In Euclidean space, OCO boasts a robust theoretical foundation and numerous real-world applications, such as online load balancing (Molinaro, 2017), optimal control (Li et al., 2019), revenue maximization (Lin et al., 2019), and portfolio management (Jézéquel et al., 2022).

We establish upper bounds on the regrets of the problem with respect to time horizon, manifold curvature, and manifold dimension.

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

The result is aO(D T) regret bound that holds uniformly for all comparatorsu X.

We study the problem of learning an optimal regression function subject to a fairness constraint. It requires that, conditionally on the sensitive feature, the distribution of the function output remains the same. This constraint naturally extends the notion of demographic parity, often used in classification, to the regression setting. We tackle this problem by leveraging on a proxy-discretized version, for which we derive an explicit expression of the optimal fair predictor. This result naturally suggests a two stage approach, in which we first estimate the (unconstrained) regression function from a set of labeled data and then we recalibrate it with another set of unlabeled data.

We additionally assume that the agent cannot interact with the environment but has access to the action-labeled transition data collected by some agents with unknown qualities.