We propose to approximate two-stage distributionally robust programs with binary recourse
decisions by their associated K-adaptability problems, which pre-select K candidate secondstage
policies here-and-now and implement the best of these policies once the uncertain parameters
have been observed. We analyze the approximation quality and the computational
complexity of the K-adaptability problem, and we derive explicit mixed-integer linear programming
reformulations. We also provide efficient procedures for bounding the probabilities with
which each of the K second-stage policies is selected.