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By Corollary 4.3, we can expect that the time
needed for convergence decreases by increasing the gain factor
. Indeed, Figure 6 shows that an optimal
exists. At higher gain factors, the discretization
introduces instabilities: The SDS ``overshoots'' within
discretization domains. Therefore performance quickly deteriorates
for large values. Finer discretization and/or more
frequent observations are needed to improve performance: for
larger values the update rate needs to be increased.
Figure 6:
Choosing an Optimal Feedback Gain.
The figure demonstrates that an optimal feedback gain exists
for SDS. Because of the stochastic nature of the process,
results depend on random factors. Therefore we calculated every result
for lower values 3 times with different random seeds.
In experiments with coarser discretizations, RL was able to
learn the task only for nonzero values.
