Effective optimization is essential for interactive systems to provide a satisfactory user experience. However, it is often challenging to find an objective to optimize for. Generally, such objectives are manually crafted and rarely capture complex user needs in an accurate manner. We propose an approach that infers the objective directly from observed user interactions. These inferences can be made regardless of prior knowledge and across different types of user behavior. We introduce interactive system optimization, a novel algorithm that uses these inferred objectives for optimization. Our main contribution is a new general principled approach to optimizing interactive systems using data-driven objectives. We demonstrate the high effectiveness of interactive system optimization over several simulations.