Esteban Leiva

We develop a computational framework for efficiently fitting Bézier distributions to bounded data using both maximum likelihood and minimum-error estimation. By exploiting the geometry of the parameter space and introducing asymptotically lossless convex restrictions, our first-order optimization algorithms achieve orders-of-magnitude speedups over existing derivative-free and nonlinear optimization methods while maintaining comparable accuracy. To support practical adoption, we also introduce bezierv, an open-source Python package for fitting, analyzing, and convolving Bézier distributions.

We propose a regularized framework for learning cost functions and policies from suboptimal expert demonstrations in Markov decision processes. By incorporating prior beliefs about cost-function structure, our approach addresses the ill-posedness of inverse reinforcement learning and formulates the problem as a regularized convex-concave min-max optimization. We solve this problem using stochastic mirror descent and provide convergence guarantees, with experiments demonstrating improved recovery of cost functions and apprentice policies.

We develop a unified and exact algorithmic framework for solving reliable shortest path problems with non-negatively correlated travel times and resource constraints. Building on the pulse algorithm, our approach efficiently solves several reliability-based routing formulations through novel reliability bounds and pruning strategies. Computational experiments on large-scale transportation networks show that the framework significantly outperforms existing methods, achieving up to an order-of-magnitude reduction in solution times.