So, what would you play in the given position? Here are some variants
1. h4, pushing the passed pawn
1. a3, blocking the Black pawn from advancing too much
1. Re1 or Re2, to defend against the threats which appear after Black moves Rb8
1. c4
1. maybe other move?
Here is what I think:
White is a pawn up and Black's pawn structure is shattered, so White should play for a win. At this point, Black has only one weekness, the pawn on g3 which is very hard to defend (his rook must permanently stay on the g file in order to guard this pawn). In fact, Black is ready to give up the second pawn on g3, hoping to get counter-chances from the activity of his rook, once it will occupy the b column. Note that, even if White will be two pawns up on the king side, advancing them will take some long time. At this moment, White's rook is quite restrained and in fact it is doing almost nothing.
Of all the candidate moves, 1. a3 is the worst, in fact it just sets up two targets for the Black rook, a3 and c3. 1. Re1 or Re2 is somehow passive, it tries to defend everything when the Black rook comes on the b file. White's hope is that he will be able eventually to advance his pawns on the kingside. In the actual game (with about one minute thinking time left), White played the normal move 1. Re2 and could not achieve more than a draw.
1. c4 - I think this is definitely the move to go. This temporary pawn sacrifice immediately turns Black's pawns on c6 and d5 into weeknesses, also giving the white rook plenty of space. Note also that in fact White gets to eat two Black pawns, for instance
1. c4 dxc4 2. Rc5 Ke6 3. Rxc4 Kd5 4. Rxa4 If 2. ...Rc8 3. d5 and Black is even worse.