env.ride_probabilities('A', '2'))
print("Ride rewards from state C with action 3", env.ride_rewards('C', '3'))
base_kwargs = {"states": states, "actions": actions,
"probabilities": probs, "rewards": rewards,
"initial_policy": initial_policy}
return base_kwargs
base_kwargs = check_taxienv()
env = TaxiEnv_HW2(**base_kwargs)
Task 1 - Policy Iteration¶
Run policy iteration on the environment and generate the policy and expected reward
In [14]:
# 1.1 Policy Iteration
def policy_iteration(taxienv, gamma):
# A list of all the states
states = taxienv.possible_states
# Initial values
values = {s: 0 for s in states}
# This is a dictionary of states to policies -> e.g {'A': '1', 'B': '2', 'C': '1'}
p = taxienv.initial_policy.copy()
## Begin code here
# Hints -
# Do not hardcode anything
# Only the final result is required for the results
# Put any extra data in "extra_info" dictonary for any plots etc
# Use the helper functions taxienv.ride_rewards, taxienv.ride_probabilities, taxienv.possible_actions
# For terminating condition use the condition exactly mentioned in the pdf
all_values = [] # Append the "values" dictionary to this after each update
all_policies = [] # Append the "policy" dictionary to this after each update
# Put your extra information needed for plots etc in this dictionary
extra_info = []
done=False
while(done==False):
while(1):
lamb=0
extra_info.append(values.copy())
for s in states:
j=values[s]
values[s] = sum(taxienv.ride_probabilities(s, p[s])*(taxienv.ride_rewards(s, p[s]) + list(gamma*np.array(list(values.values())))))
lamb=max(lamb,abs(j-values[s]))
#print(lamb)
#print(lamb)
if(lamb<0.00000001):
break
done=True
for s in states:
b=p[s]
actions=taxienv.possible_actions(s)
sum_dict = {a : 0 for a in actions}
for a in actions:
sum_dict[a] += sum(taxienv.ride_probabilities(s, a)*(taxienv.ride_rewards(s, a) + list(gamma*np.array(list(values.values())))))
temp=float('-inf')
for i in sum_dict.keys():
if(sum_dict[i]>temp):
p[s]=i
temp=sum_dict[i]
if(b!=p[s]):
done=False
## Do not edit below this line
# Final results
return {"Expected Reward": values, "Policy": p}, extra_info
Task 2 - Policy Iteration for multiple values of gamma¶
Ideally this code should run as is
In [15]:
# 1.2 Policy Iteration with different values of gamma
def run_policy_iteration(env):
gamma_values = np.arange(5, 100, 5)/100
results, extra_info = {}, {}
for gamma in gamma_values:
results[gamma], extra_info[gamma] = policy_iteration(env, gamma)
return results, extra_info
results, extra_info = run_policy_iteration(env)
Task 3 - Modifed Policy Iteration¶
Implement modified policy iteration (where Value iteration is done for fixed m number of steps)
In [31]:
# 1.3 Modified Policy Iteration
def modified_policy_iteration(taxienv, gamma, m):
# A list of all the states
states = taxienv.possible_states
# Initial values
values = {s: 0 for s in states}
# This is a dictionary of states to policies -> e.g {'A': '1', 'B': '2', 'C': '1'}
p = taxienv.initial_policy.copy()
## Begin code here
# Hints -
# Do not hardcode anything
# Only the final result is required for the results
# Put any extra data in "extra_info" dictonary for any plots etc
# Use the helper functions taxienv.ride_rewards, taxienv.ride_probabilities, taxienv.possible_actions
# For terminating condition use the condition exactly mentioned in the pdf
all_values = [] # Append the "values" dictionary to this after each update
all_policies = [] # Append the "policy" dictionary to this after each update
# Put your extra information needed for plots etc in this dictionary
extra_info =[]
done=False
while(done==False):
for itr in range(0,m+1):
for s in states:
j=values[s]
extra_info.append(values.copy())
values[s] = sum(taxienv.ride_probabilities(s, p[s])*(taxienv.ride_rewards(s, p[s]) + list(gamma*np.array(list(values.values())))))
done=True
for s in states:
b=p[s]
actions=taxienv.possible_actions(s)
sum_dict = {a : 0 for a in actions}
for a in actions:
sum_dict[a] += sum(taxienv.ride_probabilities(s, a)*(taxienv.ride_rewards(s, a) + list(gamma*np.array(list(values.values())))))
temp=float('-inf')
for i in sum_dict.keys():
if(sum_dict[i]>temp):
p[s]=i
temp=sum_dict[i]
if(b!=p[s]):
done=False
## Do not edit below this line
# Final results
return {"Expected Reward": values, "Policy": p}, extra_info
Task 4 Modified policy iteration for multiple values of m¶
Ideally this code should run as is
In [33]:
def run_modified_policy_iteration(env):
m_values = np.arange(1, 15)
gamma = 0.9
results, extra_info = {}, {}
for m in m_values:
results[m], extra_info[m] = modified_policy_iteration(env, gamma, m)
return results, extra_info
results, extra_info_mpi = run_modified_policy_iteration(env)
Task 5 Value Iteration¶
Implement value iteration and find the policy and expected rewards
In [18]:
# 1.4 Value Iteration
def value_iteration(taxienv, gamma):
# A list of all the states
states = taxienv.possible_states
# Initial values
values = {s: 0 for s in states}
# This is a dictionary of states to policies -> e.g {'A': '1', 'B': '2', 'C': '1'}
p = taxienv.initial_policy.copy()
## Begin code here
# Hints -
# Do not hardcode anything
# Only the final result is required for the results
# Put any extra data in "extra_info" dictonary for any plots etc
# Use the helper functions taxienv.ride_rewards, taxienv.ride_probabilities, taxienv.possible_actions
# For terminating condition use the condition exactly mentioned in the pdf
all_values = [] # Append the "values" dictionary to this after each update
all_policies = [] # Append the "policy" dictionary to this after each update
# Put your extra information needed for plots etc in this dictionary
extra_info = []
H={s: 0 for s in states}
l=0
while(1):
#print(values)
l=0
extra_info.append(values.copy())
for s in states:
actions=taxienv.possible_actions(s)
sum_dict = {a : 0 for a in actions}
temp=float('-inf')
#print(actions,len(actions))
for a in actions:
t1=taxienv.ride_probabilities(s, a)
t2=taxienv.ride_rewards(s, a)
for i in range(len(states)):
sum_dict[a] += t1[i]*(t2[i]+gamma*values[states[i]])
if(sum_dict[a]>temp):
temp=sum_dict[a]
p[s]=a
#print(sum_dict,p[s],temp)
H[s]=temp
l=max(l,abs(values[s]-H[s]))
for s in states:
values[s]=H[s]
if(l<0.00000001):
break
#print(values)
#print("s")
#print(values)
return {"Expected Reward": values, "Policy": p}, extra_info
Task 6 Value Iteration with multiple values of gamma¶
Ideally this code should run as is
In [19]:
def run_value_iteration(env):
gamma_values = np.arange(5, 100, 5)/100
results = {}
results, extra_info1 = {}, {}
for gamma in gamma_values:
results[gamma], extra_info1[gamma] = value_iteration(env, gamma)
return results, extra_info
results, extra_info1 = run_value_iteration(env)
(results)
Out[19]:
Task 7 Gauss Seidel Value Iteration¶
Implement Gauss Seidel Value Iteration
In [20]:
# 1.4 Gauss Seidel Value Iteration
def gauss_seidel_value_iteration(taxienv, gamma):
# A list of all the states
states = taxienv.possible_states
# Initial values
values = {s: 0 for s in states}
# This is a dictionary of states to policies -> e.g {'A': '1', 'B': '2', 'C': '1'}
p = taxienv.initial_policy.copy()
## Begin code here
# Hints -
# Do not hardcode anything
# Only the final result is required for the results
# Put any extra data in "extra_info" dictonary for any plots etc
# Use the helper functions taxienv.ride_rewards, taxienv.ride_probabilities, taxienv.possible_actions
# For terminating condition use the condition exactly mentioned in the pdf
all_values = [] # Append the "values" dictionary to this after each update
all_policies = [] # Append the "policy" dictionary to this after each update
# Put your extra information needed for plots etc in this dictionary
extra_info = []
H={s: float('-inf') for s in states}
while(1):
l=0
extra_info.append(values.copy())
for s in states:
j_old=values[s]
actions=taxienv.possible_actions(s)
sum_dict = {a : 0 for a in actions}
temp=float('-inf')
for a in actions:
sum_dict[a] = sum(taxienv.ride_probabilities(s, a)*(taxienv.ride_rewards(s, a) + list(gamma*np.array(list(values.values())))))
if(sum_dict[a]>temp):
temp=sum_dict[a]
p[s]=a
values[s]=temp
l=max(l,abs(values[s]-j_old))
#print(l)
if(l<0.00000001):
break
return {"Expected Reward": values, "Policy": p}, extra_info
In [20]:
Task 8 Gauss Seidel Value Iteration with multiple values of gamma¶
Ideally this code should run as is
In [21]:
def run_gauss_seidel_value_iteration(env):
gamma_values = np.arange(5, 100, 5)/100
results = {}
results, extra_info2 = {}, {}
for gamma in gamma_values:
results[gamma], extra_info[gamma] = gauss_seidel_value_iteration(env, gamma)
return results, extra_info
results, extra_info2 = run_gauss_seidel_value_iteration(env)
results
Out[21]:
Generate Results ✅¶
In [22]:
# Do not edit this cell
def get_results(kwargs):
taxienv = TaxiEnv_HW2(**kwargs)
policy_iteration_results = run_policy_iteration(taxienv)[0]
modified_policy_iteration_results = run_modified_policy_iteration(taxienv)[0]
value_iteration_results = run_value_iteration(taxienv)[0]
gs_vi_results = run_gauss_seidel_value_iteration(taxienv)[0]
final_results = {}
final_results["policy_iteration"] = policy_iteration_results
final_results["modifed_policy_iteration"] = modified_policy_iteration_results
final_results["value_iteration"] = value_iteration_results
final_results["gauss_seidel_iteration"] = gs_vi_results
return final_results
In [23]:
# Do not edit this cell, generate results with it as is
if not os.path.exists(AICROWD_RESULTS_DIR):
os.mkdir(AICROWD_RESULTS_DIR)
for params_file in os.listdir(DATASET_DIR):
kwargs = np.load(os.path.join(DATASET_DIR, params_file), allow_pickle=True).item()
results = get_results(kwargs)
idx = params_file.split('_')[-1][:-4]
np.save(os.path.join(AICROWD_RESULTS_DIR, 'results_' + idx), results)
Check your local score¶
This score is not your final score, and it doesn't use the marks weightages. This is only for your reference of how arrays are matched and with what tolerance.
In [24]:
# Check your score on the given test cases (There are more private test cases not provided)
target_folder = 'targets'
result_folder = AICROWD_RESULTS_DIR
def check_algo_match(results, targets):
param_matches = []
for k in results:
param_results = results[k]
param_targets = targets[k]
policy_match = param_results['Policy'] == param_targets['Policy']
rv = [v for k, v in param_results['Expected Reward'].items()]
tv = [v for k, v in param_targets['Expected Reward'].items()]
rewards_match = np.allclose(rv, tv, rtol=3)
equal = rewards_match and policy_match
param_matches.append(equal)
return np.mean(param_matches)
def check_score(target_folder, result_folder):
match = []
for out_file in os.listdir(result_folder):
res_file = os.path.join(result_folder, out_file)
results = np.load(res_file, allow_pickle=True).item()
idx = out_file.split('_')[-1][:-4] # Extract the file number
target_file = os.path.join(target_folder, f"targets_{idx}.npy")
targets = np.load(target_file, allow_pickle=True).item()
algo_match = []
for k in targets:
algo_results = results[k]
algo_targets = targets[k]
algo_match.append(check_algo_match(algo_results, algo_targets))
match.append(np.mean(algo_match))
return np.mean(match)
if os.path.exists(target_folder):
print("Shared data Score (normalized to 1):", check_score(target_folder, result_folder))
Visualize results of Policy Iteration with multiple values of gamma¶
Add code to visualize the results
In [43]:
import matplotlib.pyplot as plt
#lamda =0
extra_info_pi=extra_info[0.05]
diffs1 = []
for ii in range(0,len(extra_info_pi)):
diff = np.linalg.norm(np.array(list(extra_info_pi[ii].values())) - np.array(list(extra_info_pi[len(extra_info_pi)-1].values())))/10
diffs1.append(diff)
#lamda =0.25
extra_info_pi=extra_info[0.25]
diffs2 = []
for ii in range(0,len(extra_info_pi)):
diff = np.linalg.norm(np.array(list(extra_info_pi[ii].values())) - np.array(list(extra_info_pi[len(extra_info_pi)-1].values())))/10
diffs2.append(diff)
#lamda =0.5
extra_info_pi=extra_info[0.5]
diffs3 = []
for ii in range(0,len(extra_info_pi)):
diff = np.linalg.norm(np.array(list(extra_info_pi[ii].values())) - np.array(list(extra_info_pi[len(extra_info_pi)-1].values())))/10
diffs3.append(diff)
#lamda =0.75
extra_info_pi=extra_info[0.75]
diffs4 = []
for ii in range(0,len(extra_info_pi)):
diff = np.linalg.norm(np.array(list(extra_info_pi[ii].values())) - np.array(list(extra_info_pi[len(extra_info_pi)-1].values())))/10
diffs4.append(diff)
#lamda =0.90
extra_info_pi=extra_info[0.90]
diffs5 = []
for ii in range(0,len(extra_info_pi)):
diff = np.linalg.norm(np.array(list(extra_info_pi[ii].values())) - np.array(list(extra_info_pi[len(extra_info_pi)-1].values())))/10
diffs5.append(diff)
plt.plot(diffs1)
plt.plot(diffs2)
plt.plot(diffs3)
plt.plot(diffs4)
plt.plot(diffs5)
plt.xlabel('iterations')
plt.ylabel('Loss')
plt.legend(["lamdda 0.0", "lamdda 0.25","lamdda 0.50","lamdda 0.75","lamdda 0.90"])
plt.show()
Subjective questions¶
1.a How are values of $\gamma$ affecting results of policy iteration¶
Modify this cell/add code for your answer.
If we increase gamma , Number of iterations required for convergence increases
1.b For modified policy itetaration, do you find any improvement if you choose m=10.¶
Explain your answer.Error plot for different values of m is given below.As m increases ,Convergence to optimal value decrease
In [38]:
import matplotlib.pyplot as plt
#m =3
extra_info_pi=extra_info_mpi[3]
diffs1 = []
for ii in range(0,len(extra_info_pi)):
diff = np.linalg.norm(np.array(list(extra_info_pi[ii].values())) - np.array(list(extra_info_pi[len(extra_info_pi)-1].values())))/10
diffs1.append(diff)
#m =6
extra_info_pi=extra_info_mpi[6]
diffs2 = []
for ii in range(0,len(extra_info_pi)):
diff = np.linalg.norm(np.array(list(extra_info_pi[ii].values())) - np.array(list(extra_info_pi[len(extra_info_pi)-1].values())))/10
diffs2.append(diff)
#lamda =9
extra_info_pi=extra_info_mpi[9]
diffs3 = []
for ii in range(0,len(extra_info_pi)):
diff = np.linalg.norm(np.array(list(extra_info_pi[ii].values())) - np.array(list(extra_info_pi[len(extra_info_pi)-1].values())))/10
diffs3.append(diff)
#lamda =10
extra_info_pi=extra_info_mpi[10]
diffs4 = []
for ii in range(0,len(extra_info_pi)):
diff = np.linalg.norm(np.array(list(extra_info_pi[ii].values())) - np.array(list(extra_info_pi[len(extra_info_pi)-1].values())))/10
diffs4.append(diff)
#lamda =12
extra_info_pi=extra_info_mpi[12]
diffs5 = []
for ii in range(0,len(extra_info_pi)):
diff = np.linalg.norm(np.array(list(extra_info_pi[ii].values())) - np.array(list(extra_info_pi[len(extra_info_pi)-1].values())))/10
diffs5.append(diff)
plt.plot(diffs1)
plt.plot(diffs2)
plt.plot(diffs3)
plt.plot(diffs4)
plt.plot(diffs5)
plt.xlabel('iterations')
plt.ylabel('loss')
plt.legend(["m = 3", "m = 6","m =9","m = 10","m = 12"])
plt.show()
1.c Compare and contrast the behavior of Value Iteration and Gauss Seidel Value Iteraton¶
Add code/markdown as required
The error plots for both the algorithms coincide
In [39]:
#error plot
#gamma =0.05
import matplotlib.pyplot as plt
extra_info_1=extra_info1[0.95]
extra_info_2=extra_info2[0.95]
diffs1 = []
for ii in range(0,len(extra_info_1)):
diff = np.linalg.norm(np.array(list(extra_info_1[ii].values())) - np.array(list(extra_info_1[len(extra_info_1)-1].values())))/10
diffs1.append(diff)
diffs2 = []
for ii in range(0,len(extra_info_2)):
diff = np.linalg.norm(np.array(list(extra_info_2[ii].values())) - np.array(list(extra_info_2[len(extra_info_2)-1].values())))/10
diffs2.append(diff)
plt.plot(diffs1,'r')
plt.plot(diffs2,'b')
plt.legend(["VI", "Gauss Seidel"])
plt.show()
print(diffs1)
print(diffs2)
In [39]:
In [ ]:
Submit to AIcrowd 🚀¶
In [40]:
!DATASET_PATH=$AICROWD_DATASET_PATH aicrowd notebook submit -c iit-m-rl-assignment-2-taxi -a assets
In [ ]:
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