7,653 research outputs found
Stochastic Model Predictive Control for Autonomous Mobility on Demand
This paper presents a stochastic, model predictive control (MPC) algorithm
that leverages short-term probabilistic forecasts for dispatching and
rebalancing Autonomous Mobility-on-Demand systems (AMoD, i.e. fleets of
self-driving vehicles). We first present the core stochastic optimization
problem in terms of a time-expanded network flow model. Then, to ameliorate its
tractability, we present two key relaxations. First, we replace the original
stochastic problem with a Sample Average Approximation (SAA), and characterize
the performance guarantees. Second, we separate the controller into two
separate parts to address the task of assigning vehicles to the outstanding
customers separate from that of rebalancing. This enables the problem to be
solved as two totally unimodular linear programs, and thus easily scalable to
large problem sizes. Finally, we test the proposed algorithm in two scenarios
based on real data and show that it outperforms prior state-of-the-art
algorithms. In particular, in a simulation using customer data from DiDi
Chuxing, the algorithm presented here exhibits a 62.3 percent reduction in
customer waiting time compared to state of the art non-stochastic algorithms.Comment: Submitting to the IEEE International Conference on Intelligent
Transportation Systems 201
A Learning Theoretic Approach to Energy Harvesting Communication System Optimization
A point-to-point wireless communication system in which the transmitter is
equipped with an energy harvesting device and a rechargeable battery, is
studied. Both the energy and the data arrivals at the transmitter are modeled
as Markov processes. Delay-limited communication is considered assuming that
the underlying channel is block fading with memory, and the instantaneous
channel state information is available at both the transmitter and the
receiver. The expected total transmitted data during the transmitter's
activation time is maximized under three different sets of assumptions
regarding the information available at the transmitter about the underlying
stochastic processes. A learning theoretic approach is introduced, which does
not assume any a priori information on the Markov processes governing the
communication system. In addition, online and offline optimization problems are
studied for the same setting. Full statistical knowledge and causal information
on the realizations of the underlying stochastic processes are assumed in the
online optimization problem, while the offline optimization problem assumes
non-causal knowledge of the realizations in advance. Comparing the optimal
solutions in all three frameworks, the performance loss due to the lack of the
transmitter's information regarding the behaviors of the underlying Markov
processes is quantified
Learning optimization models in the presence of unknown relations
In a sequential auction with multiple bidding agents, it is highly
challenging to determine the ordering of the items to sell in order to maximize
the revenue due to the fact that the autonomy and private information of the
agents heavily influence the outcome of the auction.
The main contribution of this paper is two-fold. First, we demonstrate how to
apply machine learning techniques to solve the optimal ordering problem in
sequential auctions. We learn regression models from historical auctions, which
are subsequently used to predict the expected value of orderings for new
auctions. Given the learned models, we propose two types of optimization
methods: a black-box best-first search approach, and a novel white-box approach
that maps learned models to integer linear programs (ILP) which can then be
solved by any ILP-solver. Although the studied auction design problem is hard,
our proposed optimization methods obtain good orderings with high revenues.
Our second main contribution is the insight that the internal structure of
regression models can be efficiently evaluated inside an ILP solver for
optimization purposes. To this end, we provide efficient encodings of
regression trees and linear regression models as ILP constraints. This new way
of using learned models for optimization is promising. As the experimental
results show, it significantly outperforms the black-box best-first search in
nearly all settings.Comment: 37 pages. Working pape
Least absolute deviation estimation of linear econometric models: A literature review
Econometricians generally take for granted that the error terms in the econometric models are generated by distributions having a finite variance. However, since the time of Pareto the existence of error distributions with infinite variance is known. Works of many econometricians, namely, Meyer & Glauber (1964), Fama (1965) and Mandlebroth (1967), on economic data series like prices in financial and commodity markets confirm that infinite variance distributions exist abundantly. The distribution of firms by size, behaviour of speculative prices and various other recent economic phenomena also display similar trends. Further, econometricians generally assume that the disturbance term, which is an influence of innumerably many factors not accounted for in the model, approaches normality according to the Central Limit Theorem. But Bartels (1977) is of the opinion that there are limit theorems, which are just likely to be relevant when considering the sum of number of components in a regression disturbance that leads to non-normal stable distribution characterized by infinite variance. Thus, the possibility of the error term following a non-normal distribution exists. The Least Squares method of estimation of parameters of linear (regression) models performs well provided that the residuals (disturbances or errors) are well behaved (preferably normally or near-normally distributed and not infested with large size outliers) and follow Gauss-Markov assumptions. However, models with the disturbances that are prominently non-normally distributed and contain sizeable outliers fail estimation by the Least Squares method. An intensive research has established that in such cases estimation by the Least Absolute Deviation (LAD) method performs well. This paper is an attempt to survey the literature on LAD estimation of single as well as multi-equation linear econometric models.Lad estimator; Least absolute deviation estimation; econometric model; LAD Estimator; Minimum Absolute Deviation; Robust; Outliers; L1 Estimator; Review of literature
Highly Robust Error Correction by Convex Programming
This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal x â â^n (a block of n pieces of information) to a remote receiver. We ask whether it is possible to transmit this information reliably when a fraction of the transmitted codeword is corrupted by arbitrary gross errors, and when in addition, all the entries of the codeword are contaminated by smaller errors (e.g., quantization errors).
We show that if one encodes the information as Ax where A â
â^(m x n) (m ⼠n) is a suitable coding matrix, there are two decoding schemes that allow the recovery of the block of n pieces of information x with nearly the same accuracy as if no gross errors occurred upon transmission (or equivalently as if one had an oracle supplying perfect information about the sites and amplitudes of the gross errors). Moreover, both decoding strategies are very concrete and only involve solving simple convex optimization programs, either a linear program or a second-order cone program. We complement our study with numerical simulations showing that the encoder/decoder pair performs remarkably well
Solving Factored MDPs with Hybrid State and Action Variables
Efficient representations and solutions for large decision problems with
continuous and discrete variables are among the most important challenges faced
by the designers of automated decision support systems. In this paper, we
describe a novel hybrid factored Markov decision process (MDP) model that
allows for a compact representation of these problems, and a new hybrid
approximate linear programming (HALP) framework that permits their efficient
solutions. The central idea of HALP is to approximate the optimal value
function by a linear combination of basis functions and optimize its weights by
linear programming. We analyze both theoretical and computational aspects of
this approach, and demonstrate its scale-up potential on several hybrid
optimization problems
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