1,061 research outputs found
Scalable First-Order Methods for Robust MDPs
Robust Markov Decision Processes (MDPs) are a powerful framework for modeling
sequential decision-making problems with model uncertainty. This paper proposes
the first first-order framework for solving robust MDPs. Our algorithm
interleaves primal-dual first-order updates with approximate Value Iteration
updates. By carefully controlling the tradeoff between the accuracy and cost of
Value Iteration updates, we achieve an ergodic convergence rate of for the best
choice of parameters on ellipsoidal and Kullback-Leibler -rectangular
uncertainty sets, where and is the number of states and actions,
respectively. Our dependence on the number of states and actions is
significantly better (by a factor of ) than that of pure
Value Iteration algorithms. In numerical experiments on ellipsoidal uncertainty
sets we show that our algorithm is significantly more scalable than
state-of-the-art approaches. Our framework is also the first one to solve
robust MDPs with -rectangular KL uncertainty sets
Participating in the Global Competition: Denaturalizing "Flair" in Samoan Rugby
SÄmoa, Fiji, and Tonga have emerged as strong contenders in international rugby competitions in the last three decades. Meanwhile, rugby has been going through a period of âdevelopmentâ since the creation of the Rugby World Cup in 1987 and the introduction of professionalism in 1995. Here, I present an ethnography of rugby in SÄmoa that focuses on embodiment. Participant observation of practices as well as interviews illuminate how international norms and values are diffused within the sport structure, while a global sporting practice is indigenized and appropriated in the everyday practices of young Samoan men. In Samoan rugby, the emergence of âflairâ appears as a category of analysis that naturalizes an embodied characteristic of Samoan village life. By denaturalizing âflairâ in Samoan rugby, this article contributes to a critique of this notion, in addition to showing the assemblage that creates rugby in the Islands
Quantifying uncertainties on excursion sets under a Gaussian random field prior
We focus on the problem of estimating and quantifying uncertainties on the
excursion set of a function under a limited evaluation budget. We adopt a
Bayesian approach where the objective function is assumed to be a realization
of a Gaussian random field. In this setting, the posterior distribution on the
objective function gives rise to a posterior distribution on excursion sets.
Several approaches exist to summarize the distribution of such sets based on
random closed set theory. While the recently proposed Vorob'ev approach
exploits analytical formulae, further notions of variability require Monte
Carlo estimators relying on Gaussian random field conditional simulations. In
the present work we propose a method to choose Monte Carlo simulation points
and obtain quasi-realizations of the conditional field at fine designs through
affine predictors. The points are chosen optimally in the sense that they
minimize the posterior expected distance in measure between the excursion set
and its reconstruction. The proposed method reduces the computational costs due
to Monte Carlo simulations and enables the computation of quasi-realizations on
fine designs in large dimensions. We apply this reconstruction approach to
obtain realizations of an excursion set on a fine grid which allow us to give a
new measure of uncertainty based on the distance transform of the excursion
set. Finally we present a safety engineering test case where the simulation
method is employed to compute a Monte Carlo estimate of a contour line
Optimal prefix codes for pairs of geometrically-distributed random variables
Optimal prefix codes are studied for pairs of independent, integer-valued
symbols emitted by a source with a geometric probability distribution of
parameter , . By encoding pairs of symbols, it is possible to
reduce the redundancy penalty of symbol-by-symbol encoding, while preserving
the simplicity of the encoding and decoding procedures typical of Golomb codes
and their variants. It is shown that optimal codes for these so-called
two-dimensional geometric distributions are \emph{singular}, in the sense that
a prefix code that is optimal for one value of the parameter cannot be
optimal for any other value of . This is in sharp contrast to the
one-dimensional case, where codes are optimal for positive-length intervals of
the parameter . Thus, in the two-dimensional case, it is infeasible to give
a compact characterization of optimal codes for all values of the parameter
, as was done in the one-dimensional case. Instead, optimal codes are
characterized for a discrete sequence of values of that provide good
coverage of the unit interval. Specifically, optimal prefix codes are described
for (), covering the range , and
(), covering the range . The described codes produce the expected
reduction in redundancy with respect to the one-dimensional case, while
maintaining low complexity coding operations.Comment: To appear in IEEE Transactions on Information Theor
An iterative approach for counting reduced ordered binary decision diagrams
For three decades binary decision diagrams, a data structure efficiently
representing Boolean functions, have been widely used in many distinct contexts
like model verification, machine learning, cryptography and also resolution of
combinatorial problems. The most famous variant, called reduced ordered binary
decision diagram (ROBDD for short), can be viewed as the result of a compaction
procedure on the full decision tree. A useful property is that once an order
over the Boolean variables is fixed, each Boolean function is represented by
exactly one ROBDD. In this paper we aim at computing the exact distribution of
the Boolean functions in variables according to the ROBDD size}, where the
ROBDD size is equal to the number of decision nodes of the underlying directed
acyclic graph (DAG for short) structure. Recall the number of Boolean functions
with variables is equal to , which is of double exponential growth
with respect to the number of variables. The maximal size of a ROBDD with
variables is . Apart from the natural combinatorial
explosion observed, another difficulty for computing the distribution according
to size is to take into account dependencies within the DAG structure of
ROBDDs. In this paper, we develop the first polynomial algorithm to derive the
distribution of Boolean functions over variables with respect to ROBDD size
denoted by . The algorithm computes the (enumerative) generating function of
ROBDDs with variables up to size . It performs arithmetical
operations on integers and necessitates storing integers with
bit length . Our new approach relies on a decomposition of ROBDDs
layer by layer and on an inclusion-exclusion argument
Constructions for Clumps Statistics.
International audienceWe consider a component of the word statistics known as clump; starting from a finite set of words, clumps are maximal overlapping sets of these occurrences. This object has first been studied by Schbath with the aim of counting the number of occurrences of words in random texts. Later work with similar probabilistic approach used the Chen-Stein approximation for a compound Poisson distribution, where the number of clumps follows a law close to Poisson. Presently there is no combinatorial counterpart to this approach, and we fill the gap here. We also provide a construction for the yet unsolved problem of clumps of an arbitrary finite set of words. In contrast with the probabilistic approach which only provides asymptotic results, the combinatorial method provides exact results that are useful when considering short sequences
- âŠ