3 research outputs found
A Unified Approach to Online Matching with Conflict-Aware Constraints
Online bipartite matching and allocation models are widely used to analyze and design markets such as Internet advertising, online labor, and crowdsourcing. Traditionally, vertices on one side of the market are fixed and known a priori, while vertices on the other side arrive online and are matched by a central agent to the offline side. The issue of possible conflicts among offline agents emerges in various real scenarios when we need to match each online agent with a set of offline agents.For example, in event-based social networks (e.g., Meetup), offline events conflict for some users since they will be unable to attend mutually-distant events at proximate times; in advertising markets, two competing firms may prefer not to be shown to one user simultaneously; and in online recommendation systems (e.g., Amazon Books), books of the same type “conflict” with each other in some sense due to the diversity requirement for each online buyer.The conflict nature inherent among certain offline agents raises significant challenges in both modeling and online algorithm design. In this paper, we propose a unifying model, generalizing the conflict models proposed in (She et al., TKDE 2016) and (Chen et al., TKDE 16). Our model can capture not only a broad class of conflict constraints on the offline side (which is even allowed to be sensitive to each online agent), but also allows a general arrival pattern for the online side (which is allowed to change over the online phase). We propose an efficient linear programming (LP) based online algorithm and prove theoretically that it has nearly-optimal online performance. Additionally, we propose two LP-based heuristics and test them against two natural baselines on both real and synthetic datasets. Our LP-based heuristics experimentally dominate the baseline algorithms, aligning with our theoretical predictions and supporting our unified approach
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Beyond Worst-Case Analysis for Sequential Decision Making
Traditionally, algorithms have been evaluated through worst-case analysis, where the input is presumed to take its worst possible configuration. However, in many real-world settings, the data is not adversarially constructed and, on the contrary, exhibits some recognizable patterns. This often leads worst-case guarantees to be poor indicators of algorithms' performance. To overcome this limitation, a growing body of work on Beyond Worst-Case analysis has recently emerged.
In this thesis, we are concerned with sequential decision-making problems, where an agent must take successive decisions over multiple time steps without knowing in advance the forthcoming input. Examples of such settings include ride-sharing, online retail or job scheduling. Motivated by the unprecedented surge of data in these domains, which may help to overcome worst-case barriers by allowing to predict at least partially the future, we explore three distinct frameworks for Beyond Worst-Case analysis of sequential decision-making: (i) semi-random models, (ii) parametric models, and (iii) algorithms with predictions. While they all pursue the same objective — using previously collected data to provide stronger theoretical guarantees —, these frameworks mainly differ in the way the data is utilized. We examine each of them separately and present novel results for five different online optimization problems: minimum cost matching, assortment optimization (with and without inventory constraints), pricing and scheduling