Time: Thursdays 5:00 - 6:30 PM     Venue: AVW 2168

Fall 2016

September 8 Prashanth L.A.

Model-free optimization of human preferences in stochastic systems
Abstract: In several real-world systems involving humans, traditional expected value cannot explain the observed behavior and incorporating distortions in the underlying probabilities of the system can alleviate this problem. Cumulative prospect theory (CPT) is a very popular approach that is based on probabilistic distortions and is more general than the expected value. We bring this idea to a stochastic optimization framework and propose algorithms for both estimation and optimization of the CPT-value objective. We propose an empirical distribution function based scheme to estimate the CPT-value and then use this scheme in the inner loop of a CPT-value optimization procedure. We propose both gradient-based as well as gradient-free CPT-value optimization algorithms, that are based on two well-known simulation optimization ideas: simultaneous perturbation stochastic approximation (SPSA) and model-based parameter search (MPS), respectively. We provide theoretical convergence guarantees for all the proposed algorithms and also illustrate the usefulness of CPT-based criteria in a traffic signal control application.

The majority of the talk will be accessible to a broad audience.

** Joint work with Cheng Jie, Michael Fu, Steve Marcus and Csaba Szepesvari.
September 15 Alborz Alavian

Polynomial Algorithms for Lower-Bounds on the k-th Singular Value of a Polynomial Matrix
Abstract: This talk is on the minimization of the k-th singular value of a general polynomial matrix. We will discuss an equivalent optimization problem that is composed of a polynomial objective subjected to polynomial constraints, and a further rank constraint. We will then discuss two methods on the rank constraint to write this problem as a polynomial optimization problem. This can be used in conjunction with Sum-of-Squares (SOS) techniques to derive a lower-bound on the k-th singular value of a polynomial matrix. Time allowing, we will discuss applications of this problem in deriving bounds on how far an LTI dynamic system is from loosing decentralized controllability.
September 29 Zitan Chen

The Capacity of Online (Causal) q-ary Error-Erasure Channels
Abstract: In the q-ary online (causal) channel coding model, a sender wishes to communicate a message to a receiver by transmitting a codeword ${\bf x} =(x_1,...,x_n)$ symbol-by-symbol via a channel limited to at most np errors (symbol changes) and np* erasures. The channel is ``online'' (i.e., ``causal") in the sense that at the i-th step of communication the channel decides whether to corrupt the i-th symbol or not only based on its view of the symbols $(x_1,...,x_i)$. This is in contrast to the classical adversarial channel in which the corruption is chosen with full knowledge of the sent codeword ${\bf x}$. The capacities of binary online bit-flip-only channels, and separately binary online erasure-only channels have been characterized recently.
In this work we extend prior results in two important ways. First, we obtain the capacity of q-ary online channels for general $q$ (rather than just $q$=2). Second, we analyze combined error-erasure corruption models (rather than studying them separately). Characterization of this much broader class of symmetric online channels gives a fuller understanding of the effects of causality on jamming adversaries.

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