1,597 research outputs found
Approximation Algorithms for Route Planning with Nonlinear Objectives
We consider optimal route planning when the objective function is a general
nonlinear and non-monotonic function. Such an objective models user behavior
more accurately, for example, when a user is risk-averse, or the utility
function needs to capture a penalty for early arrival. It is known that as
nonlinearity arises, the problem becomes NP-hard and little is known about
computing optimal solutions when in addition there is no monotonicity
guarantee. We show that an approximately optimal non-simple path can be
efficiently computed under some natural constraints. In particular, we provide
a fully polynomial approximation scheme under hop constraints. Our
approximation algorithm can extend to run in pseudo-polynomial time under a
more general linear constraint that sometimes is useful. As a by-product, we
show that our algorithm can be applied to the problem of finding a path that is
most likely to be on time for a given deadline.Comment: 9 pages, 2 figures, main part of this paper is to be appear in
AAAI'1
Stochastic motion planning and applications to traffic
This paper presents a stochastic motion planning algorithm and its application to traffic navigation. The algorithm copes with the uncertainty of road traffic conditions by stochastic modeling of travel delay on road networks. The algorithm determines paths between two points that optimize a cost function of the delay probability distribution. It can be used to find paths that maximize the probability of reaching a destination within a particular travel deadline. For such problems, standard shortest-path algorithms don’t work because the optimal substructure property doesn’t hold. We evaluate our algorithm using both simulations and real-world drives, using delay data gathered from a set of taxis equipped with GPS sensors and a wireless network. Our algorithm can be integrated into on-board navigation systems as well as route-finding Web sites, providing drivers with good paths that meet their desired goals.National Science Foundation (U.S.) (grant EFRI-0710252)National Science Foundation (U.S.) (grant IIS-0426838
Geometrical Insights for Implicit Generative Modeling
Learning algorithms for implicit generative models can optimize a variety of
criteria that measure how the data distribution differs from the implicit model
distribution, including the Wasserstein distance, the Energy distance, and the
Maximum Mean Discrepancy criterion. A careful look at the geometries induced by
these distances on the space of probability measures reveals interesting
differences. In particular, we can establish surprising approximate global
convergence guarantees for the -Wasserstein distance,even when the
parametric generator has a nonconvex parametrization.Comment: this version fixes a typo in a definitio
Stochastic Sensor Scheduling via Distributed Convex Optimization
In this paper, we propose a stochastic scheduling strategy for estimating the
states of N discrete-time linear time invariant (DTLTI) dynamic systems, where
only one system can be observed by the sensor at each time instant due to
practical resource constraints. The idea of our stochastic strategy is that a
system is randomly selected for observation at each time instant according to a
pre-assigned probability distribution. We aim to find the optimal pre-assigned
probability in order to minimize the maximal estimate error covariance among
dynamic systems. We first show that under mild conditions, the stochastic
scheduling problem gives an upper bound on the performance of the optimal
sensor selection problem, notoriously difficult to solve. We next relax the
stochastic scheduling problem into a tractable suboptimal quasi-convex form. We
then show that the new problem can be decomposed into coupled small convex
optimization problems, and it can be solved in a distributed fashion. Finally,
for scheduling implementation, we propose centralized and distributed
deterministic scheduling strategies based on the optimal stochastic solution
and provide simulation examples.Comment: Proof errors and typos are fixed. One section is removed from last
versio
Tractable Pathfinding for the Stochastic On-Time Arrival Problem
We present a new and more efficient technique for computing the route that
maximizes the probability of on-time arrival in stochastic networks, also known
as the path-based stochastic on-time arrival (SOTA) problem. Our primary
contribution is a pathfinding algorithm that uses the solution to the
policy-based SOTA problem---which is of pseudo-polynomial-time complexity in
the time budget of the journey---as a search heuristic for the optimal path. In
particular, we show that this heuristic can be exceptionally efficient in
practice, effectively making it possible to solve the path-based SOTA problem
as quickly as the policy-based SOTA problem. Our secondary contribution is the
extension of policy-based preprocessing to path-based preprocessing for the
SOTA problem. In the process, we also introduce Arc-Potentials, a more
efficient generalization of Stochastic Arc-Flags that can be used for both
policy- and path-based SOTA. After developing the pathfinding and preprocessing
algorithms, we evaluate their performance on two different real-world networks.
To the best of our knowledge, these techniques provide the most efficient
computation strategy for the path-based SOTA problem for general probability
distributions, both with and without preprocessing.Comment: Submission accepted by the International Symposium on Experimental
Algorithms 2016 and published by Springer in the Lecture Notes in Computer
Science series on June 1, 2016. Includes typographical corrections and
modifications to pre-processing made after the initial submission to SODA'15
(July 7, 2014
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