Active Learning for Fair and Stable Online Allocations

We explore an active learning approach for dynamic fair resource allocation problems. Unlike previous work that assumes full feedback from all agents on their allocations, we consider feedback from a select subset of agents at each epoch of the online resource allocation process. Despite this restriction, our proposed algorithms provide regret bounds that are sub-linear in number of time-periods for various measures that include fairness metrics commonly used in resource allocation problems and stability considerations in matching mechanisms. The key insight of our algorithms lies in adaptively identifying the most informative feedback using dueling upper and lower confidence bounds. With this strategy, we show that efficient decision-making does not require extensive feedback and produces efficient outcomes for a variety of problem classes.

Low-Rank Online Dynamic Assortment with Dual Contextual Information

As e-commerce expands, delivering real-time personalized recommendations from vast catalogs poses a critical challenge for retail platforms. Maximizing revenue requires careful consideration of both individual customer characteristics and available item features to optimize assortments over time. In this paper, we consider the dynamic assortment problem with dual contexts -- user and item features. In high-dimensional scenarios, the quadratic growth of dimensions complicates computation and estimation. To tackle this challenge, we introduce a new low-rank dynamic assortment model to transform this problem into a manageable scale. Then we propose an efficient algorithm that estimates the intrinsic subspaces and utilizes the upper confidence bound approach to address the exploration-exploitation trade-off in online decision making. Theoretically, we establish a regret bound of $\tilde{O}((d_1+d_2)r\sqrt{T})$, where $d_1, d_2$ represent the dimensions of the user and item features respectively, $r$ is the rank of the parameter matrix, and $T$ denotes the time horizon. This bound represents a substantial improvement over prior literature, made possible by leveraging the low-rank structure. Extensive simulations and an application to the Expedia hotel recommendation dataset further demonstrate the advantages of our proposed method.

Pessimistic Causal Reinforcement Learning with Mediators for Confounded Offline Data

In real-world scenarios, datasets collected from randomized experiments are often constrained by size, due to limitations in time and budget. As a result, leveraging large observational datasets becomes a more attractive option for achieving high-quality policy learning. However, most existing offline reinforcement learning (RL) methods depend on two key assumptions--unconfoundedness and positivity--which frequently do not hold in observational data contexts. Recognizing these challenges, we propose a novel policy learning algorithm, PESsimistic CAusal Learning (PESCAL). We utilize the mediator variable based on front-door criterion to remove the confounding bias; additionally, we adopt the pessimistic principle to address the distributional shift between the action distributions induced by candidate policies, and the behavior policy that generates the observational data. Our key observation is that, by incorporating auxiliary variables that mediate the effect of actions on system dynamics, it is sufficient to learn a lower bound of the mediator distribution function, instead of the Q-function, to partially mitigate the issue of distributional shift. This insight significantly simplifies our algorithm, by circumventing the challenging task of sequential uncertainty quantification for the estimated Q-function. Moreover, we provide theoretical guarantees for the algorithms we propose, and demonstrate their efficacy through simulations, as well as real-world experiments utilizing offline datasets from a leading ride-hailing platform.

Rate-Optimal Rank Aggregation with Private Pairwise Rankings

In various real-world scenarios like recommender systems and political surveys, pairwise rankings are commonly collected and utilized for rank aggregation to obtain an overall ranking of items. However, preference rankings can reveal individuals' personal preferences, underscoring the need to protect them before releasing for downstream analysis. In this paper, we address the challenge of preserving privacy while ensuring the utility of rank aggregation based on pairwise rankings generated from the Bradley-Terry-Luce (BTL) model. Using the randomized response mechanism to perturb raw pairwise rankings is a common privacy protection strategy used in practice, but a critical challenge arises because the privatized rankings no longer adhere to the BTL model, resulting in significant bias in downstream rank aggregation tasks. Motivated from this, we propose a debiased randomized response mechanism to protect the raw pairwise rankings, ensuring consistent estimation of true preferences and rankings in downstream rank aggregation. Theoretically, we offer insights into the relationship between overall privacy guarantees and estimation errors from private ranking data, and establish minimax rates for estimation errors. This enables the determination of optimal privacy guarantees that balance consistency in rank aggregation with robust privacy protection. We also investigate convergence rates of expected ranking errors for partial and full ranking recovery, quantifying how privacy protection influences the specification of top-$K$ item sets and complete rankings. Our findings are validated through extensive simulations and a real application.

Online Tensor Inference

Recent technological advances have led to contemporary applications that demand real-time processing and analysis of sequentially arriving tensor data. Traditional offline learning, involving the storage and utilization of all data in each computational iteration, becomes impractical for high-dimensional tensor data due to its voluminous size. Furthermore, existing low-rank tensor methods lack the capability for statistical inference in an online fashion, which is essential for real-time predictions and informed decision-making. This paper addresses these challenges by introducing a novel online inference framework for low-rank tensor learning. Our approach employs Stochastic Gradient Descent (SGD) to enable efficient real-time data processing without extensive memory requirements, thereby significantly reducing computational demands. We establish a non-asymptotic convergence result for the online low-rank SGD estimator, nearly matches the minimax optimal rate of estimation error in offline models that store all historical data. Building upon this foundation, we propose a simple yet powerful online debiasing approach for sequential statistical inference in low-rank tensor learning. The entire online procedure, covering both estimation and inference, eliminates the need for data splitting or storing historical data, making it suitable for on-the-fly hypothesis testing. Given the sequential nature of our data collection, traditional analyses relying on offline methods and sample splitting are inadequate. In our analysis, we control the sum of constructed super-martingales to ensure estimates along the entire solution path remain within the benign region. Additionally, a novel spectral representation tool is employed to address statistical dependencies among iterative estimates, establishing the desired asymptotic normality.

Contextual Dynamic Pricing with Strategic Buyers

Personalized pricing, which involves tailoring prices based on individual characteristics, is commonly used by firms to implement a consumer-specific pricing policy. In this process, buyers can also strategically manipulate their feature data to obtain a lower price, incurring certain manipulation costs. Such strategic behavior can hinder firms from maximizing their profits. In this paper, we study the contextual dynamic pricing problem with strategic buyers. The seller does not observe the buyer's true feature, but a manipulated feature according to buyers' strategic behavior. In addition, the seller does not observe the buyers' valuation of the product, but only a binary response indicating whether a sale happens or not. Recognizing these challenges, we propose a strategic dynamic pricing policy that incorporates the buyers' strategic behavior into the online learning to maximize the seller's cumulative revenue. We first prove that existing non-strategic pricing policies that neglect the buyers' strategic behavior result in a linear $\Omega(T)$ regret with $T$ the total time horizon, indicating that these policies are not better than a random pricing policy. We then establish that our proposed policy achieves a sublinear regret upper bound of $O(\sqrt{T})$. Importantly, our policy is not a mere amalgamation of existing dynamic pricing policies and strategic behavior handling algorithms. Our policy can also accommodate the scenario when the marginal cost of manipulation is unknown in advance. To account for it, we simultaneously estimate the valuation parameter and the cost parameter in the online pricing policy, which is shown to also achieve an $O(\sqrt{T})$ regret bound. Extensive experiments support our theoretical developments and demonstrate the superior performance of our policy compared to other pricing policies that are unaware of the strategic behaviors.

Utility Theory of Synthetic Data Generation

Evaluating the utility of synthetic data is critical for measuring the effectiveness and efficiency of synthetic algorithms. Existing results focus on empirical evaluations of the utility of synthetic data, whereas the theoretical understanding of how utility is affected by synthetic data algorithms remains largely unexplored. This paper establishes utility theory from a statistical perspective, aiming to quantitatively assess the utility of synthetic algorithms based on a general metric. The metric is defined as the absolute difference in generalization between models trained on synthetic and original datasets. We establish analytical bounds for this utility metric to investigate critical conditions for the metric to converge. An intriguing result is that the synthetic feature distribution is not necessarily identical to the original one for the convergence of the utility metric as long as the model specification in downstream learning tasks is correct. Another important utility metric is model comparison based on synthetic data. Specifically, we establish sufficient conditions for synthetic data algorithms so that the ranking of generalization performances of models trained on the synthetic data is consistent with that from the original data. Finally, we conduct extensive experiments using non-parametric models and deep neural networks to validate our theoretical findings.

Ranking Differential Privacy

Rankings are widely collected in various real-life scenarios, leading to the leakage of personal information such as users' preferences on videos or news. To protect rankings, existing works mainly develop privacy protection on a single ranking within a set of ranking or pairwise comparisons of a ranking under the $\epsilon$-differential privacy. This paper proposes a novel notion called $\epsilon$-ranking differential privacy for protecting ranks. We establish the connection between the Mallows model (Mallows, 1957) and the proposed $\epsilon$-ranking differential privacy. This allows us to develop a multistage ranking algorithm to generate synthetic rankings while satisfying the developed $\epsilon$-ranking differential privacy. Theoretical results regarding the utility of synthetic rankings in the downstream tasks, including the inference attack and the personalized ranking tasks, are established. For the inference attack, we quantify how $\epsilon$ affects the estimation of the true ranking based on synthetic rankings. For the personalized ranking task, we consider varying privacy preferences among users and quantify how their privacy preferences affect the consistency in estimating the optimal ranking function. Extensive numerical experiments are carried out to verify the theoretical results and demonstrate the effectiveness of the proposed synthetic ranking algorithm.

Online Statistical Inference for Matrix Contextual Bandit

Contextual bandit has been widely used for sequential decision-making based on the current contextual information and historical feedback data. In modern applications, such context format can be rich and can often be formulated as a matrix. Moreover, while existing bandit algorithms mainly focused on reward-maximization, less attention has been paid to the statistical inference. To fill in these gaps, in this work we consider a matrix contextual bandit framework where the true model parameter is a low-rank matrix, and propose a fully online procedure to simultaneously make sequential decision-making and conduct statistical inference. The low-rank structure of the model parameter and the adaptivity nature of the data collection process makes this difficult: standard low-rank estimators are not fully online and are biased, while existing inference approaches in bandit algorithms fail to account for the low-rankness and are also biased. To address these, we introduce a new online doubly-debiasing inference procedure to simultaneously handle both sources of bias. In theory, we establish the asymptotic normality of the proposed online doubly-debiased estimator and prove the validity of the constructed confidence interval. Our inference results are built upon a newly developed low-rank stochastic gradient descent estimator and its non-asymptotic convergence result, which is also of independent interest.

Rate-Optimal Contextual Online Matching Bandit

Two-sided online matching platforms have been employed in various markets. However, agents' preferences in present market are usually implicit and unknown and must be learned from data. With the growing availability of side information involved in the decision process, modern online matching methodology demands the capability to track preference dynamics for agents based on their contextual information. This motivates us to consider a novel Contextual Online Matching Bandit prOblem (COMBO), which allows dynamic preferences in matching decisions. Existing works focus on multi-armed bandit with static preference, but this is insufficient: the two-sided preference changes as along as one-side's contextual information updates, resulting in non-static matching. In this paper, we propose a Centralized Contextual - Explore Then Commit (CC-ETC) algorithm to adapt to the COMBO. CC-ETC solves online matching with dynamic preference. In theory, we show that CC-ETC achieves a sublinear regret upper bound O(log(T)) and is a rate-optimal algorithm by proving a matching lower bound. In the experiments, we demonstrate that CC-ETC is robust to variant preference schemes, dimensions of contexts, reward noise levels, and contexts variation levels.