Michael Kearns

Michael Kearns, Aaron Roth, Emily Ryu

We study a distributed learning problem in which learning agents are embedded in a directed acyclic graph (DAG). There is a fixed and arbitrary distribution over feature/label pairs, and each agent or vertex in the graph is able to directly observe only a subset of the features -- potentially a different subset for every agent. The agents learn sequentially in some order consistent with a topological sort of the DAG, committing to a model mapping observations to predictions of the real-valued label. Each agent observes the predictions of their parents in the DAG, and trains their model using both the features of the instance that they directly observe, and the predictions of their parents as additional features. We ask when this process is sufficient to achieve \emph{information aggregation}, in the sense that some agent in the DAG is able to learn a model whose error is competitive with the best model that could have been learned (in some hypothesis class) with direct access to \emph{all} features, despite the fact that no single agent in the network has such access. We give upper and lower bounds for this problem for both linear and general hypothesis classes. Our results identify the \emph{depth} of the DAG as the key parameter: information aggregation can occur over sufficiently long paths in the DAG, assuming that all of the relevant features are well represented along the path, and there are distributions over which information aggregation cannot occur even in the linear case, and even in arbitrarily large DAGs that do not have sufficient depth (such as a hub-and-spokes topology in which the spoke vertices collectively see all the features). We complement our theoretical results with a comprehensive set of experiments.

Shahin Jabbari, Matthew Joseph, Michael Kearns et al.

We initiate the study of fairness in reinforcement learning, where the actions of a learning algorithm may affect its environment and future rewards. Our fairness constraint requires that an algorithm never prefers one action over another if the long-term (discounted) reward of choosing the latter action is higher. Our first result is negative: despite the fact that fairness is consistent with the optimal policy, any learning algorithm satisfying fairness must take time exponential in the number of states to achieve non-trivial approximation to the optimal policy. We then provide a provably fair polynomial time algorithm under an approximate notion of fairness, thus establishing an exponential gap between exact and approximate fairness

Matthew Joseph, Michael Kearns, Jamie Morgenstern et al.

We study fairness in linear bandit problems. Starting from the notion of meritocratic fairness introduced in Joseph et al. [2016], we carry out a more refined analysis of a more general problem, achieving better performance guarantees with fewer modelling assumptions on the number and structure of available choices as well as the number selected. We also analyze the previously-unstudied question of fairness in infinite linear bandit problems, obtaining instance-dependent regret upper bounds as well as lower bounds demonstrating that this instance-dependence is necessary. The result is a framework for meritocratic fairness in an online linear setting that is substantially more powerful, general, and realistic than the current state of the art.