<s>
Mountain	B-General_Concept
Car	I-General_Concept
,	O
a	O
standard	O
testing	O
domain	O
in	O
Reinforcement	O
learning	O
,	O
is	O
a	O
problem	O
in	O
which	O
an	O
under-powered	O
car	O
must	O
drive	O
up	O
a	O
steep	O
hill	O
.	O
</s>
<s>
The	O
mountain	B-General_Concept
car	I-General_Concept
problem	I-General_Concept
,	O
although	O
fairly	O
simple	O
,	O
is	O
commonly	O
applied	O
because	O
it	O
requires	O
a	O
reinforcement	O
learning	O
agent	O
to	O
learn	O
on	O
two	O
continuous	O
variables	O
:	O
position	O
and	O
velocity	O
.	O
</s>
<s>
The	O
mountain	B-General_Concept
car	I-General_Concept
problem	I-General_Concept
appeared	O
first	O
in	O
Andrew	O
Moore	O
's	O
PhD	O
Thesis	O
(	O
1990	O
)	O
.	O
</s>
<s>
Throughout	O
the	O
years	O
many	O
versions	O
of	O
the	O
problem	O
have	O
been	O
used	O
,	O
such	O
as	O
those	O
which	O
modify	O
the	O
reward	O
function	O
,	O
termination	O
condition	O
,	O
and/or	O
the	O
start	B-Architecture
state	I-Architecture
.	O
</s>
<s>
Q-learning	B-Algorithm
and	O
similar	O
techniques	O
for	O
mapping	O
discrete	O
states	O
to	O
discrete	O
actions	O
need	O
to	O
be	O
extended	O
to	O
be	O
able	O
to	O
deal	O
with	O
the	O
continuous	O
state	O
space	O
of	O
the	O
problem	O
.	O
</s>
<s>
Approaches	O
often	O
fall	O
into	O
one	O
of	O
two	O
categories	O
,	O
state	O
space	O
discretization	B-Algorithm
or	O
function	O
approximation	O
.	O
</s>
<s>
Tile	O
coding	O
can	O
be	O
used	O
to	O
improve	O
discretization	B-Algorithm
and	O
involves	O
continuous	O
variables	O
mapping	O
into	O
sets	O
of	O
buckets	O
offset	O
from	O
one	O
another	O
.	O
</s>
<s>
Function	O
approximation	O
is	O
another	O
way	O
to	O
solve	O
the	O
mountain	B-General_Concept
car	I-General_Concept
.	O
</s>
<s>
Unlike	O
the	O
step-wise	O
version	O
of	O
the	O
value	O
function	O
created	O
with	O
discretization	B-Algorithm
,	O
function	O
approximation	O
can	O
more	O
cleanly	O
estimate	O
the	O
true	O
smooth	O
function	O
of	O
the	O
mountain	B-General_Concept
car	I-General_Concept
domain	O
.	O
</s>
<s>
This	O
is	O
a	O
problem	O
for	O
naive	O
discretization	B-Algorithm
because	O
each	O
discrete	O
state	O
will	O
only	O
be	O
backed	O
up	O
once	O
,	O
taking	O
a	O
larger	O
number	O
of	O
episodes	O
to	O
learn	O
the	O
problem	O
.	O
</s>
<s>
Eligibility	O
traces	O
can	O
be	O
viewed	O
as	O
a	O
bridge	O
from	O
temporal	O
difference	O
learning	O
methods	O
to	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
.	O
</s>
<s>
The	O
mountain	B-General_Concept
car	I-General_Concept
problem	I-General_Concept
has	O
undergone	O
many	O
iterations	O
.	O
</s>
<s>
There	O
are	O
many	O
versions	O
of	O
the	O
mountain	B-General_Concept
car	I-General_Concept
which	O
deviate	O
in	O
different	O
ways	O
from	O
the	O
standard	O
model	O
.	O
</s>
<s>
Additionally	O
we	O
can	O
use	O
a	O
3D	O
mountain	B-General_Concept
car	I-General_Concept
with	O
a	O
4D	O
continuous	O
state	O
space	O
.	O
</s>
