Algorithmic Collusion Without Threats

There has been substantial recent concern that pricing algorithms might learn to ``collude.'' Supra-competitive prices can emerge as a Nash equilibrium of repeated pricing games, in which sellers play strategies which threaten to punish their competitors who refuse to support high prices, and these strategies can be automatically learned. In fact, a standard economic intuition is that supra-competitive prices emerge from either the use of threats, or a failure of one party to optimize their payoff. Is this intuition correct? Would preventing threats in algorithmic decision-making prevent supra-competitive prices when sellers are optimizing for their own revenue? No. We show that supra-competitive prices can emerge even when both players are using algorithms which do not encode threats, and which optimize for their own revenue. We study sequential pricing games in which a first mover deploys an algorithm and then a second mover optimizes within the resulting environment. We show that if the first mover deploys any algorithm with a no-regret guarantee, and then the second mover even approximately optimizes within this now static environment, monopoly-like prices arise. The result holds for any no-regret learning algorithm deployed by the first mover and for any pricing policy of the second mover that obtains them profit at least as high as a random pricing would -- and hence the result applies even when the second mover is optimizing only within a space of non-responsive pricing distributions which are incapable of encoding threats. In fact, there exists a set of strategies, neither of which explicitly encode threats that form a Nash equilibrium of the simultaneous pricing game in algorithm space, and lead to near monopoly prices. This suggests that the definition of ``algorithmic collusion'' may need to be expanded, to include strategies without explicitly encoded threats.

Fairness Issues and Mitigations in (Differentially Private) Socio-demographic Data Processes

Statistical agencies rely on sampling techniques to collect socio-demographic data crucial for policy-making and resource allocation. This paper shows that surveys of important societal relevance introduce sampling errors that unevenly impact group-level estimates, thereby compromising fairness in downstream decisions. To address these issues, this paper introduces an optimization approach modeled on real-world survey design processes, ensuring sampling costs are optimized while maintaining error margins within prescribed tolerances. Additionally, privacy-preserving methods used to determine sampling rates can further impact these fairness issues. The paper explores the impact of differential privacy on the statistics informing the sampling process, revealing a surprising effect: not only the expected negative effect from the addition of noise for differential privacy is negligible, but also this privacy noise can in fact reduce unfairness as it positively biases smaller counts. These findings are validated over an extensive analysis using datasets commonly applied in census statistics.

Differentially Private Data Release on Graphs: Inefficiencies and Unfairness

Networks are crucial components of many sectors, including telecommunications, healthcare, finance, energy, and transportation.The information carried in such networks often contains sensitive user data, like location data for commuters and packet data for online users. Therefore, when considering data release for networks, one must ensure that data release mechanisms do not leak information about individuals, quantified in a precise mathematical sense. Differential Privacy (DP) is the widely accepted, formal, state-of-the-art technique, which has found use in a variety of real-life settings including the 2020 U.S. Census, Apple users' device data, or Google's location data. Yet, the use of DP comes with new challenges, as the noise added for privacy introduces inaccuracies or biases and further, DP techniques can also distribute these biases disproportionately across different populations, inducing fairness issues. The goal of this paper is to characterize the impact of DP on bias and unfairness in the context of releasing information about networks, taking a departure from previous work which has studied these effects in the context of private population counts release (such as in the U.S. Census). To this end, we consider a network release problem where the network structure is known to all, but the weights on edges must be released privately. We consider the impact of this private release on a simple downstream decision-making task run by a third-party, which is to find the shortest path between any two pairs of nodes and recommend the best route to users. This setting is of highly practical relevance, mirroring scenarios in transportation networks, where preserving privacy while providing accurate routing information is crucial. Our work provides theoretical foundations and empirical evidence into the bias and unfairness arising due to privacy in these networked decision problems.

Bayesian Strategic Classification

In strategic classification, agents modify their features, at a cost, to ideally obtain a positive classification from the learner's classifier. The typical response of the learner is to carefully modify their classifier to be robust to such strategic behavior. When reasoning about agent manipulations, most papers that study strategic classification rely on the following strong assumption: agents fully know the exact parameters of the deployed classifier by the learner. This often is an unrealistic assumption when using complex or proprietary machine learning techniques in real-world prediction tasks. We initiate the study of partial information release by the learner in strategic classification. We move away from the traditional assumption that agents have full knowledge of the classifier. Instead, we consider agents that have a common distributional prior on which classifier the learner is using. The learner in our model can reveal truthful, yet not necessarily complete, information about the deployed classifier to the agents. The learner's goal is to release just enough information about the classifier to maximize accuracy. We show how such partial information release can, counter-intuitively, benefit the learner's accuracy, despite increasing agents' abilities to manipulate. We show that while it is intractable to compute the best response of an agent in the general case, there exist oracle-efficient algorithms that can solve the best response of the agents when the learner's hypothesis class is the class of linear classifiers, or when the agents' cost function satisfies a natural notion of submodularity as we define. We then turn our attention to the learner's optimization problem and provide both positive and negative results on the algorithmic problem of how much information the learner should release about the classifier to maximize their expected accuracy.

Personalized Differential Privacy for Ridge Regression

The increased application of machine learning (ML) in sensitive domains requires protecting the training data through privacy frameworks, such as differential privacy (DP). DP requires to specify a uniform privacy level $\varepsilon$ that expresses the maximum privacy loss that each data point in the entire dataset is willing to tolerate. Yet, in practice, different data points often have different privacy requirements. Having to set one uniform privacy level is usually too restrictive, often forcing a learner to guarantee the stringent privacy requirement, at a large cost to accuracy. To overcome this limitation, we introduce our novel Personalized-DP Output Perturbation method (PDP-OP) that enables to train Ridge regression models with individual per data point privacy levels. We provide rigorous privacy proofs for our PDP-OP as well as accuracy guarantees for the resulting model. This work is the first to provide such theoretical accuracy guarantees when it comes to personalized DP in machine learning, whereas previous work only provided empirical evaluations. We empirically evaluate PDP-OP on synthetic and real datasets and with diverse privacy distributions. We show that by enabling each data point to specify their own privacy requirement, we can significantly improve the privacy-accuracy trade-offs in DP. We also show that PDP-OP outperforms the personalized privacy techniques of Jorgensen et al. (2015).

Oracle Efficient Algorithms for Groupwise Regret

We study the problem of online prediction, in which at each time step $t$, an individual $x_t$ arrives, whose label we must predict. Each individual is associated with various groups, defined based on their features such as age, sex, race etc., which may intersect. Our goal is to make predictions that have regret guarantees not just overall but also simultaneously on each sub-sequence comprised of the members of any single group. Previous work such as [Blum & Lykouris] and [Lee et al] provide attractive regret guarantees for these problems; however, these are computationally intractable on large model classes. We show that a simple modification of the sleeping experts technique of [Blum & Lykouris] yields an efficient reduction to the well-understood problem of obtaining diminishing external regret absent group considerations. Our approach gives similar regret guarantees compared to [Blum & Lykouris]; however, we run in time linear in the number of groups, and are oracle-efficient in the hypothesis class. This in particular implies that our algorithm is efficient whenever the number of groups is polynomially bounded and the external-regret problem can be solved efficiently, an improvement on [Blum & Lykouris]'s stronger condition that the model class must be small. Our approach can handle online linear regression and online combinatorial optimization problems like online shortest paths. Beyond providing theoretical regret bounds, we evaluate this algorithm with an extensive set of experiments on synthetic data and on two real data sets -- Medical costs and the Adult income dataset, both instantiated with intersecting groups defined in terms of race, sex, and other demographic characteristics. We find that uniformly across groups, our algorithm gives substantial error improvements compared to running a standard online linear regression algorithm with no groupwise regret guarantees.

Randomized Quantization is All You Need for Differential Privacy in Federated Learning

Federated learning (FL) is a common and practical framework for learning a machine model in a decentralized fashion. A primary motivation behind this decentralized approach is data privacy, ensuring that the learner never sees the data of each local source itself. Federated learning then comes with two majors challenges: one is handling potentially complex model updates between a server and a large number of data sources; the other is that de-centralization may, in fact, be insufficient for privacy, as the local updates themselves can reveal information about the sources' data. To address these issues, we consider an approach to federated learning that combines quantization and differential privacy. Absent privacy, Federated Learning often relies on quantization to reduce communication complexity. We build upon this approach and develop a new algorithm called the \textbf{R}andomized \textbf{Q}uantization \textbf{M}echanism (RQM), which obtains privacy through a two-levels of randomization. More precisely, we randomly sub-sample feasible quantization levels, then employ a randomized rounding procedure using these sub-sampled discrete levels. We are able to establish that our results preserve ``Renyi differential privacy'' (Renyi DP). We empirically study the performance of our algorithm and demonstrate that compared to previous work it yields improved privacy-accuracy trade-offs for DP federated learning. To the best of our knowledge, this is the first study that solely relies on randomized quantization without incorporating explicit discrete noise to achieve Renyi DP guarantees in Federated Learning systems.

Sequential Strategic Screening

We initiate the study of strategic behavior in screening processes with multiple classifiers. We focus on two contrasting settings: a conjunctive setting in which an individual must satisfy all classifiers simultaneously, and a sequential setting in which an individual to succeed must satisfy classifiers one at a time. In other words, we introduce the combination of strategic classification with screening processes. We show that sequential screening pipelines exhibit new and surprising behavior where individuals can exploit the sequential ordering of the tests to zig-zag between classifiers without having to simultaneously satisfy all of them. We demonstrate an individual can obtain a positive outcome using a limited manipulation budget even when far from the intersection of the positive regions of every classifier. Finally, we consider a learner whose goal is to design a sequential screening process that is robust to such manipulations, and provide a construction for the learner that optimizes a natural objective.

Information Discrepancy in Strategic Learning

We study a decision-making model where a principal deploys a scoring rule and the agents strategically invest effort to improve their scores. Unlike existing work in the strategic learning literature, we do not assume that the principal's scoring rule is fully known to the agents, and agents may form different estimates of the scoring rule based on their own sources of information. We focus on disparities in outcomes that stem from information discrepancies in our model. To do so, we consider a population of agents who belong to different subgroups, which determine their knowledge about the deployed scoring rule. Agents within each subgroup observe the past scores received by their peers, which allow them to construct an estimate of the deployed scoring rule and to invest their efforts accordingly. The principal, taking into account the agents' behaviors, deploys a scoring rule that maximizes the social welfare of the whole population. We provide a collection of theoretical results that characterize the impact of the welfare-maximizing scoring rules on the strategic effort investments across different subgroups. In particular, we identify sufficient and necessary conditions for when the deployed scoring rule incentivizes optimal strategic investment across all groups for different notions of optimality. Finally, we complement and validate our theoretical analysis with experimental results on the real-world datasets Taiwan-Credit and Adult.

Algorithms and Learning for Fair Portfolio Design

We consider a variation on the classical finance problem of optimal portfolio design. In our setting, a large population of consumers is drawn from some distribution over risk tolerances, and each consumer must be assigned to a portfolio of lower risk than her tolerance. The consumers may also belong to underlying groups (for instance, of demographic properties or wealth), and the goal is to design a small number of portfolios that are fair across groups in a particular and natural technical sense. Our main results are algorithms for optimal and near-optimal portfolio design for both social welfare and fairness objectives, both with and without assumptions on the underlying group structure. We describe an efficient algorithm based on an internal two-player zero-sum game that learns near-optimal fair portfolios ex ante and show experimentally that it can be used to obtain a small set of fair portfolios ex post as well. For the special but natural case in which group structure coincides with risk tolerances (which models the reality that wealthy consumers generally tolerate greater risk), we give an efficient and optimal fair algorithm. We also provide generalization guarantees for the underlying risk distribution that has no dependence on the number of portfolios and illustrate the theory with simulation results.