We study the computational complexity of finding fair allocations of indivisible goods in the setting where a social network on the agents is given. Notions of fairness in this context are "localized", that is, agents are only concerned about the bundles allocated to their neighbors, rather than every other agent in the system. We comprehensively address the computational complexity of finding locally envy-free and Pareto efficient allocations in the setting where the agents have binary valuations for the goods and the underlying social network is modeled by an undirected graph. We study the problem in the framework of parameterized complexity. We show that the problem is computationally intractable even in fairly restricted scenarios, for instance, even when the underlying graph is a path. We show NP-hardness for settings where the graph has only two distinct valuations among the agents. We demonstrate W-hardness with respect to the number of goods or the size of the vertex cover of the underlying graph. We also consider notions of proportionality that respect the structure of the underlying graph and show that two natural versions of this notion have different complexities: allocating according to the notion that accounts for locality to the greatest degree turns out to be computationally intractable, while for other notions, the allocation problem can be modeled as a structured ILP which can be solved efficiently.
相關內容
As machine learning becomes more widely adopted across domains, it is critical that researchers and ML engineers think about the inherent biases in the data that may be perpetuated by the model. Recently, many studies have shown that such biases are also imbibed in Graph Neural Network (GNN) models if the input graph is biased. In this work, we aim to mitigate the bias learned by GNNs through modifying the input graph. To that end, we propose FairMod, a Fair Graph Modification methodology with three formulations: the Global Fairness Optimization (GFO), Community Fairness Optimization (CFO), and Fair Edge Weighting (FEW) models. Our proposed models perform either microscopic or macroscopic edits to the input graph while training GNNs and learn node embeddings that are both accurate and fair under the context of link recommendations. We demonstrate the effectiveness of our approach on four real world datasets and show that we can improve the recommendation fairness by several factors at negligible cost to link prediction accuracy.
We consider a network of agents. Associated with each agent are her covariate and outcome. Agents influence each other's outcomes according to a certain connection/influence structure. A subset of the agents participate on a platform, and hence, are observable to it. The rest are not observable to the platform and are called the latent agents. The platform does not know the influence structure of the observable or the latent parts of the network. It only observes the data on past covariates and decisions of the observable agents. Observable agents influence each other both directly and indirectly through the influence they exert on the latent agents. We investigate how the platform can estimate the dependence of the observable agents' outcomes on their covariates, taking the latent agents into account. First, we show that this relationship can be succinctly captured by a matrix and provide an algorithm for estimating it under a suitable approximate sparsity condition using historical data of covariates and outcomes for the observable agents. We also obtain convergence rates for the proposed estimator despite the high dimensionality that allows more agents than observations. Second, we show that the approximate sparsity condition holds under the standard conditions used in the literature. Hence, our results apply to a large class of networks. Finally, we apply our results to two practical settings: targeted advertising and promotional pricing. We show that by using the available historical data with our estimator, it is possible to obtain asymptotically optimal advertising/pricing decisions, despite the presence of latent agents.
Given a graph $G = (V,E)$, a threshold function $t~ :~ V \rightarrow \mathbb{N}$ and an integer $k$, we study the Harmless Set problem, where the goal is to find a subset of vertices $S \subseteq V$ of size at least $k$ such that every vertex $v\in V$ has less than $t(v)$ neighbors in $S$. We enhance our understanding of the problem from the viewpoint of parameterized complexity. Our focus lies on parameters that measure the structural properties of the input instance. We show that the problem is W[1]-hard parameterized by a wide range of fairly restrictive structural parameters such as the feedback vertex set number, pathwidth, treedepth, and even the size of a minimum vertex deletion set into graphs of pathwidth and treedepth at most three. On dense graphs, we show that the problem is W[1]-hard parameterized by cluster vertex deletion number. We also show that the Harmless Set problem with majority thresholds is W[1]-hard when parameterized by the treewidth of the input graph. We prove that the Harmless Set problem can be solved in polynomial time on graph with bounded cliquewidth. On the positive side, we obtain fixed-parameter algorithms for the problem with respect to neighbourhood diversity, twin cover and vertex integrity of the input graph. We show that the problem parameterized by the solution size is fixed parameter tractable on planar graphs. We thereby resolve two open questions stated in C. Bazgan and M. Chopin (2014) concerning the complexity of {\sc Harmless Set} parameterized by the treewidth of the input graph and on planar graphs with respect to the solution size.
Cloud platforms run many software agents on each server node. These agents manage all aspects of node operation, and in some cases frequently collect data and make decisions. Unfortunately, their behavior is typically based on pre-defined static heuristics or offline analysis; they do not leverage on-node machine learning (ML). In this paper, we first characterize the spectrum of node agents in Azure, and identify the classes of agents that are most likely to benefit from on-node ML. We then propose SOL, an extensible framework for designing ML-based agents that are safe and robust to the range of failure conditions that occur in production. SOL provides a simple API to agent developers and manages the scheduling and running of the agent-specific functions they write. We illustrate the use of SOL by implementing three ML-based agents that manage CPU cores, node power, and memory placement. Our experiments show that (1) ML substantially improves our agents, and (2) SOL ensures that agents operate safely under a variety of failure conditions. We conclude that ML-based agents show significant potential and that SOL can help build them.
AI is undergoing a paradigm shift with the rise of models (e.g., BERT, DALL-E, GPT-3) that are trained on broad data at scale and are adaptable to a wide range of downstream tasks. We call these models foundation models to underscore their critically central yet incomplete character. This report provides a thorough account of the opportunities and risks of foundation models, ranging from their capabilities (e.g., language, vision, robotics, reasoning, human interaction) and technical principles(e.g., model architectures, training procedures, data, systems, security, evaluation, theory) to their applications (e.g., law, healthcare, education) and societal impact (e.g., inequity, misuse, economic and environmental impact, legal and ethical considerations). Though foundation models are based on standard deep learning and transfer learning, their scale results in new emergent capabilities,and their effectiveness across so many tasks incentivizes homogenization. Homogenization provides powerful leverage but demands caution, as the defects of the foundation model are inherited by all the adapted models downstream. Despite the impending widespread deployment of foundation models, we currently lack a clear understanding of how they work, when they fail, and what they are even capable of due to their emergent properties. To tackle these questions, we believe much of the critical research on foundation models will require deep interdisciplinary collaboration commensurate with their fundamentally sociotechnical nature.
With the overwhelming popularity of Knowledge Graphs (KGs), researchers have poured attention to link prediction to fill in missing facts for a long time. However, they mainly focus on link prediction on binary relational data, where facts are usually represented as triples in the form of (head entity, relation, tail entity). In practice, n-ary relational facts are also ubiquitous. When encountering such facts, existing studies usually decompose them into triples by introducing a multitude of auxiliary virtual entities and additional triples. These conversions result in the complexity of carrying out link prediction on n-ary relational data. It has even proven that they may cause loss of structure information. To overcome these problems, in this paper, we represent each n-ary relational fact as a set of its role and role-value pairs. We then propose a method called NaLP to conduct link prediction on n-ary relational data, which explicitly models the relatedness of all the role and role-value pairs in an n-ary relational fact. We further extend NaLP by introducing type constraints of roles and role-values without any external type-specific supervision, and proposing a more reasonable negative sampling mechanism. Experimental results validate the effectiveness and merits of the proposed methods.
When the federated learning is adopted among competitive agents with siloed datasets, agents are self-interested and participate only if they are fairly rewarded. To encourage the application of federated learning, this paper employs a management strategy, i.e., more contributions should lead to more rewards. We propose a novel hierarchically fair federated learning (HFFL) framework. Under this framework, agents are rewarded in proportion to their pre-negotiated contribution levels. HFFL+ extends this to incorporate heterogeneous models. Theoretical analysis and empirical evaluation on several datasets confirm the efficacy of our frameworks in upholding fairness and thus facilitating federated learning in the competitive settings.
We investigate the problem of fair recommendation in the context of two-sided online platforms, comprising customers on one side and producers on the other. Traditionally, recommendation services in these platforms have focused on maximizing customer satisfaction by tailoring the results according to the personalized preferences of individual customers. However, our investigation reveals that such customer-centric design may lead to unfair distribution of exposure among the producers, which may adversely impact their well-being. On the other hand, a producer-centric design might become unfair to the customers. Thus, we consider fairness issues that span both customers and producers. Our approach involves a novel mapping of the fair recommendation problem to a constrained version of the problem of fairly allocating indivisible goods. Our proposed FairRec algorithm guarantees at least Maximin Share (MMS) of exposure for most of the producers and Envy-Free up to One item (EF1) fairness for every customer. Extensive evaluations over multiple real-world datasets show the effectiveness of FairRec in ensuring two-sided fairness while incurring a marginal loss in the overall recommendation quality.
Neural networks have succeeded in many reasoning tasks. Empirically, these tasks require specialized network structures, e.g., Graph Neural Networks (GNNs) perform well on many such tasks, but less structured networks fail. Theoretically, there is limited understanding of why and when a network structure generalizes better than others, although they have equal expressive power. In this paper, we develop a framework to characterize which reasoning tasks a network can learn well, by studying how well its computation structure aligns with the algorithmic structure of the relevant reasoning process. We formally define this algorithmic alignment and derive a sample complexity bound that decreases with better alignment. This framework offers an explanation for the empirical success of popular reasoning models, and suggests their limitations. As an example, we unify seemingly different reasoning tasks, such as intuitive physics, visual question answering, and shortest paths, via the lens of a powerful algorithmic paradigm, dynamic programming (DP). We show that GNNs align with DP and thus are expected to solve these tasks. On several reasoning tasks, our theory is supported by empirical results.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191