Bertrand Simon

Guillaume Cochard, Bertrand Simon

This paper provides and analyzes a dataset detailing the characteristics and execution data of all jobs submitted to the IN2P3 Computing Center (Villeurbanne, France), a national research and support unit of the CNRS, in 2024. The main additional value of this contribution compared to previously available datasets consists in the combination of an extended time interval considered, the inclusion of memory usage data and its recency, on top on improving the diversity of datasets provenance. This allows researchers to simulate and evaluate scheduling algorithms on a real workload over a large time window. Thus, specificities due to seasonal, monthly, and weekly user behaviors can be taken into account, which is not possible with smaller or synthetic datasets. It is composed of 44M jobs submitted by 1k users running on a cluster of a maximum of 312 machines supporting 46k concurrent threads and providing 105To of RAM.

Antonios Antoniadis, Joan Boyar, Marek Eliáš et al.

Paging is a prototypical problem in the area of online algorithms. It has also played a central role in the development of learning-augmented algorithms -- a recent line of research that aims to ameliorate the shortcomings of classical worst-case analysis by giving algorithms access to predictions. Such predictions can typically be generated using a machine learning approach, but they are inherently imperfect. Previous work on learning-augmented paging has investigated predictions on (i) when the current page will be requested again (reoccurrence predictions), (ii) the current state of the cache in an optimal algorithm (state predictions), (iii) all requests until the current page gets requested again, and (iv) the relative order in which pages are requested. We study learning-augmented paging from the new perspective of requiring the least possible amount of predicted information. More specifically, the predictions obtained alongside each page request are limited to one bit only. We consider two natural such setups: (i) discard predictions, in which the predicted bit denotes whether or not it is ``safe'' to evict this page, and (ii) phase predictions, where the bit denotes whether the current page will be requested in the next phase (for an appropriate partitioning of the input into phases). We develop algorithms for each of the two setups that satisfy all three desirable properties of learning-augmented algorithms -- that is, they are consistent, robust and smooth -- despite being limited to a one-bit prediction per request. We also present lower bounds establishing that our algorithms are essentially best possible.

Antonios Antoniadis, Christian Coester, Marek Eliáš et al.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of $\ell$ predictors, we obtain a competitive ratio of $O(\ell^2)$, and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a $(1+ε)$-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the $k$-server problem.

Spyros Angelopoulos, Marcin Bienkowski, Christoph Dürr et al.

Contract scheduling is a widely studied framework for designing real-time systems with interruptible capabilities. Previous work has showed that a prediction on the interruption time can help improve the performance of contract-based systems, however it has relied on a single prediction that is provided by a deterministic oracle. In this work, we introduce and study more general and realistic learning-augmented settings in which the prediction is in the form of a probability distribution, or it is given as a set of multiple possible interruption times. For both prediction settings, we design and analyze schedules which perform optimally if the prediction is accurate, while simultaneously guaranteeing the best worst-case performance if the prediction is adversarial. We also provide evidence that the resulting system is robust to prediction errors in the distributional setting. Last, we present an experimental evaluation that confirms the theoretical findings, and illustrates the performance improvements that can be attained in practice.

Spyros Angelopoulos, Bertrand Simon

Online bidding is a classic optimization problem, with several applications in online decision-making, the design of interruptible systems, and the analysis of approximation algorithms. In this work, we study online bidding under learning-augmented settings that incorporate stochasticity, in either the prediction oracle or the algorithm itself. In the first part, we study bidding under distributional predictions, and find Pareto-optimal algorithms that offer the best-possible tradeoff between the consistency and the robustness of the algorithm. In the second part, we study the power and limitations of randomized bidding algorithms, by presenting upper and lower bounds on the consistency/robustness tradeoffs. Previous works focused predominantly on oracles that do not leverage stochastic information on the quality of the prediction, and deterministic algorithms.

Spyros Angelopoulos, Loris Marchal, Adrien Obrecht et al.

Large language models (LLMs) have demonstrated remarkable capabilities across a variety of tasks. One of the main challenges towards the successful deployment of LLMs is memory management, since they typically involve billions of parameters. To this end, architectures based on Mixture-of-Experts have been proposed, which aim to reduce the size of the parameters that are activated when producing a token. This raises the equally critical issue of efficiently managing the limited cache of the system, in that frequently used experts should be stored in the fast cache rather than in the slower secondary memory. In this work, we introduce and study a new paging problem that models expert management optimization. Our formulation captures both the layered architecture of LLMs and the requirement that experts are cached efficiently. We first present lower bounds on the competitive ratio of both deterministic and randomized algorithms, which show that under mild assumptions, LRU-like policies have good theoretical competitive performance. We then propose a layer-based extension of LRU that is tailored to the problem at hand. Extensive simulations on both synthetic datasets and actual traces of MoE usage show that our algorithm outperforms policies for the classic paging problem, such as the standard LRU.

Antonios Antoniadis, Christian Coester, Marek Eliáš et al.

We study the online problem of minimizing power consumption in systems with multiple power-saving states. During idle periods of unknown lengths, an algorithm has to choose between power-saving states of different energy consumption and wake-up costs. We develop a learning-augmented online algorithm that makes decisions based on (potentially inaccurate) predicted lengths of the idle periods. The algorithm's performance is near-optimal when predictions are accurate and degrades gracefully with increasing prediction error, with a worst-case guarantee almost identical to the optimal classical online algorithm for the problem. A key ingredient in our approach is a new algorithm for the online ski rental problem in the learning augmented setting with tight dependence on the prediction error. We support our theoretical findings with experiments.

Alexander Lindermayr, Nicole Megow, Bertrand Simon

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.