The distributed computation of a Nash equilibrium in aggregative games is gaining increased traction in recent years. Of particular interest is the mediator-free scenario where individual players only access or observe the decisions of their neighbors due to practical constraints. Given the competitive rivalry among participating players, protecting the privacy of individual players becomes imperative when sensitive information is involved. We propose a fully distributed equilibrium-computation approach for aggregative games that can achieve both rigorous differential privacy and guaranteed computation accuracy of the Nash equilibrium. This is in sharp contrast to existing differential-privacy solutions for aggregative games that have to either sacrifice the accuracy of equilibrium computation to gain rigorous privacy guarantees, or allow the cumulative privacy budget to grow unbounded, hence losing privacy guarantees, as iteration proceeds. Our approach uses independent noises across players, thus making it effective even when adversaries have access to all shared messages as well as the underlying algorithm structure. The encryption-free nature of the proposed approach, also ensures efficiency in computation and communication. The approach is also applicable in stochastic aggregative games, able to ensure both rigorous differential privacy and guaranteed computation accuracy of the Nash equilibrium when individual players only have stochastic estimates of their pseudo-gradient mappings. Numerical comparisons with existing counterparts confirm the effectiveness of the proposed approach.
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Online advertising platforms typically use auction mechanisms to allocate ad placements. Advertisers participate in a series of repeated auctions, and must select bids that will maximize their overall rewards while adhering to certain constraints. We focus on the scenario in which the advertiser has budget and return-on-investment (ROI) constraints. We investigate the problem of budget- and ROI-constrained bidding in repeated non-truthful auctions, such as first-price auctions, and present a best-of-both-worlds framework with no-regret guarantees under both stochastic and adversarial inputs. By utilizing the notion of interval regret, we demonstrate that our framework does not require knowledge of specific parameters of the problem which could be difficult to determine in practice. Our proof techniques can be applied to both the adversarial and stochastic cases with minimal modifications, thereby providing a unified perspective on the two problems. In the adversarial setting, we also show that it is possible to loosen the traditional requirement of having a strictly feasible solution to the offline optimization problem at each round.
We consider a distributionally robust stochastic optimization problem and formulate it as a stochastic two-level composition optimization problem with the use of the mean--semideviation risk measure. In this setting, we consider a single time-scale algorithm, involving two versions of the inner function value tracking: linearized tracking of a continuously differentiable loss function, and SPIDER tracking of a weakly convex loss function. We adopt the norm of the gradient of the Moreau envelope as our measure of stationarity and show that the sample complexity of $\mathcal{O}(\varepsilon^{-3})$ is possible in both cases, with only the constant larger in the second case. Finally, we demonstrate the performance of our algorithm with a robust learning example and a weakly convex, non-smooth regression example.
This paper considers Bayesian persuasion for routing games where information about the uncertain state of the network is provided by a traffic information system (TIS) using public signals. In this setup, the TIS commits to a signalling scheme and participants form a posterior belief about the state of the network based on prior beliefs and the received signal. They subsequently select routes minimizing their individual expected travel time under their posterior beliefs, giving rise to a Wardrop equilibrium. We investigate how the TIS can infer the prior beliefs held by the participants by designing suitable signalling schemes, and observing the equilibrium flows under different signals. We show that under mild conditions a signalling scheme that allows for exact inference of the prior exists. We then provide an iterative algorithm that finds such a scheme in a finite number of steps. We show that schemes designed by our algorithm are robust, in the sense that they can still identify the prior after a small enough perturbation. We also investigate the case where the population is divided among multiple priors, and give conditions under which the fraction associated to each prior can be identified. Several examples illustrate our results.
The analysis of data stored in multiple sites has become more popular, raising new concerns about the security of data storage and communication. Federated learning, which does not require centralizing data, is a common approach to preventing heavy data transportation, securing valued data, and protecting personal information protection. Therefore, determining how to aggregate the information obtained from the analysis of data in separate local sites has become an important statistical issue. The commonly used averaging methods may not be suitable due to data nonhomogeneity and incomparable results among individual sites, and applying them may result in the loss of information obtained from the individual analyses. Using a sequential method in federated learning with distributed computing can facilitate the integration and accelerate the analysis process. We develop a data-driven method for efficiently and effectively aggregating valued information by analyzing local data without encountering potential issues such as information security and heavy transportation due to data communication. In addition, the proposed method can preserve the properties of classical sequential adaptive design, such as data-driven sample size and estimation precision when applied to generalized linear models. We use numerical studies of simulated data and an application to COVID-19 data collected from 32 hospitals in Mexico, to illustrate the proposed method.
A number of learning models used in consequential domains, such as to assist in legal, banking, hiring, and healthcare decisions, make use of potentially sensitive users' information to carry out inference. Further, the complete set of features is typically required to perform inference. This not only poses severe privacy risks for the individuals using the learning systems, but also requires companies and organizations massive human efforts to verify the correctness of the released information. This paper asks whether it is necessary to require \emph{all} input features for a model to return accurate predictions at test time and shows that, under a personalized setting, each individual may need to release only a small subset of these features without impacting the final decisions. The paper also provides an efficient sequential algorithm that chooses which attributes should be provided by each individual. Evaluation over several learning tasks shows that individuals may be able to report as little as 10\% of their information to ensure the same level of accuracy of a model that uses the complete users' information.
Hierarchical Clustering is a popular unsupervised machine learning method with decades of history and numerous applications. We initiate the study of differentially private approximation algorithms for hierarchical clustering under the rigorous framework introduced by (Dasgupta, 2016). We show strong lower bounds for the problem: that any $\epsilon$-DP algorithm must exhibit $O(|V|^2/ \epsilon)$-additive error for an input dataset $V$. Then, we exhibit a polynomial-time approximation algorithm with $O(|V|^{2.5}/ \epsilon)$-additive error, and an exponential-time algorithm that meets the lower bound. To overcome the lower bound, we focus on the stochastic block model, a popular model of graphs, and, with a separation assumption on the blocks, propose a private $1+o(1)$ approximation algorithm which also recovers the blocks exactly. Finally, we perform an empirical study of our algorithms and validate their performance.
We propose a novel Bayesian inference framework for distributed differentially private linear regression. We consider a distributed setting where multiple parties hold parts of the data and share certain summary statistics of their portions in privacy-preserving noise. We develop a novel generative statistical model for privately shared statistics, which exploits a useful distributional relation between the summary statistics of linear regression. Bayesian estimation of the regression coefficients is conducted mainly using Markov chain Monte Carlo algorithms, while we also provide a fast version to perform Bayesian estimation in one iteration. The proposed methods have computational advantages over their competitors. We provide numerical results on both real and simulated data, which demonstrate that the proposed algorithms provide well-rounded estimation and prediction.
In online advertising, automated bidding (auto-bidding) has become a widely-used tool for advertisers to automatically make bids on different impressions in real time. Instead of submitting bids for each single impression, advertisers in auto-bidding submit their high-level objectives and constraints to the auto-bidding tool, and observe the cumulative advertising performances after all the auctions within a time period have been finished. Motivated by the features of automated bidding, we aim to design auctions with private financial constraints for value-maximizing bidders. Specifically, we consider budget and ROI, the two most common financial constraints in online advertising, as the private information of advertisers, and analyse the conditions of truthfulness. We show that every non-decreasing function with budget as input could be mapped to a truthful auction mechanism with budget and ROI as input, but this mapping procedure also introduces complex value grouping structures into mechanism design. To achieve feasible and implementable auctions, we design a truthful auto-bidding auction mechanism with adjustable rank score functions. As the key design to guarantee truthfulness, our auction utilizes the bidder's budget constraint to compute a critical ROI, which enables comparisons between the budget and ROI constraint. We conduct experiments under different auto-bidding settings to validate the performance of our proposed auction in terms of revenue and social welfare.
Modern data aggregation often takes the form of a platform collecting data from a network of users. More than ever, these users are now requesting that the data they provide is protected with a guarantee of privacy. This has led to the study of optimal data acquisition frameworks, where the optimality criterion is typically the maximization of utility for the agent trying to acquire the data. This involves determining how to allocate payments to users for the purchase of their data at various privacy levels. The main goal of this paper is to characterize a fair amount to pay users for their data at a given privacy level. We propose an axiomatic definition of fairness, analogous to the celebrated Shapley value. Two concepts for fairness are introduced. The first treats the platform and users as members of a common coalition and provides a complete description of how to divide the utility among the platform and users. In the second concept, fairness is defined only among users, leading to a potential fairness-constrained mechanism design problem for the platform. We consider explicit examples involving private heterogeneous data and show how these notions of fairness can be applied. To the best of our knowledge, these are the first fairness concepts for data that explicitly consider privacy constraints.
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.
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