Understanding the bias-variance tradeoff in user representation learning is essential for improving recommendation quality in modern content platforms. While well studied in static settings, this tradeoff becomes significantly more complex when content creators strategically adapt to platform incentives. To analyze how such competition reshapes the tradeoff for maximizing user welfare, we introduce the Content Creator Competition with Bias-Variance Tradeoff (C3BV ) framework, a tractable game-theoretic model that captures the platform's decision on regularization strength in user feature estimation. We derive and compare the platform's optimal policy under two key settings: a non-strategic baseline with fixed content and a strategic environment where creators compete in response to the platform's algorithmic design.

In this paper, we present the Proportional Payoff Allocation Game (PPA-Game), which characterizes situations where agents compete for divisible resources. In the PPA-game, agents select from available resources, and their payoffs are proportionately determined based on heterogeneous weights attributed to them. Such dynamics simulate content creators on online recommender systems like YouTube and TikTok, who compete for finite consumer attention, with content exposure reliant on inherent and distinct quality. We first conduct a game-theoretical analysis of the PPA-Game. While the PPA-Game does not always guarantee the existence of a pure Nash equilibrium (PNE), we identify prevalent scenarios ensuring its existence. Simulated experiments further prove that the cases where PNE does not exist rarely happen. Beyond analyzing static payoffs, we further discuss the agents' online learning about resource payoffs by integrating a multi-player multi-armed bandit framework. We propose an online algorithm facilitating each agent's maximization of cumulative payoffs over T rounds. Theoretically, we establish that the regret of any agent is bounded by O(log^1 + η T) for any η > 0. Empirical results further validate the effectiveness of our online learning approach.

Despite the encouraging successes in numerous applications, machine learning methods grounded on the i.i.d. assumption often experience performance deterioration when confronted with the distribution shift between training and test data. This challenge has instigated recent research endeavors focusing on out-of-distribution (OOD) generalization. A particularly pervasive and intricate OOD problem is to enhance the model's generalization ability by training it on samples drawn from a single environment. In response to the problem, we propose a simple model-agnostic method tailored for a practical OOD scenario in this paper. Our approach centers on pursuing robust weighted empirical risks, utilizing randomly shifted training distributions derived through a specific sample-based weighting strategy. Furthermore, we theoretically establish that the expected risk of the shifted training distribution can bound the expected risk of the test distribution. This theoretical foundation ensures the improved prediction performance of our method when employed in uncertain test distributions. Extensive experiments conducted on diverse real-world datasets affirm the effectiveness of our method, highlighting its potential to address the distribution shifts in machine learning applications.

Personalized pricing is a business strategy to charge different prices to individual consumers based on their characteristics and behaviors. It has become common practice in many industries nowadays due to the availability of a growing amount of high granular consumer data. The discriminatory nature of personalized pricing has triggered heated debates among policymakers and academics on how to design regulation policies to balance market efficiency and equity. In this paper, we propose two sound policy instruments, i.e., capping the range of the personalized prices or their ratios. We investigate the optimal pricing strategy of a profit-maximizing monopoly under both regulatory constraints and the impact of imposing them on consumer surplus, producer surplus, and social welfare. We theoretically prove that both proposed constraints can help balance consumer surplus and producer surplus at the expense of total surplus for common demand distributions, such as uniform, logistic, and exponential distributions. Experiments on both simulation and real-world datasets demonstrate the correctness of these theoretical results1. Our findings and insights shed light on regulatory policy design for the increasingly monopolized business in the digital era.

Discovering causal structure among a set of variables is a crucial task in various scientific and industrial scenarios. Given finite i.i.d. samples from a joint distribution, causal discovery is a challenging combinatorial problem in nature. The recent development in functional causal models, especially the NOTEARS provides a differentiable optimization framework for causal discovery. They formulate the structure learning problem as a task of maximum likelihood estimation over observational data (i.e., variable reconstruction) with specified structural constraints such as acyclicity and sparsity. Despite its success in terms of scalability, we find that optimizing the objectives of these differentiable methods is not always consistent with the correctness of learned causal graph especially when the variables carry heterogeneous noises (i.e., different noise types and noise variances) in real data from wild environments. In this paper, we provide the justification that their proneness to erroneous structures is mainly caused by the over-reconstruction problem, i.e., the noises of variables are absorbed into the variable reconstruction process, leading to the dependency among variable reconstruction residuals, and thus raise structure identifiability problems according to FCM theories. To remedy this, we propose a novel differentiable method DARING by imposing explicit residual independence constraint in an adversarial way. Extensive experimental results on both simulation and real data show that our proposed method is insensitive to the heterogeneity of external noise, and thus can significantly improve the causal discovery performances.

Nowadays fairness issues have raised great concerns in decision-making systems. Various fairness notions have been proposed to measure the degree to which an algorithm is unfair. In practice, there frequently exist a certain set of variables we term as fair variables, which are pre-decision covariates such as users' choices. The effects of fair variables are irrelevant in assessing the fairness of the decision support algorithm. We thus define conditional fairness as a more sound fairness metric by conditioning on the fairness variables. Given different prior knowledge of fair variables, we demonstrate that traditional fairness notations, such as demographic parity and equalized odds, are special cases of our conditional fairness notations. Moreover, we propose a Derivable Conditional Fairness Regularizer (DCFR), which can be integrated into any decision-making model, to track the trade-off between precision and fairness of algorithmic decision making. Specifically, an adversarial representation based conditional independence loss is proposed in our DCFR to measure the degree of unfairness. With extensive experiments on three real-world datasets, we demonstrate the advantages of our conditional fairness notation and DCFR.

Recent years witness the merge of social networks and user-generated content (UGC) platforms. In these new platforms, users establish links to others not only driven by their social relationships in the physical world but also driven by the contents published by others. During this merging process, social networks gradually integrate both social and content links and become unprecedentedly complicated, with the motivation to exploit both the advantages of social viscosity and content attractiveness to reach the best customer retention situation. However, due to the lack of fine-grained data recording such merging phenomena, the co-driven mechanism of social and content links in churn remains unexplored. How do social and content factors jointly influence customers' churn? What is the best ratio of social and content links for retention? Is there a model to capture this co-driven mechanism in churn phenomena? In this paper, we collect a real-world dataset with more than 5.77 million users and 1.15 billion links, with each link being tagged as a social one or a content one. We find that both social and content links have a significant impact on users' churn and they work jointly as a complicated mixture effect. As a result, we propose a novel survival model, which incorporates both social and content factors, to predict churn probability over time. Our model successfully fits the churn distribution in reality and accurately predicts the churn rate of different subpopulations in the future. By analyzing the modeling parameters, we try to strike a balance between social-driven and content-driven links in a user's social network to reach the lowest churn rate. Our model and findings may have potential implications for the design of future social media.