A number of gradient-based bilevel algorithms have been proposed via AIDand ITD-based hypergradient approximations. For example, AID-based hypergradient computation [4, 33, 10, 11, 19] estimates the Hessian-inverse-vector product by solving a linear system with an efficient iterative algorithm. ITD-based hypergradient computation [31, 8, 9, 6, 35, 17] involves a backpropagation over the inner-loop gradient-based optimization path. Convergence rate of AIDand ITD-based bilevel methods has been studied recently. For example, [10, 19] and [19, 17] analyzed the convergence rate and complexity of AIDand ITD-based bilevel algorithms, respectively.

We introduce the study of fairness in multi-armed bandit problems. Our fairness definition demands that, given a pool of applicants, a worse applicant is never favored over a better one, despite a learning algorithm's uncertainty over the true payoffs. In the classic stochastic bandits problem we provide a provably fair algorithm based on "chained" confidence intervals, and prove a cumulative regret bound with a cubic dependence on the number of arms. We further show that any fair algorithm must have such a dependence, providing a strong separation between fair and unfair learning that extends to the general contextual case. In the general contextual case, we prove a tight connection between fairness and the KWIK (Knows What It Knows) learning model: a KWIK algorithm for a class of functions can be transformed into a provably fair contextual bandit algorithm and vice versa. This tight connection allows us to provide a provably fair algorithm for the linear contextual bandit problem with a polynomial dependence on the dimension, and to show (for a different class of functions) a worst-case exponential gap in regret between fair and non-fair learning algorithms.

Neural Information Processing Systems http://nips.cc/

Weshowaseparation result: on one hand, if the query radiusλis strictly smaller than the adversary's perturbation budgetρ, then distribution-free robust learning is impossible for a widevarietyofconcept classes; ontheotherhand,thesettingλ=ρallowsusto develop robust ERM algorithms.

Query embedding (QE)--which aims to embed entities and first-order logical (FOL) queries inlow-dimensional spaces--has showngreatpowerinmulti-hop reasoningoverknowledgegraphs.

A major challenge is thus in designing sample-efficient agents that can transfer their existing knowledge to solve new tasks quickly.