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Will Wei Sun

Publications and source records attributed to Will Wei Sun.

At least 37 records · Page 2Linked to original sources

Dual Active Learning for Reinforcement Learning from Human Feedback

Aligning large language models (LLMs) with human preferences is critical to recent advances in generative artificial intelligence. Reinforcement learning from human feedback (RLHF) is widely applied to achieve this objective. A key step in RLHF is to learn the reward function from human feedback. However, human feedback is costly and time-consuming, making it essential to collect high-quality conversation data for human teachers to label. Additionally, different human teachers have different levels of expertise. It is thus critical to query the most appropriate teacher for their opinions. In this paper, we use offline reinforcement learning (RL) to formulate the alignment problem. Motivated by the idea of $D$-optimal design, we first propose a dual active reward learning algorithm for the simultaneous selection of conversations and teachers. Next, we apply pessimistic RL to solve the alignment problem, based on the learned reward estimator. Theoretically, we show that the reward estimator obtained through our proposed adaptive selection strategy achieves minimal generalized variance asymptotically, and prove that the sub-optimality of our pessimistic policy scales as $O(1/\sqrt{T})$ with a given sample budget $T$. Through simulations and experiments on LLMs, we demonstrate the effectiveness of our algorithm and its superiority over state-of-the-arts.

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Jointly Modeling and Clustering Tensors in High Dimensions

We consider the problem of jointly modeling and clustering populations of tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, we employ plausible dimension reduction assumptions that exploit the intrinsic structures of tensors such as low-rankness in the mean and separability in the covariance. In estimation, we develop an efficient high-dimensional expectation-conditional-maximization (HECM) algorithm that breaks the intractable optimization in the M-step into a sequence of much simpler conditional optimization problems, each of which is convex, admits regularization and has closed-form updating formulas. Our theoretical analysis is challenged by both the non-convexity in the EM-type estimation and having access to only the solutions of conditional maximizations in the M-step, leading to the notion of dual non-convexity. We demonstrate that the proposed HECM algorithm, with an appropriate initialization, converges geometrically to a neighborhood that is within statistical precision of the true parameter. The efficacy of our proposed method is demonstrated through comparative numerical experiments and an application to a medical study, where our proposal achieves an improved clustering accuracy over existing benchmarking methods.

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Privacy-Preserving Dynamic Assortment Selection

With the growing demand for personalized assortment recommendations, concerns over data privacy have intensified, highlighting the urgent need for effective privacy-preserving strategies. This paper presents a novel framework for privacy-preserving dynamic assortment selection using the multinomial logit (MNL) bandits model. Our approach employs a perturbed upper confidence bound method, integrating calibrated noise into user utility estimates to balance between exploration and exploitation while ensuring robust privacy protection. We rigorously prove that our policy satisfies Joint Differential Privacy (JDP), which better suits dynamic environments than traditional differential privacy, effectively mitigating inference attack risks. This analysis is built upon a novel objective perturbation technique tailored for MNL bandits, which is also of independent interest. Theoretically, we derive a near-optimal regret bound of $\tilde{O}(\sqrt{T})$ for our policy and explicitly quantify how privacy protection impacts regret. Through extensive simulations and an application to the Expedia hotel dataset, we demonstrate substantial performance enhancements over the benchmark method.

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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 $Ω(T)$ 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.

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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.

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Dynamic Matching Bandit For Two-Sided Online Markets

Two-sided online matching platforms are employed in various markets. However, agents' preferences in the current market are usually implicit and unknown, thus needing to be learned from data. With the growing availability of dynamic side information involved in the decision process, modern online matching methodology demands the capability to track shifting preferences for agents based on contextual information. This motivates us to propose a novel framework for this dynamic online matching problem with contextual information, which allows for dynamic preferences in matching decisions. Existing works focus on online matching with static preferences, but this is insufficient: the two-sided preference changes as soon as one side's contextual information updates, resulting in non-static matching. In this paper, we propose a dynamic matching bandit algorithm to adapt to this problem. The key component of the proposed dynamic matching algorithm is an online estimation of the preference ranking with a statistical guarantee. Theoretically, we show that the proposed dynamic matching algorithm delivers an agent-optimal stable matching result with high probability. In particular, we prove a logarithmic regret upper bound $\mathcal{O}(\log(T))$ and construct a corresponding instance-dependent matching regret lower bound. In the experiments, we demonstrate that dynamic matching algorithm is robust to various preference schemes, dimensions of contexts, reward noise levels, and context variation levels, and its application to a job-seeking market further demonstrates the practical usage of the proposed method.

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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.

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Stochastic Low-rank Tensor Bandits for Multi-dimensional Online Decision Making

Multi-dimensional online decision making plays a crucial role in many real applications such as online recommendation and digital marketing. In these problems, a decision at each time is a combination of choices from different types of entities. To solve it, we introduce stochastic low-rank tensor bandits, a class of bandits whose mean rewards can be represented as a low-rank tensor. We consider two settings, tensor bandits without context and tensor bandits with context. In the first setting, the platform aims to find the optimal decision with the highest expected reward, a.k.a, the largest entry of true reward tensor. In the second setting, some modes of the tensor are contexts and the rest modes are decisions, and the goal is to find the optimal decision given the contextual information. We propose two learning algorithms tensor elimination and tensor epoch-greedy for tensor bandits without context, and derive finite-time regret bounds for them. Comparing with existing competitive methods, tensor elimination has the best overall regret bound and tensor epoch-greedy has a sharper dependency on dimensions of the reward tensor. Furthermore, we develop a practically effective Bayesian algorithm called tensor ensemble sampling for tensor bandits with context. Extensive simulations and real analysis in online advertising data back up our theoretical findings and show that our algorithms outperform various state-of-the-art approaches that ignore the tensor low-rank structure.

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Online Regularization towards Always-Valid High-Dimensional Dynamic Pricing

Devising dynamic pricing policy with always valid online statistical learning procedure is an important and as yet unresolved problem. Most existing dynamic pricing policy, which focus on the faithfulness of adopted customer choice models, exhibit a limited capability for adapting the online uncertainty of learned statistical model during pricing process. In this paper, we propose a novel approach for designing dynamic pricing policy based regularized online statistical learning with theoretical guarantees. The new approach overcomes the challenge of continuous monitoring of online Lasso procedure and possesses several appealing properties. In particular, we make the decisive observation that the always-validity of pricing decisions builds and thrives on the online regularization scheme. Our proposed online regularization scheme equips the proposed optimistic online regularized maximum likelihood pricing (OORMLP) pricing policy with three major advantages: encode market noise knowledge into pricing process optimism; empower online statistical learning with always-validity over all decision points; envelop prediction error process with time-uniform non-asymptotic oracle inequalities. This type of non-asymptotic inference results allows us to design more sample-efficient and robust dynamic pricing algorithms in practice. In theory, the proposed OORMLP algorithm exploits the sparsity structure of high-dimensional models and secures a logarithmic regret in a decision horizon. These theoretical advances are made possible by proposing an optimistic online Lasso procedure that resolves dynamic pricing problems at the process level, based on a novel use of non-asymptotic martingale concentration. In experiments, we evaluate OORMLP in different synthetic and real pricing problem settings, and demonstrate that OORMLP advances the state-of-the-art methods.

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Distribution-free Contextual Dynamic Pricing

Contextual dynamic pricing aims to set personalized prices based on sequential interactions with customers. At each time period, a customer who is interested in purchasing a product comes to the platform. The customer's valuation for the product is a linear function of contexts, including product and customer features, plus some random market noise. The seller does not observe the customer's true valuation, but instead needs to learn the valuation by leveraging contextual information and historical binary purchase feedbacks. Existing models typically assume full or partial knowledge of the random noise distribution. In this paper, we consider contextual dynamic pricing with unknown random noise in the valuation model. Our distribution-free pricing policy learns both the contextual function and the market noise simultaneously. A key ingredient of our method is a novel perturbed linear bandit framework, where a modified linear upper confidence bound algorithm is proposed to balance the exploration of market noise and the exploitation of the current knowledge for better pricing. We establish the regret upper bound and a matching lower bound of our policy in the perturbed linear bandit framework and prove a sub-linear regret bound in the considered pricing problem. Finally, we demonstrate the superior performance of our policy on simulations and a real-life auto-loan dataset.

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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 $ε$-differential privacy. This paper proposes a novel notion called $ε$-ranking differential privacy for protecting ranks. We establish the connection between the Mallows model (Mallows, 1957) and the proposed $ε$-ranking differential privacy. This allows us to develop a multistage ranking algorithm to generate synthetic rankings while satisfying the developed $ε$-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 $ε$ 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.

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Online Bootstrap Inference For Policy Evaluation in Reinforcement Learning

The recent emergence of reinforcement learning has created a demand for robust statistical inference methods for the parameter estimates computed using these algorithms. Existing methods for statistical inference in online learning are restricted to settings involving independently sampled observations, while existing statistical inference methods in reinforcement learning (RL) are limited to the batch setting. The online bootstrap is a flexible and efficient approach for statistical inference in linear stochastic approximation algorithms, but its efficacy in settings involving Markov noise, such as RL, has yet to be explored. In this paper, we study the use of the online bootstrap method for statistical inference in RL. In particular, we focus on the temporal difference (TD) learning and Gradient TD (GTD) learning algorithms, which are themselves special instances of linear stochastic approximation under Markov noise. The method is shown to be distributionally consistent for statistical inference in policy evaluation, and numerical experiments are included to demonstrate the effectiveness of this algorithm at statistical inference tasks across a range of real RL environments.

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Covariate-assisted Sparse Tensor Completion

We aim to provably complete a sparse and highly-missing tensor in the presence of covariate information along tensor modes. Our motivation comes from online advertising where users click-through-rates (CTR) on ads over various devices form a CTR tensor that has about 96% missing entries and has many zeros on non-missing entries, which makes the standalone tensor completion method unsatisfactory. Beside the CTR tensor, additional ad features or user characteristics are often available. In this paper, we propose Covariate-assisted Sparse Tensor Completion (COSTCO) to incorporate covariate information for the recovery of the sparse tensor. The key idea is to jointly extract latent components from both the tensor and the covariate matrix to learn a synthetic representation. Theoretically, we derive the error bound for the recovered tensor components and explicitly quantify the improvements on both the reveal probability condition and the tensor recovery accuracy due to covariates. Finally, we apply COSTCO to an advertisement dataset consisting of a CTR tensor and ad covariate matrix, leading to 23% accuracy improvement over the baseline. An important by-product is that ad latent components from COSTCO reveal interesting ad clusters, which are useful for better ad targeting.

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Partially Observed Dynamic Tensor Response Regression

In modern data science, dynamic tensor data is prevailing in numerous applications. An important task is to characterize the relationship between such dynamic tensor and external covariates. However, the tensor data is often only partially observed, rendering many existing methods inapplicable. In this article, we develop a regression model with partially observed dynamic tensor as the response and external covariates as the predictor. We introduce the low-rank, sparsity and fusion structures on the regression coefficient tensor, and consider a loss function projected over the observed entries. We develop an efficient non-convex alternating updating algorithm, and derive the finite-sample error bound of the actual estimator from each step of our optimization algorithm. Unobserved entries in tensor response have imposed serious challenges. As a result, our proposal differs considerably in terms of estimation algorithm, regularity conditions, as well as theoretical properties, compared to the existing tensor completion or tensor response regression solutions. We illustrate the efficacy of our proposed method using simulations, and two real applications, a neuroimaging dementia study and a digital advertising study.

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Generalized Connectivity Matrix Response Regression with Applications in Brain Connectivity Studies

Multiple-subject network data are fast emerging in recent years, where a separate connectivity matrix is measured over a common set of nodes for each individual subject, along with subject covariates information. In this article, we propose a new generalized matrix response regression model, where the observed networks are treated as matrix-valued responses and the subject covariates as predictors. The new model characterizes the population-level connectivity pattern through a low-rank intercept matrix, and the effect of subject covariates through a sparse slope tensor. We develop an efficient alternating gradient descent algorithm for parameter estimation, and establish the non-asymptotic error bound for the actual estimator from the algorithm, which quantifies the interplay between the computational and statistical errors. We further show the strong consistency for graph community recovery, as well as the edge selection consistency. We demonstrate the efficacy of our method through simulations and two brain connectivity studies.

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Sparse Tensor Additive Regression

Tensors are becoming prevalent in modern applications such as medical imaging and digital marketing. In this paper, we propose a sparse tensor additive regression (STAR) that models a scalar response as a flexible nonparametric function of tensor covariates. The proposed model effectively exploits the sparse and low-rank structures in the tensor additive regression. We formulate the parameter estimation as a non-convex optimization problem, and propose an efficient penalized alternating minimization algorithm. We establish a non-asymptotic error bound for the estimator obtained from each iteration of the proposed algorithm, which reveals an interplay between the optimization error and the statistical rate of convergence. We demonstrate the efficacy of STAR through extensive comparative simulation studies, and an application to the click-through-rate prediction in online advertising.

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Provable Convex Co-clustering of Tensors

Cluster analysis is a fundamental tool for pattern discovery of complex heterogeneous data. Prevalent clustering methods mainly focus on vector or matrix-variate data and are not applicable to general-order tensors, which arise frequently in modern scientific and business applications. Moreover, there is a gap between statistical guarantees and computational efficiency for existing tensor clustering solutions due to the nature of their non-convex formulations. In this work, we bridge this gap by developing a provable convex formulation of tensor co-clustering. Our convex co-clustering (CoCo) estimator enjoys stability guarantees and its computational and storage costs are polynomial in the size of the data. We further establish a non-asymptotic error bound for the CoCo estimator, which reveals a surprising "blessing of dimensionality" phenomenon that does not exist in vector or matrix-variate cluster analysis. Our theoretical findings are supported by extensive simulated studies. Finally, we apply the CoCo estimator to the cluster analysis of advertisement click tensor data from a major online company. Our clustering results provide meaningful business insights to improve advertising effectiveness.

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Tensor Graphical Model: Non-convex Optimization and Statistical Inference

We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. A critical challenge in the estimation and inference of this model is the fact that its penalized maximum likelihood estimation involves minimizing a non-convex objective function. To address it, this paper makes two contributions: (i) In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with an optimal statistical rate of convergence. (ii) We propose a de-biased statistical inference procedure for testing hypotheses on the true support of the sparse precision matrices, and employ it for testing a growing number of hypothesis with false discovery rate (FDR) control. The asymptotic normality of our test statistic and the consistency of FDR control procedure are established. Our theoretical results are backed up by thorough numerical studies and our real applications on neuroimaging studies of Autism spectrum disorder and users' advertising click analysis bring new scientific findings and business insights. The proposed methods are encoded into a publicly available R package Tlasso.

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