Database Reference
In-Depth Information
4.2 Multiple Recommendations
So far, we have been assuming that there is only a single recommendation
a
. REs,
however, generally recommend more than one product. We therefore now turn to
the case of multiple (or composite) recommendations, i.e.,
a ¼ a
1
,
ð
,
a
k
Þ
...
is a recommendation composed of
k
single recommendations (Fig.
4.3
).
From the point of the reinforcement learni
ng
theory as presented in Chap.
3
,
we can consider composite recommendations
a
as single actions in absolute the
same way as we did it with our single recommendations
a.
The problems which we
are facing are of rather computational nature since the number of admissible actions
a
in a state
s
may be huge and in general we are no more able to process all actions,
e.g., for calculating the policy. However, we will solve this problem step by step.
First, we notice that due to Assumption 4.2, we do not need to care about
multiple recommendations in the transition reward, i.e.,
r
ss
0
¼ r
ss
0
:
Much more demanding is the problem of the transition probabilities. We will
introduce
t
wo approaches on how transition probabilities for multiple recommen-
dations
p
ss
0
can be expressed through transition probabilities of single recommen-
dations
p
ss
0
(the latter will be studied in the next chapter).
We firstly make the following assumption, which is usual for statistics:
Assumption 4.3 (Multiple re
co
mmendation probability property): For
the multiple recommendation
a
, the transition probabilities of the single
recommendations
p
a
i
ss
0
can be considered as stochastically independent.
That means we assume that recommendations are not mutually cannibalistic.
This is a reasonable assumption.
4.2.1 Linear Approach
Based on Assumption 4.3, the following a
pp
roach is suitable: the transition
probability for multiple recommendations
p
ss
0
is equal to the average of the
a
1
a
2
a
3
a
n
−2
a
n
−1
s
1
s
2
s
3
s
n
−1
s
n
s
A
Fig. 4.3 Sequence of products and multiple recommendations as states and actions
