TL;DR
- Pedaling in the introduction is up to the performer.
- Pedaling for the remainder of the piece follows the pattern set in the first markings.
The first three pedal markings are there to set the pattern for the rest of the piece. The intention is that one continues to pedal each half-measure. Exceptions would be left up to the experience and musical intention of the performer.
I also own a Henle edition of this Nocturne, which includes two versions of the piece: the one posted in the question, and a second one with no pedal markings at all. The reason for the two versions is that there is no known copy in Chopin's handwriting, and there are two different manuscripts by different engravers, both of whom, it seems, Henle considers reliable sources, plus the Polish First Edition (PFE).
The sources for this Nocturne are available at the Online Chopin Variorum EditionOnline Chopin Variorum Edition. In the list of works, look for "Lento con gran espressione". Of the three that show the first measures, none have pedal markings in the introduction, and only PFE has pedal marks in the first measures of the main melody. Interestingly, they're slightly different than the Henle pedaling in that the third pedal mark extends for the entire measure rather than the half measure.
Since none of the sources indicate pedaling in the intro measures, that is left up to the interpreter.