775 research outputs found
Learning-Augmented Weighted Paging
We consider a natural semi-online model for weighted paging, where at any
time the algorithm is given predictions, possibly with errors, about the next
arrival of each page. The model is inspired by Belady's classic optimal offline
algorithm for unweighted paging, and extends the recently studied model for
learning-augmented paging (Lykouris and Vassilvitskii, 2018) to the weighted
setting.
For the case of perfect predictions, we provide an -competitive
deterministic and an -competitive randomized algorithm, where
is the number of distinct weight classes. Both these bounds are tight,
and imply an - and -competitive ratio, respectively,
when the page weights lie between and . Previously, it was not known how
to use these predictions in the weighted setting and only bounds of and
were known, where is the cache size. Our results also
generalize to the interleaved paging setting and to the case of imperfect
predictions, with the competitive ratios degrading smoothly from and
to and , respectively, as the prediction error
increases.
Our results are based on several insights on structural properties of
Belady's algorithm and the sequence of page arrival predictions, and novel
potential functions that incorporate these predictions. For the case of
unweighted paging, the results imply a very simple potential function based
proof of the optimality of Belady's algorithm, which may be of independent
interest
Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system
Firms worldwide are taking major initiatives to reduce the carbon footprint of their supply chains in response to the growing governmental and consumer pressures. In real life, these supply chains face stochastic and non-stationary demand but most of the studies on inventory lot-sizing problem with emission concerns consider deterministic demand. In this paper, we study the inventory lot-sizing problem under non-stationary stochastic demand condition with emission and cycle service level constraints considering carbon cap-and-trade regulatory mechanism. Using a mixed integer linear programming model, this paper aims to investigate the effects of emission parameters, product- and system-related features on the supply chain performance through extensive computational experiments to cover general type business settings and not a specific scenario. Results show that cycle service level and demand coefficient of variation have significant impacts on total cost and emission irrespective of level of demand variability while the impact of product’s demand pattern is significant only at lower level of demand variability. Finally, results also show that increasing value of carbon price reduces total cost, total emission and total inventory and the scope of emission reduction by increasing carbon price is greater at higher levels of cycle service level and demand coefficient of variation.The analysis of results helps supply chain managers to take right decision in different demand and service level situations
Online learning with imperfect hints
We consider a variant of the classical online linear
optimization problem in which at every step,
the online player receives a “hint” vector before
choosing the action for that round. Rather surprisingly,
it was shown that if the hint vector is
guaranteed to have a positive correlation with the
cost vector, then the online player can achieve
a regret of O(log T), thus significantly improving
over the O(pT) regret in the general setting.
However, the result and analysis require the correlation
property at all time steps, thus raising the
natural question: can we design online learning
algorithms that are resilient to bad hints?
In this paper we develop algorithms and nearly
matching lower bounds for online learning with
imperfect directional hints. Our algorithms are
oblivious to the quality of the hints, and the regret
bounds interpolate between the always-correlated
hints case and the no-hints case. Our results also
generalize, simplify, and improve upon previous
results on optimistic regret bounds, which can be
viewed as an additive version of hints.http://proceedings.mlr.press/v119/bhaskara20a.htmlPublished versio
Stress partitioning in a near-β Titanium alloy induced by elastic and plastic phase anisotropies: experimental and modeling
International audienceThe load transfer induced by the elas c and plas c phase anisotropies of a Ti-10V-2Fe-3Al tanium alloy is studied. The microstructure consists in α nodules embedded in elongated β grains. EBSD performed on the alloy shows no crystallographic texture neither for α nor β phase. Tensile tests along the elonga on direc on, at a strain rate of 2 x 10-3 s-1 give a yield stress of 830 MPa with 13% duc lity. Simula ons based on an advanced two-phase polycrystalline elasto-viscoplas c self-consistent (EVPSC) model predict that the β phase first plas fies with a sequen al onset of plas city star ng from oriented β grains, then and finally oriented β grains. This leads to a strong load transfer from the β grains to the α nodules whose average behavior remains elas c up to high stresses (~940 MPa). However, addi onal simula ons considering exclusively β grains of specific orienta on show that the behavior of α nodules is strongly dependent on the β texture in which they are embedded. Especially, in β grains, which plas fy the latest, the model predicts the onset of plas city in favorably orientated α nodules. Moreover, the orienta on spread within the β grains can modify the average plas c behavior of α phase. In future, these results will be compared to data obtained from in-situ High Energy XRD and SEM/EBSD experiments
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