This story says Arnold Schwarzenegger is considering running for U.S. Senate in 2018 as an independent. If he does that, his own top-two law will not permit him to have the ballot label “independent”. The law, which he backed with all his resources, says independents are on the ballot as “party preference: none.”
The California U.S. Senate seat up in 2018 is held by U.S. Senator Dianne Feinstein, who was born in 1933 and will therefore be age 85 in 2018. She has not said whether she intends to run for re-election in 2018 or not.
UPDATE: Per comments on this article, Schwarzenegger has announced he will not run.