411 research outputs found
Limit value for optimal control with general means
We consider optimal control problem with an integral cost which is a mean of
a given function. As a particular case, the cost concerned is the Ces\`aro
average. The limit of the value with Ces\`aro mean when the horizon tends to
infinity is widely studied in the literature. We address the more general
question of the existence of a limit when the averaging parameter converges,
for values defined with means of general types.
We consider a given function and a family of costs defined as the mean of the
function with respect to a family of probability measures -- the evaluations --
on R_+. We provide conditions on the evaluations in order to obtain the uniform
convergence of the associated value function (when the parameter of the family
converges).
Our main result gives a necessary and sufficient condition in term of the
total variation of the family of probability measures on R_+. As a byproduct,
we obtain the existence of a limit value (for general means) for control
systems having a compact invariant set and satisfying suitable nonexpansive
property.Comment: 21 pages, 2 figure
On the Power of Advice and Randomization for Online Bipartite Matching
While randomized online algorithms have access to a sequence of uniform
random bits, deterministic online algorithms with advice have access to a
sequence of advice bits, i.e., bits that are set by an all powerful oracle
prior to the processing of the request sequence. Advice bits are at least as
helpful as random bits, but how helpful are they? In this work, we investigate
the power of advice bits and random bits for online maximum bipartite matching
(MBM).
The well-known Karp-Vazirani-Vazirani algorithm is an optimal randomized
-competitive algorithm for \textsc{MBM} that requires access
to uniform random bits. We show that
advice bits are necessary and
sufficient in order to obtain a
-competitive deterministic advice algorithm. Furthermore, for a
large natural class of deterministic advice algorithms, we prove that
advice bits are required in order to improve on the
-competitiveness of the best deterministic online algorithm, while
it is known that bits are sufficient.
Last, we give a randomized online algorithm that uses random bits, for
integers , and a competitive ratio that approaches
very quickly as is increasing. For example if , then the difference
between and the achieved competitive ratio is less than
Online Computation with Untrusted Advice
The advice model of online computation captures the setting in which the online algorithm is given some partial information concerning the request sequence. This paradigm allows to establish tradeoffs between the amount of this additional information and the performance of the online algorithm. However, unlike real life in which advice is a recommendation that we can choose to follow or to ignore based on trustworthiness, in the current advice model, the online algorithm treats it as infallible. This means that if the advice is corrupt or, worse, if it comes from a malicious source, the algorithm may perform poorly. In this work, we study online computation in a setting in which the advice is provided by an untrusted source. Our objective is to quantify the impact of untrusted advice so as to design and analyze online algorithms that are robust and perform well even when the advice is generated in a malicious, adversarial manner. To this end, we focus on well- studied online problems such as ski rental, online bidding, bin packing, and list update. For ski-rental and online bidding, we show how to obtain algorithms that are Pareto-optimal with respect to the competitive ratios achieved; this improves upon the framework of Purohit et al. [NeurIPS 2018] in which Pareto-optimality is not necessarily guaranteed. For bin packing and list update, we give online algorithms with worst-case tradeoffs in their competitiveness, depending on whether the advice is trusted or not; this is motivated by work of Lykouris and Vassilvitskii [ICML 2018] on the paging problem, but in which the competitiveness depends on the reliability of the advice. Furthermore, we demonstrate how to prove lower bounds, within this model, on the tradeoff between the number of advice bits and the competitiveness of any online algorithm. Last, we study the effect of randomization: here we show that for ski-rental there is a randomized algorithm that Pareto-dominates any deterministic algorithm with advice of any size. We also show that a single random bit is not always inferior to a single advice bit, as it happens in the standard model
Paid Exchanges are Worth the Price
We consider the list update problem as defined in the seminal work on competitive analysis by Sleator and Tarjan [12]. In this problem, a sequence of requests, consisting of items to access in a linked list, is given. After an item is accessed it can be moved to any position forward in the list at no cost (free exchange), and, at any time, any two adjacent items can be swapped at a cost of 1 (paid exchange). The cost to access an item is its current position in the list. The goal is to dynamically rearrange the list so as to minimize the total cost (accrued from accesses and exchanges) over the request sequence.
We show a lower bound of 12/11 on the worst-case ratio between the performance of an (offline) optimal algorithm that can only perform free exchanges and that of an (offline) optimal algorithm that can perform both paid and free exchanges. This answers an outstanding question that has been open since 1996 [10]
Online Computation with Untrusted Advice
The advice model of online computation captures a setting in which the
algorithm is given some partial information concerning the request sequence.
This paradigm allows to establish tradeoffs between the amount of this
additional information and the performance of the online algorithm. However, if
the advice is corrupt or, worse, if it comes from a malicious source, the
algorithm may perform poorly. In this work, we study online computation in a
setting in which the advice is provided by an untrusted source. Our objective
is to quantify the impact of untrusted advice so as to design and analyze
online algorithms that are robust and perform well even when the advice is
generated in a malicious, adversarial manner. To this end, we focus on
well-studied online problems such as ski rental, online bidding, bin packing,
and list update. For ski-rental and online bidding, we show how to obtain
algorithms that are Pareto-optimal with respect to the competitive ratios
achieved; this improves upon the framework of Purohit et al. [NeurIPS 2018] in
which Pareto-optimality is not necessarily guaranteed. For bin packing and list
update, we give online algorithms with worst-case tradeoffs in their
competitiveness, depending on whether the advice is trusted or not; this is
motivated by work of Lykouris and Vassilvitskii [ICML 2018] on the paging
problem, but in which the competitiveness depends on the reliability of the
advice. Furthermore, we demonstrate how to prove lower bounds, within this
model, on the tradeoff between the number of advice bits and the
competitiveness of any online algorithm. Last, we study the effect of
randomization: here we show that for ski-rental there is a randomized algorithm
that Pareto-dominates any deterministic algorithm with advice of any size. We
also show that a single random bit is not always inferior to a single advice
bit, as it happens in the standard model
Spotlight on the invasion of a carabid beetle on an oceanic island over a 105-year period island
The flightless beetle Merizodus soledadinus, native to the Falkland Islands and southern South America, was introduced to the sub-Antarctic Kerguelen Islands in the early Twentieth Century. Using available literature data, in addition to collecting more than 2000 new survey (presence/absence) records of M. soledadinus over the 1991–2018 period, we confirmed the best estimate of the introduction date of M. soledadinus to the archipelago, and tracked subsequent changes in its abundance and geographical distribution. The range expansion of this flightless insect was initially slow, but has accelerated over the past 2 decades, in parallel with increased local abundance. Human activities may have facilitated further local colonization by M. soledadinus, which is now widespread in the eastern part of the archipelago. This predatory insect is a major threat to the native invertebrate fauna, in particular to the endemic wingless flies Anatalanta aptera and Calycopteryx moseleyi which can be locally eliminated by the beetle. Our distribution data also suggest an accelerating role of climate change in the range expansion of M. soledadinus, with populations now thriving in low altitude habitats. Considering that no control measures, let alone eradication, are practicable, it is essential to limit any further local range expansion of this aggressively invasive insect through human assistance. This study confirms the crucial importance of long term biosurveillance for the detection and monitoring of non-native species and the timely implementation of control measures
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