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"""Reinforcement Learning (Chapter 22)"""
import
random
from
collections
import
defaultdict
from
mdp4e
import
MDP
,
policy_evaluation
# _________________________________________
# 22.2 Passive Reinforcement Learning
# 22.2.1 Direct utility estimation
class
PassiveDUEAgent
:
"""
Passive (non-learning) agent that uses direct utility estimation
on a given MDP and policy.
import sys
from mdp4e import sequential_decision_7x6_environment
north = (0, 1)
south = (0,-1)
west = (-1, 0)
east = (1, 0)
policy = {(0, 2): east, (1, 2): east, (2, 2): east, (3, 2): None, (0, 1): north, (2, 1): north,
(3, 1): None, (0, 0): north, (1, 0): west, (2, 0): west, (3, 0): west,}
agent = PassiveDUEAgent(policy, sequential_decision_environment)
for i in range(200):
run_single_trial(agent,sequential_decision_environment)
agent.estimate_U()
agent.U[(0, 0)] > 0.2
True
"""
def
__init__
(
self
,
pi
,
mdp
):
self
.
pi
=
pi
self
.
mdp
=
mdp
self
.
U
=
{}
self
.
s
=
None
self
.
a
=
None
self
.
s_history
=
[]
self
.
r_history
=
[]
self
.
init
=
mdp
.
init
def
__call__
(
self
,
percept
):
s1
,
r1
=
percept
self
.
s_history
.
append
(
s1
)
self
.
r_history
.
append
(
r1
)
##
##
if
s1
in
self
.
mdp
.
terminals
:
self
.
s
=
self
.
a
=
None
else
:
self
.
s
,
self
.
a
=
s1
,
self
.
pi
[
s1
]
return
self
.
a
def
estimate_U
(
self
):
# this function can be called only if the MDP has reached a terminal state
# it will also reset the mdp history
assert
self
.
a
is
None
,
'MDP is not in terminal state'
assert
len
(
self
.
s_history
)
==
len
(
self
.
r_history
)
# calculating the utilities based on the current iteration
U2
=
{
s
: []
for
s
in
set
(
self
.
s_history
)}
for
i
in
range
(
len
(
self
.
s_history
)):
s
=
self
.
s_history
[
i
]
U2
[
s
]
+=
[
sum
(
self
.
r_history
[
i
:])]
U2
=
{
k
:
sum
(
v
)
/
max
(
len
(
v
),
1
)
for
k
,
v
in
U2
.
items
()}
# resetting history
self
.
s_history
,
self
.
r_history
=
[], []
# setting the new utilities to the average of the previous
# iteration and this one
for
k
in
U2
.
keys
():
if
k
in
self
.
U
.
keys
():
self
.
U
[
k
]
=
(
self
.
U
[
k
]
+
U2
[
k
])
/
2
else
:
self
.
U
[
k
]
=
U2
[
k
]
return
self
.
U
def
update_state
(
self
,
percept
):
"""To be overridden in most cases. The default case
assumes the percept to be of type (state, reward)"""
return
percept
def
print_U
(
self
):
sorted_dict
=
dict
(
sorted
(
self
.
U
.
items
()))
print
(
'
\n
'
.
join
([
str
(
k
)
+
':'
+
str
(
v
)
for
k
,
v
in
sorted_dict
.
items
()]))
return
# 22.2.2 Adaptive dynamic programming
class
PassiveADPAgent
:
"""
[Figure 22.2]
Passive (non-learning) agent that uses adaptive dynamic programming
on a given MDP and policy.
import sys
from mdp import sequential_decision_7x6_environment
north = (0, 1)
south = (0,-1)
west = (-1, 0)
east = (1, 0)
policy = {(0, 2): east, (1, 2): east, (2, 2): east, (3, 2): None, (0, 1): north, (2, 1): north,
(3, 1): None, (0, 0): north, (1, 0): west, (2, 0): west, (3, 0): west,}
agent = PassiveADPAgent(policy, sequential_decision_environment)
for i in range(100):
run_single_trial(agent,sequential_decision_environment)
agent.U[(0, 0)] > 0.2
True
agent.U[(0, 1)] > 0.2
True
"""
class
ModelMDP
(
MDP
):
"""Class for implementing modified Version of input MDP with
an editable transition model P and a custom function T."""
def
__init__
(
self
,
init
,
actlist
,
terminals
,
gamma
,
states
):
super
().
__init__
(
init
,
actlist
,
terminals
,
states
=
states
,
gamma
=
gamma
)
nested_dict
=
lambda
:
defaultdict
(
nested_dict
)
# StackOverflow:whats-the-best-way-to-initialize-a-dict-of-dicts-in-python
self
.
P
=
nested_dict
()
def
T
(
self
,
s
,
a
):
"""Return a list of tuples with probabilities for states
based on the learnt model P."""
return
[(
prob
,
res
)
for
(
res
,
prob
)
in
self
.
P
[(
s
,
a
)].
items
()]
def
__init__
(
self
,
pi
,
mdp
):
self
.
pi
=
pi
self
.
mdp
=
PassiveADPAgent
.
ModelMDP
(
mdp
.
init
,
mdp
.
actlist
,
mdp
.
terminals
,
mdp
.
gamma
,
mdp
.
states
)
self
.
U
=
{}
self
.
Nsa
=
defaultdict
(
int
)
self
.
Ns1_sa
=
defaultdict
(
int
)
self
.
s
=
None
self
.
a
=
None
self
.
visited
=
set
()
# keeping track of visited states
def
__call__
(
self
,
percept
):
s1
,
r1
=
percept
mdp
=
self
.
mdp
R
,
P
,
terminals
,
pi
=
mdp
.
reward
,
mdp
.
P
,
mdp
.
terminals
,
self
.
pi
s
,
a
,
Nsa
,
Ns1_sa
,
U
=
self
.
s
,
self
.
a
,
self
.
Nsa
,
self
.
Ns1_sa
,
self
.
U
if
s1
not
in
self
.
visited
:
# Reward is only known for visited state.
U
[
s1
]
=
R
[
s1
]
=
r1
self
.
visited
.
add
(
s1
)
if
s
is
not
None
:
Nsa
[(
s
,
a
)]
+=
1
Ns1_sa
[(
s1
,
s
,
a
)]
+=
1
# for each t such that Ns′|sa [t, s, a] is nonzero
for
t
in
[
res
for
(
res
,
state
,
act
),
freq
in
Ns1_sa
.
items
()
if
(
state
,
act
)
==
(
s
,
a
)
and
freq
!=
0
]:
P
[(
s
,
a
)][
t
]
=
Ns1_sa
[(
t
,
s
,
a
)]
/
Nsa
[(
s
,
a
)]
self
.
U
=
policy_evaluation
(
pi
,
U
,
mdp
)
##
##
self
.
Nsa
,
self
.
Ns1_sa
=
Nsa
,
Ns1_sa
if
s1
in
terminals
:
self
.
s
=
self
.
a
=
None
else
:
self
.
s
,
self
.
a
=
s1
,
self
.
pi
[
s1
]
return
self
.
a
def
update_state
(
self
,
percept
):
"""To be overridden in most cases. The default case
assumes the percept to be of type (state, reward)."""
return
percept
# 22.2.3 Temporal-difference learning
class
PassiveTDAgent
:
"""
[Figure 22.4]
The abstract class for a Passive (non-learning) agent that uses
temporal differences to learn utility estimates. Override update_state
method to convert percept to state and reward. The mdp being provided
should be an instance of a subclass of the MDP Class.
import sys
from mdp import sequential_decision_environment
north = (0, 1)
south = (0,-1)
west = (-1, 0)
east = (1, 0)
policy = {(0, 2): east, (1, 2): east, (2, 2): east, (3, 2): None, (0, 1): north, (2, 1): north,
(3, 1): None, (0, 0): north, (1, 0): west, (2, 0): west, (3, 0): west,}
agent = PassiveTDAgent(policy, sequential_decision_environment, alpha=lambda n: 60./(59+n))
for i in range(200):
run_single_trial(agent,sequential_decision_environment)
agent.U[(0, 0)] > 0.2
True
agent.U[(0, 1)] > 0.2
True
"""
def
__init__
(
self
,
pi
,
mdp
,
alpha
=
None
):
self
.
pi
=
pi
self
.
U
=
{
s
:
0.
for
s
in
mdp
.
states
}
self
.
Ns
=
{
s
:
0
for
s
in
mdp
.
states
}
self
.
s
=
None
self
.
a
=
None
self
.
r
=
None
self
.
gamma
=
mdp
.
gamma
self
.
terminals
=
mdp
.
terminals
if
alpha
:
self
.
alpha
=
alpha
else
:
self
.
alpha
=
lambda
n
:
1
/
(
1
+
n
)
# udacity video
def
__call__
(
self
,
percept
):
s1
,
r1
=
self
.
update_state
(
percept
)
pi
,
U
,
Ns
,
s
,
r
=
self
.
pi
,
self
.
U
,
self
.
Ns
,
self
.
s
,
self
.
r
alpha
,
gamma
,
terminals
=
self
.
alpha
,
self
.
gamma
,
self
.
terminals
if
not
Ns
[
s1
]:
U
[
s1
]
=
r1
if
s
is
not
None
:
Ns
[
s
]
+=
1
U
[
s
]
+=
alpha
(
Ns
[
s
])
*
(
r
+
gamma
*
U
[
s1
]
-
U
[
s
])
if
s1
in
terminals
:
self
.
s
=
self
.
a
=
self
.
r
=
None
else
:
self
.
s
,
self
.
a
,
self
.
r
=
s1
,
pi
[
s1
],
r1
return
self
.
a
def
update_state
(
self
,
percept
):
"""To be overridden in most cases. The default case
assumes the percept to be of type (state, reward)."""
return
percept
def
run_single_trial
(
agent_program
,
mdp
):
"""Execute trial for given agent_program
and mdp. mdp should be an instance of subclass
of mdp.MDP """
def
take_single_action
(
mdp
,
s
,
a
):
"""
Select outcome of taking action a
in state s. Weighted Sampling.
"""
x
=
random
.
uniform
(
0
,
1
)
cumulative_probability
=
0.0
for
probability_state
in
mdp
.
T
(
s
,
a
):
probability
,
state
=
probability_state
cumulative_probability
+=
probability
if
x
<
cumulative_probability
:
break
return
state
current_state
=
mdp
.
init
while
True
:
current_reward
=
mdp
.
R
(
current_state
)
percept
=
(
current_state
,
current_reward
)
next_action
=
agent_program
(
percept
)
if
next_action
is
None
:
break
current_state
=
take_single_action
(
mdp
,
current_state
,
next_action
)
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