In this study, we have proposed a novel technique to
employ sparse coding in transfer learning for
reinforcement learning. By applying the knowledge to the
bases of sparse coding dictionary matrix, we succeeded to
choose the correct knowledge that should be transferred
to new environment target tasks. We experimented the
proposed method on the 5 target tasks and confirmed that
the method provided jumpstart and reduced the total cell
costs. By the result of these experiments, our proposed
method was able to contribute significant improvement
on the effective online transfer learning for reinforcement
learning. However, as mentioned in section VII-E,
negative transfer happened on some cells of the target
task.
For future work, to solve this problem we would like to
reconsider the number of bases and the quality of the
dictionary, and then aim to improve the accuracy of
transfer learning. In concrete, we will increase the
number of source tasks to obtain a larger dictionary and
obtain a large number of high diversity bases in the
dictionary. On the other hand, we also have to take the
processing time into account. It will become unrealistic if
the number of bases becomes enormous. So, in practice
we have to limit the maximum number of bases. In this
point, to deal with this problem, we are going to take the
methods employed by prior studies such as [9] in our
study and aim to construct an ideal dictionary within the
upper limit of the number of bases.

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A Study on Efficient Transfer Learning for
Reinforcement Learning Using Sparse Coding
Midori Saito and Ichiro Kobayashi
Advanced Sciences, Graduate School of Humanities and Sciences, Ochanomizu University, Tokyo, Japan
Email: {saito.midori, koba}@is.ocha.ac.jp
Abstract—By applying the knowledge previously obtained
by reinforcement learning to new tasks, transfer learning
has been successful in achieving efficient learning, rather
than re-learning knowledge about action policies from
scratch. However, in the case of applying transfer learning
to reinforcement learning, it is not easy to determine which
and how much the obtained knowledge should be
transferred. With this background, in this study, we propose
a novel method that enables to decide the knowledge and to
determine the ratio of transference by adopting sparse
coding in transfer learning. The transferred knowledge is
represented as a linear combination of the accumulated
knowledge by means of sparse coding. In the experiments,
we have adopted colored mazes as tasks and confirmed that
our proposed method significantly improved in terms of
jumpstart and of the reduction of the total learning cost,
compared with normal Q-learning.
Index Terms—sparse coding, transfer learning,
reinforcement learning, maze
I. INTRODUCTION
In reinforcement learning [1], an agent explores a
target environment repeatedly, performing given tasks by
trial and error to obtain optimal action policies in the
environment. However, the way of learning requires quite
a number of random explores until satisfied action
policies are obtained, so this is regarded as a big problem
with the method [2]. To solve this problem, many
approaches have been studied to aim to reduce the
number of exploration steps. Among such approaches, it
has been reported that transfer learning is especially
useful and succeeds in achieving efficient reinforcement
learning by reusing the previously learned action policies
in similar environments in the target environment [3][4].
However, because the similarities among task
environments are not clearly defined in the framework of
transfer learning, the similarity is required to be
calculated in response to each task [5]. If the number of
the states of a task and the number of agents’ actions are
a quite a few, the information to be transferred shall be a
huge amount, and then the calculation shall be so much
complicated. With respect to this problem, in this paper,
we employ sparse coding to calculate the similarities
between the environments of a source task and a target
task, and determine which and how much action policies
Manuscript received June 11, 2015; revised October 2, 2015.
are transferred. By this, we aim to make possible to
efficiently transfer action policies to new target tasks.
II. RELATED STUDIES
This section presents the related studies to our study, in
particular, the ones focus on transfer learning employed
in reinforcement learning and also sparse coding
employed in transfer learning. First, as for the transfer
learning employed in reinforcement learning, it has been
successful in generalizing information across multiple
tasks. Even though between two different tasks,
transferring the knowledge an agent has learned in a
source task is useful in a target task [6]. Fernando et al. [3]
employed Policy Reuse as a technique to improve
transfer efficiency in reinforcement learning by reusing
similar policies leaned in a past. The technique improves
its exploration in target environments by probabilistically
including the exploitation of those past policies. Then,
they succeeded to improve the learning performance over
different strategies with policy reuse, and contributed
policy reuse as transfer learning among different domains
[4]. Trung et al. [7] proposed a method to transfer old
knowledge, and evaluated new options to see if they
worked better. They succeeded in achieving efficient and
online transfer, and improved jumpstart and faster
convergence to near optimum policy. Furthermore, they
proposed model-based reinforcement learning that
supports efficient online-learning of the relevant features
and introduced an online sparse coding learning
technique for feature selection in high-dimensional
spaces [8]. Then, they demonstrated practicality of their
proposed model in both simulated and real robotics
domains.
Next, as for sparse coding, sparse coding was
originally developed to achieve a good result in the field
of signal processing, i.e., audio and natural images. It can
approximately represent the input signal expressed by a
vector with the linear combination of a few bases of the
vector well [9]. For instance, in the field of image
processing, Kai et al. [10] presented a method for earning
image representations using a two-layer sparse coding
scheme. The algorithm provided excellent results for
hand-written digit recognition and object recognition, and
achieved to automatically learn the features of the target.
In this research, they proposed an approach that accounts
for high-order dependency among patterns in a local
image neighborhood. Then, as an example of applying
Journal of Automation and Control Engineering Vol. 4, No. 4, August 2016
©2016 Journal of Automation and Control Engineering
doi: 10.18178/joace.4.4.324-330
324
sparse coding to transfer learning, Haithman et al. [5][11]
proposed a novel transfer learning for reinforcement
learning method capable of autonomously creating an
inter-task mapping by using a novel combination of
sparse coding. They succeeded to show not only transfer
of information between similar tasks, but also between
two very different domains in their experiments. Then,
they illustrated that the learned inter-task mapping can be
successfully used to improve the performance of a
learned policy, reduce the learning times, and converge
faster to a near-optimal policy.
In this study, we propose a novel online transfer
method making use of sparse coding in reinforcement
learning, based on those state-of-the-art researches
mentioned above.
III. REINFORCEMENT LEARNING AND TRANSFER
LEARNING
A. Reinforcement Learning
The reinforcement learning [1] is a machine learning
method to obtain optimal action policies by making an
agent repeatedly search in a target environment. In
concrete, the learning process is shown as the following
three steps:
1. An agent observes the states of an environment.
2. An agent selects and performs an action among the
possible actions in the current environment.
3. The action performed at an environment is evaluated
by being given reward or a penalty.
The reinforcement learning is defined as a Markov
Decision Processes (MDPs), and its state is represented as
a tuple, . Here, S is a set of states; A is a set
of actions; P is the transition probability expressed as
P=Pr{st+1=s’ | st=s, at=a}; and R is reward given to an
agent from the environment. An agent's action policy is
expressed as π(s, a)=Pr{at=a | st=s}. The reinforcement
learning aims to acquire the optimal action policies that
maximize the total expectation value of the reward given
from an environment as in (1).
}|{}|{)( 1
0
ssrEssREsV tkt
k
k
tt
(1)
here, V
π
(s)is called state-value function for policyπ.
γ indicates the discount ratio.
B. Q-learning
We employ Q-learning [14] as a reinforcement
learning algorithm. It is a kind of Temporal Differential
learning, and aims to maximize the evaluation value of
actions, called Q-value. The equation for updating Q-
value is shown in (2).
Q(st,at ) =Q(st,at )+ a(r +g maxaQ(st+1,a) -Q(st,at )) (2)
here, Q(s,a)=E[R|st=s,at=a], called action-value function,
which expresses the value obtained from the action a at
the state s. αindicates the learning ratio and γ indicates
the discount ratio. In this study, we employ ε-greedy
algorithm in deciding agent's action. In the action
selection by ε-greedy algorithm, the actions are randomly
selected with the probability of ε, and are selected so as
maximum Q-value with the probability of 1-ε.
C. Transfer Learning
The transfer learning employed in the framework for
reinforcement learning aims to reduce the number of
random exploration in a new task. First, we obtain
knowledge as action policies or Q-values by executing
reinforcement learning in a source task, and then apply
the obtained knowledge to a target task. Thereby, the
efficiency of learning the target task will be improved,
even if the target task is not the same as the source task.
However, if the environment of the target task is
considerably different from that of the source task, the
transferred knowledge is useless at the target task. So, we
should correctly choose the knowledge to be transferred
in accordance with the situation of the target task.
Therefore, we introduce sparse coding into transfer
learning.
IV. SPARSE CODING
A. Sparse Coding
In this study, we propose a method to realize efficient
transfer learning in the framework for reinforcement
learning by introducing sparse coding [13]. Sparse coding
is a method of the signal processing. It selects the number
of the basis vectors as small as possible for a signal, and
expresses input signal with linear combination of the
basis vectors. We show an equation representing the idea
of sparse coding below.
y = Dx (3)
here, y indicates an input signal, D is a set of basis
vectors called dictionary, and x is an activation matrix
which indicates a set of coefficient corresponding to each
of the base. Like this, in sparse coding, y is represented in
two matrices, D and x. The objective function to be
optimized for sparse coding is defined in (4).
x* = minx
1
2
y - Dx
2
2
+ l x
1
(4)
here, the first right term of (4) indicates the term for
minimizing the square error between the original
information y and the restored information Dx, and the
second term is for regularization which provides a
constraint on deriving x in a sparse condition. λ is the
parameter for regularization. By (4), we obtain an optimal
sparse activation matrix x.
B. Sparse Coding for Transfer Learning
Now we explain an overview of how to apply sparse
coding to transfer learning. In the case of reusing the
knowledge, i.e., action policies, obtained by
reinforcement learning in a new target task environment,
the accuracy of transfer learning will be considerably
different depending on which pieces of knowledge are
chosen from a huge quantity of knowledge. Moreover,
only a part of the whole accumulated knowledge is used
to search an appropriate action policy for a target task in
short term, though a huge quantity of knowledge is
Journal of Automation and Control Engineering Vol. 4, No. 4, August 2016
©2016 Journal of Automation and Control Engineering 325
necessary for the whole transfer. Therefore, it is thought
that sparse coding works well in transfer learning by
regarding one piece of knowledge obtained in a source
task environment as one basic vector of dictionary matrix,
namely, all accumulated knowledge is regarded as a set
of basis vectors. Then, by regarding the state s observed
in a target task as input vector, it can be represented with
linear combination of knowledge in the dictionary matrix.
C. Proposed Method
As seen in Fig. 1, at first, in the target task, the costs of
the target cell and its surrounding 5-5 square cells are
observed and compiled as an input vector (step 1).
Secondary, sparse coding is applied to the input vector
with the dictionary built by source task, and an activation
matrix is calculated (step 2). Then, the Q-value obtained
in the source tasks which corresponds to the index of the
non-zero elements of the activation matrix is multiplied
with the value of the non-zero elements of the activation
matrix (step 3). Lastly, the Q-value calculated in step 3 is
returned to the current target cell (step4). In this way, in
the target task, by repeating the above 4 steps and
sequentially providing the Q-value obtained in the source
tasks as the value of the target cell, an efficient transfer
learning is achieved. The detail of this our proposed
method is described in section V.
Figure 1. Overview of proposed method.
V. EXPERIMENTS
A. Source Task
At first, in order to construct a dictionary by means of
sparse cording, we prepared 4 different source tasks (see,
Fig. 2).We adopted colored mazes as tasks in [14], these
mazes have 5 different cell colors in themselves, and the
size of all 4 source tasks are the same, the height is 30
cells and the width is 30 cells. Each color has its own
cost: i.e., white: 0.0, blue : -2.0, green : -3.0, red : -5.0,
and black : -10.0. We regard the cell costs as the reward,
and +100 is given when an agent arrives at goal. In each
cell, the agent can select an action among 4 actions, i.e.,
moving 1 cell in either up, down, right, or left direction.
The task we adopt in our experiments is moving to the
goal at the right corner of the bottom of the maze from
the start point at the left corner of the top of the maze. As
for the parameter settings for Q-learning, α is set as 0.1
and γ is set as 0.9. Moreover, as the algorithm of
selecting actions, we employ ε-greedy algorithm in which
it takes random action with 20% probability and the
action based on maximum Q-value with 80% probability,
aiming that the agent can learn action policies to find the
optimal route to the goal with total cell costs and total
steps as low as possible. With these settings, the agent
executed Q-learning and learned the optimal route to the
goal. We took reinforcement learning for 1000000
episodes repeatedly on each maze, and after 1000000
episodes simulation, we recorded the information about
cost and Q-value of each cell as the knowledge to be used
for transfer learning.
B. Construction of a Dictionay Matrix
As mentioned in V-A, a dictionary matrix is
constructed based on the information obtained from the
result of 1000000 episodes Q-learning.
Figure 2. 4 different source tasks.
We regard the information in 5-5 square cell costs of
the source tasks as a basis vector in a dictionary and
extract possible information in 5-5 square cells from 30-
30 square cells. By this, the number of basis vectors in
each task is 676 (=26*26) and then becomes 2704 in total
(=676*4 tasks). So, the size of the dictionary matrix
becomes 25*2704. The image of how to make a
dictionary is shown in Fig. 3.
C. Target Task
As for target tasks, we use the same size square
colored mazes as the source tasks. As well as the source
tasks, the start point is at the left corner of the top of the
maze and the goal point is at the right corner of the
bottom of the maze (Fig. 4). As explained at step 1 in IV-
C, the agent obtained the cell cost data of the currently
exploring cell and its 5-5 square surroundings, and
regarded as an input vector. Then, sparse coding chose
some environment in 4 source tasks (the bases of the
dictionary shown in V-B) that are similar to the target 5-5
square cell cost information, and calculated how similar
those chosen environment (the results of the activations).
Next, we extracted the index of non-zero activations from
Journal of Automation and Control Engineering Vol. 4, No. 4, August 2016
©2016 Journal of Automation and Control Engineering 326
the activation matrix, and the 5-5 cells’ Q-value data
(gained in V-A) corresponding to that index, is multiplied
by the corresponding activation values, and lastly took
these linear combination. In that calculated Q-value data,
the Q-value data for 4 action policies: up, down, right and
left, corresponding to the middle cell of 5-5 square was
extracted, and it returned to the target cell as its Q-value.
While exploring the target task, if it is the first time for
the agent to visit the cell, because there is no prior
knowledge about a proper action at the cell, Q-value is
transferred through the execution of sparse coding. On
the other hand, if the agent visits the cell more than twice,
normal Q-learning is applied to update the Q-value of the
cell because there already exists prior knowledge about
actions.
Figure 3.
How to construct a dictionary matrix.
D.
Experimental Settings
In
this paper, we examined our proposed method with
5 different target tasks (see,
Fig. 4).
In order to show the
effectiveness
of our proposed method, we employed a
normal Q-learning as a baseline method to compare.
The
Q-learning parameters of the proposed method and the
base line method are α=0.1,γ=0.9, and ε
=0.2 of ε-greedy.
We set the total value of the elements in the activation
matrix to be 10.0 for
a sparse coding setting. These
parameter settings are empirically decided.
Fig. 5 shows
the relation between bases in
the dictionary matrix and
the elements in the activation matrix
at a particular input
cell when the total value of the elements of the activation
matrix
changes in the range of [0,100].For example,
when
the total activation value gets 40
in horizontal axis, we
see that 3 bases in the dictionary are used to represent the
input and the sum of the activation values of those 3
bases gets 40.
Fig. 6 shows the result
that activation value
when the total value of activations
changed to 1, 10, and
50. As seen from this figure, a few bases contain non-
zero value in their activation, other bases have 0
activation value by
sparse coding.
Through these
experiments, we evaluated
2 points: how the proposed
method could reduce the total cell cost and supported
jumpstart which means the reduction
of number of steps
necessary to reach
the goal.
Figure 4. 5 different target tasks.
Value of total activations
V
al
u
e
o
f
e
ac
h
a
ct
iv
at
io
n
Figure 5. The trace of activations.
Number of bases
V
al
u
e
o
f
ac
ti
va
ti
o
n
s
o
f
ea
ch
b
as
e
Figure 6. The value of activations.
E. Result
Fig. 7-Fig. 11 represent the experimental results of the
number of total steps and the values of total cell costs
obtained in 5 target tasks. In the experiments, each task is
repeatedly performed 100 times. In all the figures, the red
lines indicate the proposed method and the blue lines are
normal Q-learning. And these figures show the number of
episodes in the horizontal-axis and the number of total
steps or the value of total cell costs in the vertical-axis.
Journal of Automation and Control Engineering Vol. 4, No. 4, August 2016
©2016 Journal of Automation and Control Engineering 327
Figure 7. The result of target task 1.
Figure 8. The result of target task 2.
Figure 9. The result of target task 3.
Figure 10. The result of target task 4.
Figure 11. The result of target task 5.
F. Discussions
Table I shows the number of total steps and total cell
costs when the agent first arrived at the goal in 5 target
tasks. As this table shows, the proposed method could
decrease the number of necessary steps taken to reach the
goal. We see clearly from the results that the jumpstart
was achieved. We also see that the total costs decreased.
On the whole, the proposed method, which transfers
the Q-values obtained in the source tasks to the target
task, was more efficiently than the normal Q-learning that
learns Q-value of the target task from scratch. However,
as seen in Fig. 7-Fig. 11, there are some points where the
proposed method did not work well than the normal Q-
learning, especially in task 3 and 5. As the reason for this,
it can be thought that the negative transfer has arisen at
some cells in the target task and then more steps were
necessary to get recovered from the problem. That also
led the value of total cell cost to be much worse.
Depending on task environment, there is some difference
among the effect of transfer via sparse coding. We have
verified the assumption that negative transfer happened in
the target tasks. As clear examples, we focus on the 61
st
episode that took the largest number of steps to reach the
goal and the 2
nd
episode that took the smallest number of
steps in target task 5. Fig. 12 shows how many times the
agent arrived at each cell of target task 5 in the 61
st
episode. In the figure, the horizontal-axis is the x-
coordinate of the target task5, the depth-axis is the y-
coordinate and vertical-axis is the number of steps at each
cell. We see that the top left corner of the x-y plane is the
start point and the front of bottom right corner is the goal
point. As this graph shows, there are many useless steps
observed at around the bottom left. Likewise, it is
observed that the number of steps increased around the
bottom left in 2
nd
episode, though the total number of
steps is considerably lower than that of 61
st
episode (see,
Fig. 13).
TABLE I. THE RESULT OF THE FIRST EPISODE
Task1 Task2 Task3 Task4 Task5
steps
proposed 208 196 480 166 506
Q-learinig 5728 7878 5910 5972 13238
costs
proposed -125 -196 -476 -157 -208
Q-learning -10522 -12391 -9783 -9516 -15016
Figure 12. Number of steps in 61st Episode of target task 5.
Figure 13.
Number of steps in 2nd
Episode of target task5
Among the steps each cell took, the number of steps of
the cell at (8, 28) in 61
st
episode took 516 steps, the
largest steps in the episode. Therefore, we investigated
which piece of knowledge was transferred to the cell at (8,
Journal of Automation and Control Engineering Vol. 4, No. 4, August 2016
©2016 Journal of Automation and Control Engineering 328
28). Fig. 14 shows knowledge transfer happened in the
cell at (8, 28) of target task 5. The left 5-5 square cell of
Fig. 14 indicates the cell cost, obtained when the agent
steps into the cell at (8, 28), which is used as input
information for sparse coding. In the case of the 5-5
square, we treat the cost of the bottom row as -100,
because of the out of search range. Depending on the
input information, sparse coding is executed. As the
result of execution of sparse coding, we confirmed that
100% of the Q-value of the cell at (23, 24) in source task
3 was transferred to the target cell. However, even though
compared the left target circumstance to the right source
circumstance, there is less similar between the two
environments. It can therefore be thought that the transfer
was influenced by the cost at the bottom row of the target
task. In addition, Fig. 15 shows a result of the case where
the input information for sparse coding does not include
the cost at the bottom row. Here, the figure shows the
case where knowledge is transferred to the cell at (10,6)
of the target task 5. As a result of this case, there were
several bases employed as the knowledge to be
transferred. Among the bases, the base of the cell at (23,
14) in the source task 1 had the largest transfer ratio,
which was about 55.8%. In this example, we see that the
transferred Q-value was successfully represented as linear
combination of the Q-values of several bases. To consider
the difference between these two transfers, because there
were lack of the bases which correspond to the out of
range, that led transfer accuracy to get worse. In this
study, we think if the bases including the out of range
cost, the influence by those bases might cause imbalance
knowledge transfer, so, we did not take those bases in the
dictionary. Thereby, we think the reason why knowledge
transfer did not work well at some points as the
dictionary was not well prepared.
Figure 14. Bad transfer.
Figure 15. Good transfer.
VI. CONCLUSIONS
REFERENCES
[1] R. S. Sutton and A. G. Barto, Reinforcement Learning: An
Introduction, The MIT Press, 1998.
[2] T. Takano, H. Takase, H. Kawanaka, and S. Tsuruoka, “A study
on selection method of transfer knowledge in same transition
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[3] F. Fernandez and M. Veloso, “Probabilistic policy reuse in a
reinforcement learning agent,” AAMAS’06, May 8–12, 2006.
[4] F. Fernández, J. García, and M. Veloso, “Probabilistic policy reuse
for inter-task transfer learning,” Robotics and Autonomous
Systems 58, pp. 866–871, 2010.
[5] H. B. Ammar, K. Tuyls, M. E. Taylor, K. Driessens, and G. Weiss,
“Reinforcement learning transfer via sparse coding,” in Proc. the
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[6] M. E. Taylor and P. Stone, “An introduction to inter-task transfer
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Journal of Automation and Control Engineering Vol. 4, No. 4, August 2016
©2016 Journal of Automation and Control Engineering 329
In this study, we have proposed a novel technique to
employ sparse coding in transfer learning for
reinforcement learning. By applying the knowledge to the
bases of sparse coding dictionary matrix, we succeeded to
choose the correct knowledge that should be transferred
to new environment target tasks. We experimented the
proposed method on the 5 target tasks and confirmed that
the method provided jumpstart and reduced the total cell
costs. By the result of these experiments, our proposed
method was able to contribute significant improvement
on the effective online transfer learning for reinforcement
learning. However, as mentioned in section VII-E,
negative transfer happened on some cells of the target
task.
For future work, to solve this problem we would like to
reconsider the number of bases and the quality of the
dictionary, and then aim to improve the accuracy of
transfer learning. In concrete, we will increase the
number of source tasks to obtain a larger dictionary and
obtain a large number of high diversity bases in the
dictionary. On the other hand, we also have to take the
processing time into account. It will become unrealistic if
the number of bases becomes enormous. So, in practice
we have to limit the maximum number of bases. In this
point, to deal with this problem, we are going to take the
methods employed by prior studies such as [9] in our
study and aim to construct an ideal dictionary within the
upper limit of the number of bases.
[12] B. A. Olshausen and D. J. Field, “Emergence of simple-cell
receptive field properties by learning a sparse code for natural
images,” Nature, vol. 381, pp. 607-609, 1996.
[13] A. Wilson, A. Fern, and P. Tadepalli, “Transfer learning in
sequential decision problems: a hierarchical bayesian approach,”
JMLR: Workshop and Conference Proceedings, vol. 27, pp. 217–
227, 2012.
[14] C. J. C. H. Watkins, “Learning from delayed rewards,” PhD thesis,
King’s College, Cambridge, UK, 1989．
Midori Saito (Aichi, Mar. 16th, 1991),
Master student at Advanced Sciences,
Graduated School of Humanities and
Sciences, Ochanomizu University. She
graduated from Dept. of Information
Sciences, Faculty of Sciences, Ochanomizu
University in 2013.
Ichiro Kobayashi
(Tokyo, Aug. 2nd, 1965),
2011-
Professor, Advanced Sciences,
Graduated School of Humanities and Sciences,
Ochanomizu University.
2003-2010 Associate
Professor, Advanced Sciences, Graduated
School of Humanities and Sciences,
Ochanomizu University.
1996-2003 Associate Professor, Faculty of
Economics, Hosei University.
1995 Assistant
Professor, Faculty of Economics, Hosei
University.
Journal of Automation and Control Engineering Vol. 4, No. 4, August 2016
©2016 Journal of Automation and Control Engineering 330

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