How to poll input for a gui in libgdx?

Trust me look into Scene2D. It handles everything input related for you. You can even do timed based actions on it, which are very nice. Its also built into libGDX. Truuuuust me its super easy once you get the hang of it. Honestly, I now write everything in Scene2D.

If your having issues getting started with it, Heres a little sample code for you

 Stage stage;
    ImageButton title; //(there are several types of these, even just simply Image)
    InputListener titleListen; //(also several variants)


 ///----------------------------------------
    //init phase
            stage = new Stage();
            stage.setViewport(Gdx.graphics.getWidth(), Gdx.graphics.getHeight(), false);
            Gdx.input.setInputProcessor(stage); //important


            titleListen = new InputListener(){
    //many different types of inputs to override
                @Override
                public boolean touchDown(InputEvent event, float x, float y,
                        int pointer, int button) {
                    //something
                    return super.touchDown(event, x, y, pointer, button);
                }

            };




    ImageButtonStyle style = new ImageButtonStyle();
            style.up = new TextureRegionDrawable(assets.title); //has to be a textureregion
            style.down = new TextureRegionDrawable(assets.title);
            title = new ImageButton(style);
            title.setSize(title.getWidth()*assets.scaleX, title.getHeight()*assets.scaleY);
            title.setPosition(whereever);
            stage.addActor(title);//adds it to the Scene
            play.addListener(titleListen); //adds the listener

  ///----------------------------------------  
    //game loop
//
//
//
    stage.act(delta); //updates Scene and grabs inputs

    stage.draw(); //draws Scene