The use of machine learning models in consequential decision making often exacerbates societal inequity, in particular yielding disparate impact on members of marginalized groups defined by race and gender. The area under the ROC curve (AUC) is widely used to evaluate the performance of a scoring function in machine learning, but is studied in algorithmic fairness less than other performance metrics. Due to the pairwise nature of the AUC, defining an AUC-based group fairness metric is pairwise-dependent and may involve both \emph{intra-group} and \emph{inter-group} AUCs. Importantly, considering only one category of AUCs is not sufficient to mitigate unfairness in AUC optimization. In this paper, we propose a minimax learning and bias mitigation framework that incorporates both intra-group and inter-group AUCs while maintaining utility. Based on this Rawlsian framework, we design an efficient stochastic optimization algorithm and prove its convergence to the minimum group-level AUC. We conduct numerical experiments on both synthetic and real-world datasets to validate the effectiveness of the minimax framework and the proposed optimization algorithm.
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We consider the linear contextual multi-class multi-period packing problem~(LMMP) where the goal is to pack items such that the total vector of consumption is below a given budget vector and the total value is as large as possible. We consider the setting where the reward and the consumption vector associated with each action is a class-dependent linear function of the context, and the decision-maker receives bandit feedback. LMMP includes linear contextual bandits with knapsacks and online revenue management as special cases. We establish a new more efficient estimator which guarantees a faster convergence rate, and consequently, a lower regret in such problems. We propose a bandit policy that is a closed-form function of said estimated parameters. When the contexts are non-degenerate, the regret of the proposed policy is sublinear in the context dimension, the number of classes, and the time horizon~$T$ when the budget grows at least as $\sqrt{T}$. We also resolve an open problem posed in Agrawal & Devanur (2016), and extend the result to a multi-class setting. Our numerical experiments clearly demonstrate that the performance of our policy is superior to other benchmarks in the literature.
Evaluating fairness can be challenging in practice because the sensitive attributes of data are often inaccessible due to privacy constraints. The go-to approach that the industry frequently adopts is using off-the-shelf proxy models to predict the missing sensitive attributes, e.g. Meta [Alao et al., 2021] and Twitter [Belli et al., 2022]. Despite its popularity, there are three important questions unanswered: (1) Is directly using proxies efficacious in measuring fairness? (2) If not, is it possible to accurately evaluate fairness using proxies only? (3) Given the ethical controversy over inferring user private information, is it possible to only use weak (i.e. inaccurate) proxies in order to protect privacy? Our theoretical analyses show that directly using proxy models can give a false sense of (un)fairness. Second, we develop an algorithm that is able to measure fairness (provably) accurately with only three properly identified proxies. Third, we show that our algorithm allows the use of only weak proxies (e.g. with only 68.85%accuracy on COMPAS), adding an extra layer of protection on user privacy. Experiments validate our theoretical analyses and show our algorithm can effectively measure and mitigate bias. Our results imply a set of practical guidelines for practitioners on how to use proxies properly. Code is available at github.com/UCSC-REAL/fair-eval.
We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory conditions.We present a computationally efficient policy optimization algorithm for the challenging general setting of unknown dynamics and bandit feedback, featuring a combination of mirror-descent and least squares policy evaluation in an auxiliary MDP used to compute exploration bonuses.Our algorithm obtains an $\widetilde O(K^{6/7})$ regret bound, improving significantly over previous state-of-the-art of $\widetilde O (K^{14/15})$ in this setting. In addition, we present a version of the same algorithm under the assumption a simulator of the environment is available to the learner (but otherwise no exploratory assumptions are made), and prove it obtains state-of-the-art regret of $\widetilde O (K^{2/3})$.
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.
Distributed stochastic optimization has drawn great attention recently due to its effectiveness in solving large-scale machine learning problems. However, despite that numerous algorithms have been proposed with empirical successes, their theoretical guarantees are restrictive and rely on certain boundedness conditions on the stochastic gradients, varying from uniform boundedness to the relaxed growth condition. In addition, how to characterize the data heterogeneity among the agents and its impacts on the algorithmic performance remains challenging. In light of such motivations, we revisit the classical FedAvg algorithm for solving the distributed stochastic optimization problem and establish the convergence results under only a mild variance condition on the stochastic gradients for smooth nonconvex objective functions. Almost sure convergence to a stationary point is also established under the condition. Moreover, we discuss a more informative measurement for data heterogeneity as well as its implications.
We propose and study a novel mechanism design setup where each bidder holds two kinds of private information: (1) type variable, which can be misreported; (2) information variable, which the bidder may want to conceal or partially reveal, but importantly, not to misreport. We refer to bidders with such behaviors as strategically reticent bidders. Among others, one direct motivation of our model is the ad auction in which many ad platforms today elicit from each bidder not only their private value per conversion but also their private information about Internet users (e.g., user activities on the advertiser's websites) in order to improve the platform's estimation of conversion rates. We show that in this new setup, it is still possible to design mechanisms that are both Incentive and Information Compatible (IIC). We develop two different black-box transformations, which convert any mechanism $\mathcal{M}$ for classic bidders to a mechanism $\bar{\mathcal{M}}$ for strategically reticent bidders, based on either outcome of expectation or expectation of outcome, respectively. We identify properties of the original mechanism $\mathcal{M}$ under which the transformation leads to IIC mechanisms $\bar{\mathcal{M}}$. Interestingly, as corollaries of these results, we show that running VCG with bidders' expected values maximizes welfare, whereas the mechanism using expected outcome of Myerson's auction maximizes revenue. Finally, we study how regulation on the auctioneer's usage of information can lead to more robust mechanisms.
To address the bias exhibited by machine learning models, fairness criteria impose statistical constraints for ensuring equal treatment to all demographic groups, but typically at a cost to model performance. Understanding this tradeoff, therefore, underlies the design of fair and effective algorithms. This paper completes the characterization of the inherent tradeoff of demographic parity on classification problems in the most general multigroup, multiclass, and noisy setting. Specifically, we show that the minimum error rate is given by the optimal value of a Wasserstein-barycenter problem. More practically, this reformulation leads to a simple procedure for post-processing any pre-trained predictors to satisfy demographic parity in the general setting, which, in particular, yields the optimal fair classifier when applied to the Bayes predictor. We provide suboptimality and finite sample analyses for our procedure, and demonstrate precise control of the tradeoff of error rate for fairness on real-world datasets provided sufficient data.
In this paper, we study kernelized bandits with distributed biased feedback. This problem is motivated by several real-world applications (such as dynamic pricing, cellular network configuration, and policy making), where users from a large population contribute to the reward of the action chosen by a central entity, but it is difficult to collect feedback from all users. Instead, only biased feedback (due to user heterogeneity) from a subset of users may be available. In addition to such partial biased feedback, we are also faced with two practical challenges due to communication cost and computation complexity. To tackle these challenges, we carefully design a new \emph{distributed phase-then-batch-based elimination (\texttt{DPBE})} algorithm, which samples users in phases for collecting feedback to reduce the bias and employs \emph{maximum variance reduction} to select actions in batches within each phase. By properly choosing the phase length, the batch size, and the confidence width used for eliminating suboptimal actions, we show that \texttt{DPBE} achieves a sublinear regret of $\tilde{O}(T^{1-\alpha/2}+\sqrt{\gamma_T T})$, where $\alpha\in (0,1)$ is the user-sampling parameter one can tune. Moreover, \texttt{DPBE} can significantly reduce both communication cost and computation complexity in distributed kernelized bandits, compared to some variants of the state-of-the-art algorithms (originally developed for standard kernelized bandits). Furthermore, by incorporating various \emph{differential privacy} models (including the central, local, and shuffle models), we generalize \texttt{DPBE} to provide privacy guarantees for users participating in the distributed learning process. Finally, we conduct extensive simulations to validate our theoretical results and evaluate the empirical performance.
The industrialization of catalytic processes is of far more importance today than it has ever been before and kinetic models are essential tools for their industrialization. Kinetic models affect the design, the optimization and the control of catalytic processes, but they are not easy to obtain. Classical paradigms, such as mechanistic modeling require substantial domain knowledge, while data-driven and hybrid modeling lack interpretability. Consequently, a different approach called automated knowledge discovery has recently gained popularity. Many methods under this paradigm have been developed, where ALAMO, SINDy and genetic programming are notable examples. However, these methods suffer from important drawbacks: they require assumptions about model structures, scale poorly, lack robust and well-founded model selection routines, and they are sensitive to noise. To overcome these challenges, the present work constructs two methodological frameworks, Automated Discovery of Kinetics using a Strong/Weak formulation of symbolic regression, ADoK-S and ADoK-W, for the automated generation of catalytic kinetic models. We leverage genetic programming for model generation, a sequential optimization routine for model refinement, and a robust criterion for model selection. Both frameworks are tested against three computational case studies of increasing complexity. We showcase their ability to retrieve the underlying kinetic rate model with a limited amount of noisy data from the catalytic system, indicating a strong potential for chemical reaction engineering applications.
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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