360 research outputs found
Improved Learning-Augmented Algorithms for the Multi-Option Ski Rental Problem via Best-Possible Competitive Analysis
In this paper, we present improved learning-augmented algorithms for the
multi-option ski rental problem. Learning-augmented algorithms take ML
predictions as an added part of the input and incorporates these predictions in
solving the given problem. Due to their unique strength that combines the power
of ML predictions with rigorous performance guarantees, they have been
extensively studied in the context of online optimization problems. Even though
ski rental problems are one of the canonical problems in the field of online
optimization, only deterministic algorithms were previously known for
multi-option ski rental, with or without learning augmentation. We present the
first randomized learning-augmented algorithm for this problem, surpassing
previous performance guarantees given by deterministic algorithms. Our
learning-augmented algorithm is based on a new, provably best-possible
randomized competitive algorithm for the problem. Our results are further
complemented by lower bounds for deterministic and randomized algorithms, and
computational experiments evaluating our algorithms' performance improvements.Comment: 23 pages, 1 figur
Learning Augmented Online Facility Location
Following the research agenda initiated by Munoz & Vassilvitskii [1] and
Lykouris & Vassilvitskii [2] on learning-augmented online algorithms for
classical online optimization problems, in this work, we consider the Online
Facility Location problem under this framework. In Online Facility Location
(OFL), demands arrive one-by-one in a metric space and must be (irrevocably)
assigned to an open facility upon arrival, without any knowledge about future
demands.
We present an online algorithm for OFL that exploits potentially imperfect
predictions on the locations of the optimal facilities. We prove that the
competitive ratio decreases smoothly from sublogarithmic in the number of
demands to constant, as the error, i.e., the total distance of the predicted
locations to the optimal facility locations, decreases towards zero. We
complement our analysis with a matching lower bound establishing that the
dependence of the algorithm's competitive ratio on the error is optimal, up to
constant factors. Finally, we evaluate our algorithm on real world data and
compare our learning augmented approach with the current best online algorithm
for the problem
A Novel Prediction Setup for Online Speed-Scaling
Given the rapid rise in energy demand by data centers and computing systemsin general, it is fundamental to incorporate energy considerations whendesigning (scheduling) algorithms. Machine learning can be a useful approach inpractice by predicting the future load of the system based on, for example,historical data. However, the effectiveness of such an approach highly dependson the quality of the predictions and can be quite far from optimal whenpredictions are sub-par. On the other hand, while providing a worst-caseguarantee, classical online algorithms can be pessimistic for large classes ofinputs arising in practice. This paper, in the spirit of the new area of machine learning augmentedalgorithms, attempts to obtain the best of both worlds for the classical,deadline based, online speed-scaling problem: Based on the introduction of anovel prediction setup, we develop algorithms that (i) obtain provably lowenergy-consumption in the presence of adequate predictions, and (ii) are robustagainst inadequate predictions, and (iii) are smooth, i.e., their performancegradually degrades as the prediction error increases.<br
Canadian Traveller Problem with Predictions
In this work, we consider the -Canadian Traveller Problem (-CTP) under
the learning-augmented framework proposed by Lykouris & Vassilvitskii. -CTP
is a generalization of the shortest path problem, and involves a traveller who
knows the entire graph in advance and wishes to find the shortest route from a
source vertex to a destination vertex , but discovers online that some
edges (up to ) are blocked once reaching them. A potentially imperfect
predictor gives us the number and the locations of the blocked edges.
We present a deterministic and a randomized online algorithm for the
learning-augmented -CTP that achieve a tradeoff between consistency (quality
of the solution when the prediction is correct) and robustness (quality of the
solution when there are errors in the prediction). Moreover, we prove a
matching lower bound for the deterministic case establishing that the tradeoff
between consistency and robustness is optimal, and show a lower bound for the
randomized algorithm. Finally, we prove several deterministic and randomized
lower bounds on the competitive ratio of -CTP depending on the prediction
error, and complement them, in most cases, with matching upper bounds
Double Coverage with Machine-Learned Advice
We study the fundamental online k-server problem in a learning-augmented
setting. While in the traditional online model, an algorithm has no information
about the request sequence, we assume that there is given some advice (e.g.
machine-learned predictions) on an algorithm's decision. There is, however, no
guarantee on the quality of the prediction and it might be far from being
correct.
Our main result is a learning-augmented variation of the well-known Double
Coverage algorithm for k-server on the line (Chrobak et al., SIDMA 1991) in
which we integrate predictions as well as our trust into their quality. We give
an error-dependent competitive ratio, which is a function of a user-defined
confidence parameter, and which interpolates smoothly between an optimal
consistency, the performance in case that all predictions are correct, and the
best-possible robustness regardless of the prediction quality. When given good
predictions, we improve upon known lower bounds for online algorithms without
advice. We further show that our algorithm achieves for any k an almost optimal
consistency-robustness tradeoff, within a class of deterministic algorithms
respecting local and memoryless properties.
Our algorithm outperforms a previously proposed (more general)
learning-augmented algorithm. It is remarkable that the previous algorithm
crucially exploits memory, whereas our algorithm is memoryless. Finally, we
demonstrate in experiments the practicability and the superior performance of
our algorithm on real-world data.Comment: Accepted at ITCS 202
Learning-Augmented Online TSP on Rings, Trees, Flowers and (Almost) Everywhere Else
We study the Online Traveling Salesperson Problem (OLTSP) with predictions. In OLTSP, a sequence of initially unknown requests arrive over time at points (locations) of a metric space. The goal is, starting from a particular point of the metric space (the origin), to serve all these requests while minimizing the total time spent. The server moves with unit speed or is "waiting" (zero speed) at some location. We consider two variants: in the open variant, the goal is achieved when the last request is served. In the closed one, the server additionally has to return to the origin. We adopt a prediction model, introduced for OLTSP on the line [Gouleakis et al., 2023], in which the predictions correspond to the locations of the requests and extend it to more general metric spaces.
We first propose an oracle-based algorithmic framework, inspired by previous work [Bampis et al., 2023]. This framework allows us to design online algorithms for general metric spaces that provide competitive ratio guarantees which, given perfect predictions, beat the best possible classical guarantee (consistency). Moreover, they degrade gracefully along with the increase in error (smoothness), but always within a constant factor of the best known competitive ratio in the classical case (robustness).
Having reduced the problem to designing suitable efficient oracles, we describe how to achieve this for general metric spaces as well as specific metric spaces (rings, trees and flowers), the resulting algorithms being tractable in the latter case. The consistency guarantees of our algorithms are tight in almost all cases, and their smoothness guarantees only suffer a linear dependency on the error, which we show is necessary. Finally, we provide robustness guarantees improving previous results
Smoothed Online Optimization with Unreliable Predictions
We examine the problem of smoothed online optimization, where a decision
maker must sequentially choose points in a normed vector space to minimize the
sum of per-round, non-convex hitting costs and the costs of switching decisions
between rounds. The decision maker has access to a black-box oracle, such as a
machine learning model, that provides untrusted and potentially inaccurate
predictions of the optimal decision in each round. The goal of the decision
maker is to exploit the predictions if they are accurate, while guaranteeing
performance that is not much worse than the hindsight optimal sequence of
decisions, even when predictions are inaccurate. We impose the standard
assumption that hitting costs are globally -polyhedral. We propose a
novel algorithm, Adaptive Online Switching (AOS), and prove that, for a large
set of feasible , it is -competitive if predictions are
perfect, while also maintaining a uniformly bounded competitive ratio of
even when predictions are
adversarial. Further, we prove that this trade-off is necessary and nearly
optimal in the sense that \emph{any} deterministic algorithm which is
-competitive if predictions are perfect must be at least
-competitive when predictions are
inaccurate. In fact, we observe a unique threshold-type behavior in this
trade-off: if is not in the set of feasible options, then \emph{no}
algorithm is simultaneously -competitive if predictions are
perfect and -competitive when predictions are inaccurate for any . Furthermore, we discuss that memory is crucial in AOS by proving
that any algorithm that does not use memory cannot benefit from predictions. We
complement our theoretical results by a numerical study on a microgrid
application.Comment: 38 pages, 4 figure
Learning-Augmented Algorithms for Online TSP on the Line
We study the online Traveling Salesman Problem (TSP) on the line augmentedwith machine-learned predictions. In the classical problem, there is a streamof requests released over time along the real line. The goal is to minimize themakespan of the algorithm. We distinguish between the open variant and theclosed one, in which we additionally require the algorithm to return to theorigin after serving all requests. The state of the art is a -competitivealgorithm and a -competitive algorithm for the closed and open variants,respectively \cite{Bjelde:1.64}. In both cases, a tight lower bound is known\cite{Ausiello:1.75, Bjelde:1.64}. In both variants, our primary prediction model involves predicted positionsof the requests. We introduce algorithms that (i) obtain a tight 1.5competitive ratio for the closed variant and a 1.66 competitive ratio for theopen variant in the case of perfect predictions, (ii) are robust againstunbounded prediction error, and (iii) are smooth, i.e., their performancedegrades gracefully as the prediction error increases. Moreover, we further investigate the learning-augmented setting in the openvariant by additionally considering a prediction for the last request served bythe optimal offline algorithm. Our algorithm for this enhanced setting obtainsa 1.33 competitive ratio with perfect predictions while also being smooth androbust, beating the lower bound of 1.44 we show for our original predictionsetting for the open variant. Also, we provide a lower bound of 1.25 for thisenhanced setting.<br
Proportionally Fair Online Allocation of Public Goods with Predictions
We design online algorithms for the fair allocation of public goods to a set
of agents over a sequence of rounds and focus on improving their
performance using predictions. In the basic model, a public good arrives in
each round, the algorithm learns every agent's value for the good, and must
irrevocably decide the amount of investment in the good without exceeding a
total budget of across all rounds. The algorithm can utilize (potentially
inaccurate) predictions of each agent's total value for all the goods to
arrive. We measure the performance of the algorithm using a proportional
fairness objective, which informally demands that every group of agents be
rewarded in proportion to its size and the cohesiveness of its preferences.
In the special case of binary agent preferences and a unit budget, we show
that proportional fairness can be achieved without using any
predictions, and that this is optimal even if perfectly accurate predictions
were available. However, for general preferences and budget no algorithm can
achieve better than proportional fairness without predictions. We
show that algorithms with (reasonably accurate) predictions can do much better,
achieving proportional fairness. We also extend this
result to a general model in which a batch of public goods arrive in each
round and achieve proportional fairness. Our
exact bounds are parametrized as a function of the error in the predictions and
the performance degrades gracefully with increasing errors
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