We conduct an independent, third-party audit for bias of LinkedIn's Talent Search ranking system, focusing on potential ranking bias across two attributes: gender and race. To do so, we first construct a dataset of rankings produced by the system, collecting extensive Talent Search results across a diverse set of occupational queries. We then develop a robust labeling pipeline that infers the two demographic attributes of interest for the returned users. To evaluate potential biases in the collected dataset of real-world rankings, we utilize two exposure disparity metrics: deviation from group proportions and MinSkew@k. Our analysis reveals an under-representation of minority groups in early ranks across many queries. We further examine potential causes of this disparity, and discuss why they may be difficult or, in some cases, impossible to fully eliminate among the early ranks of queries. Beyond static metrics, we also investigate the concept of subgroup fairness over time, highlighting \emph{temporal disparities} in exposure and retention, which are often more difficult to audit for in practice. In employer recruiting platforms such as LinkedIn Talent Search, the persistence of a particular candidate over multiple days in the ranking can directly impact the probability that the given candidate is selected for opportunities. Our analysis reveals demographic disparities in this temporal stability, with some groups experiencing greater volatility in their ranked positions than others. We contextualize all our findings alongside LinkedIn’s published self-audits of its Talent Search system and reflect on the methodological constraints of a black-box external evaluation, including limited observability and noisy demographic inference. Our work contributes empirical insights and practical guidance for conducting third-party audits of modern socio-technical systems which go beyond the well-studied and standard algorithmic fairness guarantees of predictors.

Calibration is a critical property for establishing the trustworthiness of predictors that provide uncertainty estimates. Multicalibration is a strengthening of calibration which requires that predictors be calibrated on a potentially overlapping collection of subsets of the domain. As multicalibration grows in popularity with practitioners, an essential question is: how do we measure how multicalibrated a predictor is? Błasiok et al. (2023) considered this question for standard calibration by introducing the distance to calibration framework (dCE) to understand how calibration metrics relate to each other and the ground truth. Building on the dCE framework, we consider the auditability of the distance to multicalibration of a predictor $f$. We begin by considering two natural generalizations of dCE to multiple subgroups: worst group dCE (wdMC), and distance to multicalibration (dMC). We argue that there are two essential properties of any multicalibration error metric: 1) the metric should capture how much $f$ would need to be modified in order to be perfectly multicalibrated; and 2) the metric should be auditable in an information theoretic sense. We show that wdMC and dMC each fail to satisfy one of these two properties, and that similar barriers arise when considering the auditability of general distance to multigroup fairness notions. We then propose two (equivalent) multicalibration metrics which do satisfy these requirements: 1) a continuized variant of dMC; and 2) a distance to intersection multicalibration, which leans on intersectional fairness desiderata. Along the way, we shed light on the loss-landscape of distance to multicalibration and the geometry of the set of perfectly multicalibrated predictors. Our findings may have implications for the development of stronger multicalibration algorithms as well as multigroup auditing more generally.

Proper learning refers to the setting in which learners must emit predictors in the underlying hypothesis class $\mathcal{H}$, and often leads to learners with simple algorithmic forms (e.g., empirical risk minimization (ERM), structural risk minimization (SRM)). The limitation of proper learning, however, is that there exist problems which can only be learned improperly, e.g. in multiclass classification. Thus, we ask: Under what assumptions on the hypothesis class or the information provided to the learner is a problem properly learnable? We first demonstrate that when the unlabeled data distribution is given, there always exists an optimal proper learner governed by \emph{distributional regularization}, a randomized generalization of regularization. We refer to this setting as the \emph{distribution-fixed} PAC model, and continue to evaluate the learner on its worst-case performance over all distributions. Our result holds for all metric loss functions and any finite learning problem (with no dependence on its size). Further, we demonstrate that sample complexities in the distribution-fixed PAC model can shrink by only a logarithmic factor from the classic PAC model, strongly refuting the role of unlabeled data in PAC learning (from a worst-case perspective). We complement this with impossibility results which obstruct any characterization of proper learnability in the classic (realizable) PAC model. First, we observe that there are problems whose proper learnability is logically \emph{undecidable}, i.e., independent of the ZFC axioms. We then show that proper learnability is not a monotone property of the underlying hypothesis class, and that it is not a \emph{local} property (in a precise sense). We also point out how the non-monotonicity of proper learning obstructs relaxations of the distribution-fixed model that preserve proper learnability, including natural notions of class-conditional learning of the unlabeled data distribution. Our impossibility results all hold even for the fundamental setting of multiclass classification, and go through a reduction of EMX learning (Ben-David et al., 2019) to proper classification which may be of independent interest.

The quintessential learning algorithm of empirical risk minimization (ERM) is known to fail in various settings for which uniform convergence does not characterize learning. Relatedly, the practice of machine learning is rife with considerably richer algorithmic techniques, perhaps the most notable of which is regularization. Nevertheless, no such technique or principle has broken away from the pack to characterize optimal learning in these more general settings. The purpose of this work is to precisely characterize the role of regularization in perhaps the simplest setting for which ERM fails: multiclass learning with arbitrary label sets. Using one-inclusion graphs (OIGs), we exhibit optimal learning algorithms that dovetail with tried-and-true algorithmic principles: Occam’s Razor as embodied by structural risk minimization (SRM), the principle of maximum entropy, and Bayesian inference. We also extract from OIGs a combinatorial sequence we term the Hall complexity, which is the first to characterize a problem’s transductive error rate exactly. Lastly, we introduce a generalization of OIGs and the transductive learning setting to the agnostic case, where we show that optimal orientations of Hamming graphs – judged using nodes’ outdegrees minus a system of node-dependent credits – characterize optimal learners exactly. We demonstrate that an agnostic version of the Hall complexity again characterizes error rates exactly, and exhibit an optimal learner using maximum entropy programs.

Multiclass classification is the simple generalization of binary classification to arbitrary label sets. Despite its simplicity, it has been remarkably resistant to study: a characterization of multiclass learnability was established only two years ago by Brukhim et al. 2022, and the understanding of optimal learners for multiclass problems remains fairly limited. We ask whether there exists a simple algorithmic template — akin to empirical risk minimization (ERM) for binary classification — which characterizes multiclass learning. Namely, we ask whether local regularization, introduced by Asilis et al. 2024, is sufficiently expressive to learn all multiclass problems possible. Towards (negatively) resolving the problem, we propose a hypothesis class which may not be learnable by any such local regularizer.

Rankings are ubiquitous across many applications, from search engines to hiring committees. In practice, many rankings are derived from the output of predictors. However, when predictors trained for classification tasks have intrinsic uncertainty, it is not obvious how this uncertainty should be represented in the derived rankings. Our work considers ranking functions: maps from individual predictions for a classification task to distributions over rankings. We focus on two aspects of ranking functions: stability to perturbations in predictions and fairness towards both individuals and subgroups. Not only is stability an important requirement for its own sake, but --- as we show --- it composes harmoniously with individual fairness in the sense of Dwork et al. (2012). While deterministic ranking functions cannot be stable aside from trivial scenarios, we show that the recently proposed uncertainty aware (UA) ranking functions of Singh et al. (2021) are stable. Our main result is that UA rankings also achieve group fairness through successful composition with multiaccurate or multicalibrated predictors. Our work demonstrates that UA rankings naturally interpolate between group and individual level fairness guarantees, while simultaneously satisfying stability guarantees important whenever machine-learned predictions are used.

We demonstrate a compactness result holding broadly across supervised learning with a general class of loss functions: Any hypothesis class $\mathcal{H}$ is learnable with transductive sample complexity $m$ precisely when all of its finite projections are learnable with sample complexity $m$. We prove that this exact form of compactness holds for realizable and agnostic learning with respect to all proper metric loss functions (e.g., any norm on $\mathbb{R}^d$) and any continuous loss on a compact space (e.g., cross-entropy, squared loss). For realizable learning with improper metric losses, we show that exact compactness of sample complexity can fail, and provide matching upper and lower bounds of a factor of 2 on the extent to which such sample complexities can differ. We conjecture that larger gaps are possible for the agnostic case. Furthermore, invoking the equivalence between sample complexities in the PAC and transductive models (up to lower order factors, in the realizable case) permits us to directly port our results to the PAC model, revealing an almost-exact form of compactness holding broadly in PAC learning.

Calibration is a well-studied property of predictors which guarantees meaningful uncertainty estimates. Multicalibration is a related notion --- originating in algorithmic fairness --- which requires predictors to be simultaneously calibrated over a potentially complex and overlapping collection of protected subpopulations (such as groups defined by ethnicity, race, or income). We conduct the first comprehensive study evaluating the usefulness of multicalibration post-processing across a broad set of tabular, image, and language datasets for models spanning from simple decision trees to 90 million parameter fine-tuned LLMs. Our findings can be summarized as follows: (1) models which are calibrated out of the box tend to be relatively multicalibrated without any additional post-processing; (2) multicalibration can help inherently uncalibrated models and also large vision and language models; and (3) traditional calibration measures may sometimes provide multicalibration implicitly. More generally, we also distill many independent observations which may be useful for practical and effective applications of multicalibration post-processing in real-world contexts.

The prevalence and importance of algorithmic two-sided marketplaces has drawn attention to the issue of fairness in such settings. Algorithmic decisions are used in assigning students to schools, users to advertisers, and applicants to job interviews. These decisions should heed the preferences of individuals, and simultaneously be fair with respect to their merits (synonymous with fit, future performance, or need). Merits conditioned on observable features are always *uncertain*, a fact that is exacerbated by the widespread use of machine learning algorithms to infer merit from the observables. As our key contribution, we carefully axiomatize a notion of individual fairness in the two-sided marketplace setting which respects the uncertainty in the merits; indeed, it simultaneously recognizes uncertainty as the primary potential cause of unfairness and an approach to address it. We design a linear programming framework to find fair utility-maximizing distributions over allocations, and we show that the linear program is robust to perturbations in the estimated parameters of the uncertain merit distributions, a key property in combining the approach with machine learning techniques.

Many reinforcement learning (RL) environments in practice feature enormous state spaces that may be described compactly by a "factored" structure, that may be modeled by Factored Markov Decision Processes (FMDPs). We present the first polynomial time algorithm for RL in Factored State MDPs (generalizing FMDPs) that neither relies on an oracle planner nor requires a linear transition model; it only requires a linear value function with a suitable local basis with respect to the factorization, permitting efficient variable elimination. With this assumption, we can solve this family of Factored State MDPs in polynomial time by constructing an efficient separation oracle for convex optimization. Importantly, and in contrast to prior work on FMDPs, we do not assume that the transitions on various factors are conditionally independent.

The emergence of diverse network applications demands more flexible and responsive resource allocation for networks. Network slicing is a key enabling technology that provides each network service with a tailored set of network resources to satisfy specific service requirements. The focus of this paper is the network slicing of access networks realized by Passive Optical Networks (PONs). This paper proposes a learning-based Dynamic Bandwidth Allocation (DBA) algorithm for PON access networks, considering slice-awareness, demand-responsiveness, and allocation fairness. Our online convex optimization-based algorithm learns the implicit traffic trend over time and determines the most robust window allocation that reduces the average latency. Our simulation results indicate that the proposed algorithm reduces the average latency by prioritizing delay-sensitive and heavily-loaded ONUs while guaranteeing a minimal window allocation to all ONUs.

The increasing demand for diverse network services entails more flexible networks that are realized by virtualized network equipment and functions. When such advanced network systems face a massive failure by natural disasters or attacks, the recovery of the entire system may be conducted progressively due to limited repair resources. The prioritization of network equipment in the recovery phase influences the interim computation and communication capability of systems since the systems are operated under partial functionality. Hence, finding the best recovery order is a critical problem, which is further complicated by virtualization due to the interdependence between virtual network functions and infrastructure elements. This paper deals with a progressive recovery problem under limited resources in networks with VNFs, where some interdependencies exist. We prove the NP-hardness of the progressive recovery problem and approach the optimum solution by introducing DeepPR, a progressive recovery technique based on Deep Reinforcement Learning (Deep RL). Our simulation results indicate that DeepPR can achieve near-optimal solutions in certain networks and is more robust to adversarial failures, compared to a baseline heuristic algorithm.

The increasing reliance upon cloud services entails more flexible networks that are realized by virtualized network equipment and functions. When such advanced network systems face a massive failure by natural disasters or attacks, the recovery of the entire system may be conducted in a progressive way due to limited repair resources. The prioritization of network equipment in the recovery phase influences the interim computation and communication capability of systems, since the systems are operated under partial functionality. Hence, finding the best recovery order is a critical problem, which is further complicated by virtualization due to dependency among network nodes and layers. This paper deals with a progressive recovery problem under limited resources in networks with VNFs, where some dependent network layers exist. We prove the NP-hardness of the progressive recovery problem and approach the optimum solution by introducing DeepPR, a progressive recovery technique based on deep reinforcement learning. Our simulation results indicate that DeepPR can obtain 98.4% of the theoretical optimum in certain networks.