In this manuscript, we provide an online learning framework that will aim at distributing travel demand in a given transportation network resulting in a socially-optimal mobility system that travelers would be willing to accept. It is expected that connected and automated vehicles (CAVs) will gradually penetrate the market in ways that will improve safety and transportation efficiency over the next several years. However, we anticipate that efficient transportation and travel cost reduction might alter human travel behavior causing rebound effects, e.g., by improving effi-ciency, travel cost is decreased, hence willingness-to-travel is increased. The latter would increase overall vehicle miles traveled, which in turn might negate the benefits in terms of energy and travel time. Our aim is to develop a holistic and rigorous framework to capture the societal impact of CAVs and provide solutions that mitigate any potential rebound effects, e.g., increased vehicle miles traveled, increased travel demand, empty vehicle trips, while enhancing accessibility, safety, and equity in transportation.