Our starting point is the traditional online learning model. In this setting a learner makes a series of decisions, receives a loss after each decision, and aims to achieve a total loss which is nearly as low as if they had chosen the best fixed decision-making strategy in hindsight.
We extend this model by introducing a set of users U. Each of the learner’s decisions is made on behalf of a particular user u ∈ U, and u reports the loss they incur from the decision. We assume that there is some (unknown ) set of “honest” users H ⊂ U, who report their losses honestly, while the other users may behave adversarially. Our goal is to ensure that the total loss incurred by users in H is nearly as small as if all users in H had used the single best fixed decision-making strategy in hindsight. We say that an algorithm is manipulation-resistant if it achieves a bound of this form.
This dissertation proposes and analyzes manipulation-resistant algorithms for prediction with expert advice, contextual bandits, and collaborative filtering. These algorithms guarantee that the honest users perform nearly as well as if they had known each others’ identities in advance, pooled all of their data, and then used a traditional learning algorithm. This bounds the total amount of damage that can be done per manipulative user. More significantly, we give bounds that can be considerably smaller in the realistic setting where the users are vertices of a graph (such as a social graph) with disproportionately few edges between honest and manipulative users.
As a key technical ingredient, we introduce the problem of online local learning, and propose a novel semidefinite programming algorithm for this problem. This algorithm allows us to effectively perform online learning over the exponentially large space of all possible sets H ⊂ U, and as a side-effect provides the first asymptotically optimal algorithm for online max cut.