204,956 research outputs found
Robustness of computer algorithms to simulate optimal experimentation problems.
Three methods have been developed by the authors for solving optimal experimentation problems. David Kendrick (1981, 2002, Ch.10) uses quadratic approximation of the value function and linear approximation of the equation of motion to simulate general optimal experimentation (active learning) problems. Beck and Volker Wieland (2002) use dynamic programming methods to develop an algorithm for optimal experimentation problems. Cosimano (2003) and Cosimano and Gapen (2005) use the Perturbation method to develop an algorithm for solving optimal experimentation problems. The perturbation is in the neighborhood of the augmented linear regulator problems of Hansen and Sargent (2004). In this paper we take an example from Beck and Wieland which fits into the setup of all three algorithms. Using this example we examine the cost and benefits of the various algorithms for solving optimal experimentation problems.
Non-Uniform Robust Network Design in Planar Graphs
Robust optimization is concerned with constructing solutions that remain
feasible also when a limited number of resources is removed from the solution.
Most studies of robust combinatorial optimization to date made the assumption
that every resource is equally vulnerable, and that the set of scenarios is
implicitly given by a single budget constraint. This paper studies a robustness
model of a different kind. We focus on \textbf{bulk-robustness}, a model
recently introduced~\cite{bulk} for addressing the need to model non-uniform
failure patterns in systems.
We significantly extend the techniques used in~\cite{bulk} to design
approximation algorithm for bulk-robust network design problems in planar
graphs. Our techniques use an augmentation framework, combined with linear
programming (LP) rounding that depends on a planar embedding of the input
graph. A connection to cut covering problems and the dominating set problem in
circle graphs is established. Our methods use few of the specifics of
bulk-robust optimization, hence it is conceivable that they can be adapted to
solve other robust network design problems.Comment: 17 pages, 2 figure
Adaptive traffic signal control using approximate dynamic programming
This thesis presents a study on an adaptive traffic signal controller for real-time operation.
An approximate dynamic programming (ADP) algorithm is developed for controlling traffic
signals at isolated intersection and in distributed traffic networks. This approach is derived
from the premise that classic dynamic programming is computationally difficult to solve, and
approximation is the second-best option for establishing sequential decision-making for
complex process. The proposed ADP algorithm substantially reduces computational burden
by using a linear approximation function to replace the exact value function of dynamic
programming solution. Machine-learning techniques are used to improve the approximation
progressively. Not knowing the ideal response for the approximation to learn from, we use the
paradigm of unsupervised learning, and reinforcement learning in particular. Temporal-difference
learning and perturbation learning are investigated as appropriate candidates in the
family of unsupervised learning. We find in computer simulation that the proposed method
achieves substantial reduction in vehicle delays in comparison with optimised fixed-time
plans, and is competitive against other adaptive methods in computational efficiency and
effectiveness in managing varying traffic. Our results show that substantial benefits can be
gained by increasing the frequency at which the signal plans are revised. The proposed ADP
algorithm is in compliance with a range of discrete systems of resolution from 0.5 to 5
seconds per temporal step. This study demonstrates the readiness of the proposed approach
for real-time operations at isolated intersections and the potentials for distributed network
control
Intersection bounds: estimation and inference
We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with a potentially infinite constraint set. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are non-separable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the size of the identified set, we also offer a median-bias-corrected estimator of such bounds as a natural by-product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel-based empirical processes by a sequence of "penultimate" Gaussian processes. These penultimate processes are generally not weakly convergent, and thus non-Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest.
- …