The duel between the two Masters of the Force is great and I'd like to express my opinion about the duel.
Some Fans say Palpatine defeated Yoda and that's the why Yoda went to hiding: I don't think so and I'll explain why.

1. Their first "contest"
Palpatine uses Force Lightnings against Yoda and the Jedi Master is pushed away but after few seconds Yoda rises and pushed the Emperor away too, Palpatine is surprised and attempt to escape, Yoda bocks him and the ignite their Lightsaber: it's clear this first contest is draw.

2. The Lightsaber duel

Both of them fight very well and their fight continues in the Senate and it doesn't seem the Emperor is at advantage: Yoda and Palpatine attack and defend with a great mastery; at a certain point Palpatine stops using his lightsaber and starts launching chambers to Yoda who dodges them all and pushes one of them back to Palpatine who fall to an othe chamber: It' clear Palpatine was in difficoulty here and Yoda has shown to be very powerful

3. Force lightnings

At this point Yoda reaches Palpatine who unleashes Force Lightnigs:Yoda blocks them and the Emperor is very in trouble(look at his expression) then Yoda deflecs them back to him but unfortunatly the "counterblow" makes fall the Jedi master too and he doesn't find a anything to grip and fall.

Yoda failed in his mission , kill the Emperor , but he didn't lose the duel he was unluky because at this point he wasn't able to return back and fight Palpatine: that's the why he went to exyle bucause he failed to kill the Sith Lord.
If Yoda didn't won the duel neither do Palpatine