Distributionally Robust Optimization for Sequential Decision Making

The distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust policy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we study distributionally robust MDPs where ambiguity sets for the uncertain parameters are of a format that can easily incorporate in its description the uncertainty's generalized moment as well as statistical distance information. In this way, we generalize existing works on distributionally robust MDP with generalized-moment-based and statistical-distance-based ambiguity sets to incorporate information from the former class such as moments and dispersions to the latter class that critically depends on empirical observations of the uncertain parameters. We show that, under this format of ambiguity sets, the resulting distributionally robust MDP remains tractable under mild technical conditions. To be more specific, a distributionally robust policy can be constructed by solving a sequence of one-stage convex optimization subproblems

RISK-AVERSE AND AMBIGUITY-AVERSE MARKOV DECISION PROCESSES

Ph.DDOCTOR OF PHILOSOPH

Fed+: A Unified Approach to Robust Personalized Federated Learning

We present a class of methods for robust, personalized federated learning, called Fed+, that unifies many federated learning algorithms. The principal advantage of this class of methods is to better accommodate the real-world characteristics found in federated training, such as the lack of IID data across parties, the need for robustness to outliers or stragglers, and the requirement to perform well on party-specific datasets. We achieve this through a problem formulation that allows the central server to employ robust ways of aggregating the local models while keeping the structure of local computation intact. Without making any statistical assumption on the degree of heterogeneity of local data across parties, we provide convergence guarantees for Fed+ for convex and non-convex loss functions and robust aggregation. The Fed+ theory is also equipped to handle heterogeneous computing environments including stragglers without additional assumptions; specifically, the convergence results cover the general setting where the number of local update steps across parties can vary. We demonstrate the benefits of Fed+ through extensive experiments across standard benchmark datasets as well as on a challenging real-world problem in financial portfolio management where the heterogeneity of party-level data can lead to training failure in standard federated learning approaches