Liouville PDE-based sliced-Wasserstein flow for fair regression

The sliced Wasserstein flow (SWF), a nonparametric and implicit generative gradient flow, is applied to fair regression. We have improved the SWF in a few aspects. First, the stochastic diffusive term from the Fokker-Planck equation-based Monte Carlo is transformed to Liouville partial differential equation (PDE)-based transport with density estimation, however, without the diffusive term. Now, the computation of the Wasserstein barycenter is approximated by the SWF barycenter with the prescription of Kantorovich potentials for the induced gradient flow to generate its samples. These two efforts improve the convergence in training and testing SWF and SWF barycenters with reduced variance. Applying the generative SWF barycenter for fair regression demonstrates competent profiles in the accuracy-fairness Pareto curves.

Meta-reinforcement learning with minimum attention

Minimum attention applies the least action principle in the changes of control concerning state and time, first proposed by Brockett. The involved regularization is highly relevant in emulating biological control, such as motor learning. We apply minimum attention in reinforcement learning (RL) as part of the rewards and investigate its connection to meta-learning and stabilization. Specifically, model-based meta-learning with minimum attention is explored in high-dimensional nonlinear dynamics. Ensemble-based model learning and gradient-based meta-policy learning are alternately performed. Empirically, we show that the minimum attention does show outperforming competence in comparison to the state-of-the-art algorithms in model-free and model-based RL, i.e., fast adaptation in few shots and variance reduction from the perturbations of the model and environment. Furthermore, the minimum attention demonstrates the improvement in energy efficiency.