The Nelson-Siegel and the Svensson models are two of the most widely used models for the term structure of interest rates. Even though the models are quite simple and intuitive, fitting them to market data is numerically challenging and various difficulties have been reported. In this paper, a novel mathematical analysis of the fitting problem … Read more
In this paper, we consider convex quadratic optimization problems with indicators on the continuous variables. In particular, we assume that the Hessian of the quadratic term is a Stieltjes matrix, which naturally appears in sparse graphical inference problems and others. We describe an explicit convex formulation for the problem by studying the Stieltjes polyhedron arising … Read more
In the classical best approximation pair (BAP) problem, one is given two nonempty, closed, convex and disjoint subsets in a finite- or an infinite-dimensional Hilbert space, and the goal is to find a pair of points, each from each subset, which realizes the distance between the subsets. We discuss the problem in more general normed … Read more
Factored Markov decision processes (MDPs) are a prominent paradigm within the artificial intelligence community for modeling and solving large-scale MDPs whose rewards and dynamics decompose into smaller, loosely interacting components. Through the use of dynamic Bayesian networks and context-specific independence, factored MDPs can achieve an exponential reduction in the state space of an MDP and … Read more
Gradient computation of multivariate distribution functions calls for considerable effort. A standard procedure is component-wise computation, hence coordinate descent is an attractive choice. This paper deals with constrained convex problems. We apply random coordinate descent in an approximation scheme that is an inexact cutting-plane method from a dual viewpoint. We present convergence proofs and a … Read more
We use the PAC-Bayesian theory for the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-Bayesian bounds) and explicit trade-off between convergence guarantees and convergence speed, which contrasts with the typical worst-case analysis. Our learned optimization algorithms provably outperform related ones … Read more
Problem definition: Drone delivery has recently garnered significant attention due to its potential for faster delivery at a lower cost than other delivery options. When scheduling drones from a depot for delivery to various destinations, the dispatcher must take into account the uncertain wind conditions, which affect the delivery times of drones to their destinations, … Read more
We prove new convergence rates for a generalized version of stochastic Nesterov acceleration under interpolation conditions. Unlike previous analyses, our approach accelerates any stochastic gradient method which makes sufficient progress in expectation. The proof, which proceeds using the estimating sequences framework, applies to both convex and strongly convex functions and is easily specialized to accelerated … Read more
To explore convex optimization on Hadamard spaces, we consider an iteration in the style of a subgradient algorithm. Traditionally, such methods assume that the underlying spaces are manifolds and that the objectives are geodesically convex: the methods are described using tangent spaces and exponential maps. By contrast, our iteration applies in a general Hadamard space, … Read more
We study two-stage distributionally robust optimization (DRO) problems with decision-dependent information discovery (DDID) wherein (a portion of) the uncertain parameters are revealed only if an (often costly) investment is made in the first stage. This class of problems finds many important applications in selection problems (e.g., in hiring, project portfolio optimization, or optimal sensor location). … Read more