Coordination of Communication in Robot Teams by Reinforcement Learning - Foundations on Natural and Artificial Computation - page 161

P opulation s uccesses v s . round. 1 0 robots 2x2 Populati o n succes s es vs. round. 10 ro b ots 3x3

100

140

Maximum succcess Maximum succcess

80 120

100

60

80

40 60

40

20

20

0 0

0 2 4 6 8 10 12 0 2 4 6 8 10 12 14

Round Round

(a) 2 × 2 lexicon (MS = 90) (b) 3 × 3 lexicon (MS = 135)

Populati o n succes s es vs. ro u nd. 10 ro b ots 4x4 Population successes vs. r ound. 10 robots 5 x5

200 250

Maximum succcess Maximum succcess

200

150

150

100

100

50

50

0 0

0 2 4 6 8 10 12 14 0 5 10 15

Round Round

(c) 4 × 4 lexicon (MS = 180) (d) 5 × 5 lexicon (MS = 225)

Fig. 5. Convergence to a Saussurean communication system with different lexicon sizes
for the case of 10 robots teams. In these graphs the number of round is displayed on
the horizontal axis and the vertical axis is for the number of success. Maximum success
(MS) is indicated in each graph.

In Fig. 4 and Fig. 5 we present some cases of learning curves displaying the
convergence results when consensus is achieved. In all cases the maximum success
per round (MS) is calculated using the formula:

N · ( N − 1)

MS = · n (6)

2

where N is the number of robots, and n is the number of meanings. Thus,
N· ( N− 1)
2

is the number of encounters and N· ( N− 1)
2

n is the number of communi-
cations per round. Each communication success is counted once and at the end
of the round it is verified if all communications were successful (i.e. number of
successes is equal to MS). In case this happens for three times we consider that
the system has achieved the consensus to a Saussurean system.
In the experiments reported in this paper and carried out under the reinforce-
ment learning paradigm, most of the cases of successful convergence to to an
optimal Saussurean communication system happened before the fiftieth round.

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