We consider sequential decision problems where a first action is made prior to seeing any uncertainty (“here-and-now” optimization variable) and then, after uncertainty arrives, one makes a second corrective action that can depend on the observed uncertainty value (“wait-and-see” optimization variable), which is followed by the arrival of yet another uncertain input that closes the process. Given a sample of observations of the uncertainties, we assume one makes a cautious selection of the “here-and-now” and wait-and-see” actions that guards against the worst-case scenarios and asks for the risk that this actions will meet a shortfall in a new out-of-sample case so that the performance will worsen as compared to the expectation constructed from the observations. We present sample complexity results for this setup based on new compression schemes and discuss various extensions and the difficulties therein.