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Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…
Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…
We consider the stochastic sequential assignment problem of Derman, Lieberman and Ross (1972) corresponding to a discrete distribution supported on a finite set of points. We use large deviation estimates to compute the asymptotics of the…
Diffusion on complex networks is often modeled as a stochastic process. Yet, recent work on strategic diffusion emphasizes the decision power of agents and treats diffusion as a strategic problem. Here we study the computational aspects of…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
In this work we study the sets of two-party correlations generated from a Bell scenario involving two spatially separated systems with respect to various physical models. We show that the sets of classical, quantum, no-signaling and…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
We consider nonlinear stochastic systems that arise in path planning and control of mobile robots. As is typical of almost all nonlinear stochastic systems, the optimally solving problem is intractable. We provide a design approach which…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
We consider the dynamic inventory problem with non-stationary demands. It has long been known that non-stationary (s, S) policies are optimal for this problem. However, finding optimal policy parameters remains a computational challenge as…
We consider the problem of approximating optimal in the Minimum Mean Squared Error (MMSE) sense nonlinear filters in a discrete time setting, exploiting properties of stochastically convergent state process approximations. More…
We discuss the estimation of the distance of a given mixed many-body quantum state to the set of fully separable states, applied to the concrete scenario of collective spin states. Concretely, we discuss lower bounds to distances from the…
In this two-part paper, we address the problem of finding the optimal precoding/multiplexing scheme for a set of non-cooperative links sharing the same physical resources, e.g., time and bandwidth. We consider two alternative optimization…
We consider approximate dynamic programming for the infinite-horizon stationary $\gamma$-discounted optimal control problem formalized by Markov Decision Processes. While in the exact case it is known that there always exists an optimal…
Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…