Browsing by Subject "Stochastic approximation"
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Item Deterministic approximations in stochastic programming with applications to a class of portfolio allocation problems(2001-08) Dokov, Steftcho Pentchev; Morton, David P.Optimal decision making under uncertainty involves modeling stochastic systems and developing solution methods for such models. The need to incorporate randomness in many practical decision-making problems is prompted by the uncertainties associated with today’s fast-paced technological environment. The complexity of the resulting models often exceeds the capabilities of commercially available optimization software, and special purpose solution techniques are required. Three main categories of solution approaches exist for attacking a particular stochastic programming instance. These are: large-scale mathematical programming algorithms, Monte-Carlo sampling-based techniques, and deterministically valid bound-based approximations. This research contributes to the last category. First, second-order lower and upper bounds are developed on the expectation of a convex function of a random vector. Here, a “second-order bound” means that only the first and second moments of the underlying random parameters are needed to compute the bound. The vector’s random components are assumed to be independent and to have bounded support contained in a hyper-rectangle. Applications to stochastic programming test problems and analysis of numerical performance are also presented. Second, assuming additional relevant moment information is available, higher-order upper bounds are developed. In this case the underlying random vector can have support contained in either a hyper-rectangle or a multidimensional simplex, and the random parameters can be either dependent or independent. The higher-order upper bounds form a decreasing sequence converging to the true expectation, and yielding convergence of the optimal decisions. Finally, applications of the higher-order upper bounds to a class of portfolio optimization problems are presented. Mean-variance and mean-varianceskewness efficient portfolio frontiers are considered in the context of a specific portfolio allocation model as well as in general and connected with applications of the higher-order upper bounds in utility theoryItem Radio frequency interference modeling and mitigation in wireless receivers(2011-08) Gulati, Kapil; Evans, Brian L. (Brian Lawrence), 1965-; Andrews, Jeffrey G.; Popova, Elmira; Vikalo, Haris; Vishwanath, SriramIn wireless communication systems, receivers have generally been designed under the assumption that the additive noise in system is Gaussian. Wireless receivers, however, are affected by radio frequency interference (RFI) generated from various sources such as other wireless users, switching electronics, and computational platforms. RFI is well modeled using non-Gaussian impulsive statistics and can severely degrade the communication performance of wireless receivers designed under the assumption of additive Gaussian noise. Methods to avoid, cancel, or reduce RFI have been an active area of research over the past three decades. In practice, RFI cannot be completely avoided or canceled at the receiver. This dissertation derives the statistics of the residual RFI and utilizes them to analyze and improve the communication performance of wireless receivers. The primary contributions of this dissertation are to (i) derive instantaneous statistics of co-channel interference in a field of Poisson and Poisson-Poisson clustered interferers, (ii) characterize throughput, delay, and reliability of decentralized wireless networks with temporal correlation, and (iii) design pre-filters to mitigate RFI in wireless receivers.Item Stochastic methods in computational stereo(2011-05) Coffman, Thayne Richard; Bovik, Alan C. (Alan Conrad), 1958-; Aggarwal, J. K.; Evans, Brian L.; Miikkulainen, Risto; Powers, Edward J.Computational stereo estimates 3D structure by analyzing visual changes between two or more passive images of a scene that are captured from different viewpoints. It is a key enabler for ubiquitous autonomous systems, large-scale surveying, virtual reality, and improved techniques for compression, tracking, and object recognition. The fact that computational stereo is an under-constrained inverse problem causes many challenges. Its computational and memory requirements are high. Typical heuristics and assumptions, used to constrain solutions or reduce computation, prevent treatment of key realities such as reflection, translucency, ambient lighting changes, or moving objects in the scene. As a result, a general solution is lacking. Stochastic models are common in computational stereo, but stochastic algorithms are severely under-represented. In this dissertation I present two stochastic algorithms and demonstrate their advantages over deterministic approaches. I first present the Quality-Efficient Stochastic Sampling (QUESS) approach. QUESS reduces the number of match quality function evaluations needed to estimate dense stereo correspondences. This facilitates the use of complex quality metrics or metrics that take unique values at non-integer disparities. QUESS is shown to outperform two competing approaches, and to have more attractive memory and scaling properties than approaches based on exhaustive sampling. I then present a second novel approach based on the Hough transform and extend it with distributed ray tracing (DRT). DRT is a stochastic anti-aliasing technique common to computer rendering but which has not been used in computational stereo. I demonstrate that the DRT-enhanced approach outperforms the unenhanced approach, a competing variation that uses re-accumulation in the Hough domain, and another baseline approach. DRT’s advantages are particularly strong for reduced image resolution and/or reduced accumulator matrix resolution. In support of this second approach, I develop two novel variations of the Hough transform that use DRT, and demonstrate that they outperform competing variations on a traditional line segment detection problem. I generalize these two examples to draw broader conclusions, suggest future work, and call for a deeper exploration by the community. Both practical and academic gaps in the state of the art can be reduced by a renewed exploration of stochastic computational stereo techniques.Item The algorithmic learning equations(2023-05-04) Waldon, Harrison; Zariphopoulou, Thaleia, 1962-; Gamba, Irene; Sirbu, Mihai; Stinchcombe, MaxwellThis thesis presents the Algorithmic Learning Equations (ALEs) to study tacit algorithmic collusion. The ALEs are a set of differential equations that characterizes the finite-time and asymptotic behavior of state-dependent learning algorithms in stochastic and repeated games. The ALEs are derived rigorously, drawing upon stochastic approximation theory. The ALEs are analyzed to show, numerically and theoretically, that decentralized, self-interested learning algorithms can learn to collude. The final chapter of this thesis presents preliminaries using inverse reinforcement learning to detect collusion in a data-driven way. The contents of this thesis are primarily drawn from joint work with Professor Álvaro Cartea, Professor José Penalva, and Patrick Chang during various research visits to the Oxford-Man Institute of Quantitative Finance in 2022 and 2023.