Motivated by the recent popularity of machine learning training services, we introduce a contract design problem in which a provider sells a service that results in an outcome of uncertain quality for the buyer. The seller has a set of actions that lead to different distributions over outcomes. We focus on a setting in which the seller has the ability to commit to an action and the buyer is free to accept or reject the outcome after seeing its realized quality. Our model is related to Mussa and Rosen's classic paper on selling products of differing qualities and monopolist lottery pricing, as well as recent work on selling hidden actions.

We study a repeated persuasion setting between a sender and a receiver, where at each time t, the sender shares information about a payoff-relevant state with the receiver. The state at each time t is drawn independently and identically from an unknown distribution, and subsequent to receiving information about it, the receiver (myopically) chooses an action from a finite set. The sender seeks to persuade the receiver into choosing actions that are aligned with her preference by selectively sharing information about the state. In contrast to the standard persuasion setting, we focus on the case where neither the sender nor the receiver knows the distribution of the payoff relevant state. Instead, the sender learns this distribution over time by observing the state realizations. We adopt the assumption common in the literature on Bayesian persuasion that at each time period, prior to observing the realized state in that period, the sender commits to a signaling mechanism that maps each state to a possibly random action recommendation. Subsequent to the state observation, the sender recommends an action as per the chosen signaling mechanism.