Stage stage = ... // Create stage
Button button = ... // Create button

// Stretch button out, then in, then out, etc.
Action stretchSequence = Actions.sequence(Actions.sizeBy(10, 0, 1), Actions.sizeBy(-10, 0, -1));
// Repeat that sequence indefinitely
button.addAction(Actions.repeat(RepeatAction.FOREVER, stretchSequence));

stage.addActor(button);

// Then in your render() method
stage.act();
stage.draw();