In this work we study the classic problem of online weighted paging with a probabilistic prediction model, in which we are given additional information about the input in the form of distributions over page requests, known as distributional online paging (DOP). This work continues a recent line of research on learning-augmented algorithms that incorporates machine-learning predictions in online algorithms, so as to go beyond traditional worst-case competitive analysis, thus circumventing known lower bounds for online paging. We first provide an efficient online algorithm that achieves a constant factor competitive ratio with respect to the best online algorithm (policy) for weighted DOP that follows from earlier work on the stochastic k-server problem. Our main contribution concerns the question of whether distributional information over a limited horizon suffices for obtaining a constant competitive factor. To this end, we define in a natural way a new predictive model with limited horizon, which we call Per-Request Stochastic Prediction (PRSP). We show that we can obtain a constant factor competitive algorithm with respect to the optimal online algorithm for this model.

Royi Rassin, Yaron Fairstein, Oren Kalinsky, Guy Kushilevitz, Nachshon Cohen, Alexander Libov, Yoav Goldberg. Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing. 2024.

Implicit feedback from users behavior is a natural and scalable source for training and evaluating ranking models in human-interactive systems. However, inherent biases such as the position bias are key obstacles to its effective usage. This is further accentuated in cases of extreme bias, where behavioral feedback can be collected exclusively on the top ranked result. In fact, in such cases, state-of-art debiasing methods cannot be applied. A prominent use case of extreme position bias is the voice shopping medium, where only a small amount of information can be presented to the user during a single interaction, resulting in user behavioral signals that are almost exclusively limited to the top offer. There is no way to know how the user would have reacted to a different offer than the top one he was actually exposed to. Thus, any new ranker we wish to evaluate with respect to a behavioral metric, requires online experimentation. We propose a novel approach, based on anexternal estimator model, for accurately predicting offline the performance of a new ranker. The accuracy of our solution is proven theoretically, as well as demonstrated by a line of experiments. In these experiments, we focus on the use case of purchase prediction, and show that our estimator can accurately predict offline the purchase rate of different rankers over a segment of voice shopping traffic. Our prediction is validated online, as being compared to the actual performance obtained by each ranker when being exposed to users.

The world is dynamic and changes over time, thus any optimization problem used to model real life problems must address this dynamic nature, taking into account the cost of changes to a solution over time. The multistage model was introduced with this goal in mind. In this model we are given a series of instances of an optimization problem, corresponding to different times, and a solution is provided for each instance. The strive for obtaining near-optimal solutions for each instance on one hand, while maintaining similar solutions for consecutive time units on the other hand, is quantified and integrated into the objective function. In this paper we consider the Generalized Multistage $d$-Knapsack problem, a generalization of the multistage variants of the Multiple Knapsack problem, as well as the $d$-Dimensional Knapsack problem. We present a PTAS for Generalized Multistage $d$-Knapsack.

A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to bin capacities. In this paper we present a unified algorithm that yields efficient approximations for a wide class of submodular and modular optimization problems involving multiple knapsack constraints. One notable example is a polynomial time approximation scheme for Multiple-Choice Multiple Knapsack, improving upon the best known ratio of $2$. Another example is Non-monotone Submodular Multiple Knapsack, for which we obtain a $(0.385-\varepsilon)$-approximation, matching the best known ratio for a single knapsack constraint. The robustness of our algorithm is achieved by applying a novel fractional variant of the classical linear grouping technique, which is of independent interest.

Multi-access Edge Computing (MEC) is a new networking paradigm considered to be one of the enablers of 5G networks. In particular, it allows for network operators to provide low latency services by moving the service logic from centralized datacenters to small distributed locations at the edge of a network. However, computing and storage resources at these edge nodes are scarce and thus efficient resource allocation becomes an essential building block in any MEC orchestration solution. In this paper we address one particular challenge in this domain - how to place network functions at the edge nodes in a way that maximizes the customers benefit. Thus, we formulate the Capacitated MEC Allocation Problem (CMAP) and provide multiple algorithms with analytical performance guarantees for this problem. Furthermore, we use extensive simulations to evaluate the performance of our algorithms in realistic scenarios and show that they outperform both the analytical worst case guarantees, as well as currently used network function placement methods.

We study the problem of maximizing a monotone submodular function subject to a Multiple Knapsack constraint (SMKP). The input is a set I of items, each associated with a non-negative weight, and a set of bins having arbitrary capacities. Also, we are given a submodular, monotone and non-negative function f over subsets of the items. The objective is to find a subset of items A ⊆ I and a packing of these items in the bins, such that f(A) is maximized. SMKP is a natural extension of both Multiple Knapsack and the problem of monotone submodular maximization subject to a knapsack constraint. Our main result is a nearly optimal polynomial time (1-e^{-1}-ε)-approximation algorithm for the problem, for any ε > 0. Our algorithm relies on a refined analysis of techniques for constrained submodular optimization combined with sophisticated application of tools used in the development of approximation schemes for packing problems.