Publications

Key challenges in running a retail business include how to select products to present to consumers (the assortment problem), and how to price products (the pricing problem) to maximize revenue or profit. Instead of considering these problems in isolation, we propose a joint approach to assortment-pricing based on contextual bandits. Our model is doubly high-dimensional, in that both context vectors and actions allowed to take values in high-dimensional spaces. In order to circumvent the curse of dimensionality, we propose a simple yet flexible model that captures the interactions between covariates and actions via a (near) low-rank representation matrix. The resulting class of models is reasonably expressive while remaining interpretable through latent factors, and includes various structured linear bandit and pricing models as particular cases. We propose a computationally tractable procedure that combines an exploration/exploitation protocol with an efficient low-rank matrix estimator, and we prove bounds on its regret. Simulation results show that this method has lower regret than state-of-the-art methods applied to various standard bandit and pricing models. We also illustrate the gains achievable using our method by two case studies on real-world assortment-pricing problems for an industry-leading instant noodles company, and a smaller beauty start-up. In each case, we show both the gains in revenue achievable by our bandit methods, as well as the interpretability of the latent factor models that are learned.

The centrality in a network is often used to measure nodes’ importance and model network effects on a certain outcome. Empirical studies widely adopt a two-stage procedure, which first estimates the centrality from the observed noisy network and then infers the network effect from the estimated centrality, even though it lacks theoretical understanding. We propose a unified modeling framework, under which we first prove the shortcomings of the two-stage procedure, including the inconsistency of the centrality estimation and the invalidity of the network effect inference. Furthermore, we propose a supervised centrality estimation methodology, which aims to simultaneously estimate both centrality and network effect. The advantages in both regards are proved theoretically and demonstrated numerically via extensive simulations and a case study in predicting currency risk premiums from the global trade network.

Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a non-asymptotic local minimax framework, where the performance of a procedure is evaluated at individual functions. Fully adaptive and computationally efficient algorithms are proposed and sharp minimax lower bounds are given for both the estimation accuracy and expected length of confidence intervals for the minimizer and minimum. The non-asymptotic local minimax framework brings out new phenomena in simultaneous estimation and inference for the minimizer and minimum. We establish a novel Uncertainty Principle that provides a fundamental limit on how well the minimizer and minimum can be estimated simultaneously for any convex regression function. A similar result holds for the expected length of the confidence intervals for the minimizer and minimum.

This is the supplement to the paper Estimation and Inference for Minimizer and Minimum of Convex Functions: Optimality, Adaptivity, and Uncertainty Principles. It is organized into four sections. Section A presents the simulation results. Section B offers a comparison between our procedures and the methods based on convexity-constrained least squares for the minimizer, along with a discussion of the connections with the classical minimax framework. Section C provides the proofs of the main results, and Section D contains the proofs of supporting technical lemmas.

Reinforcement learning (RL), while has achieved remarkable success in low-stake fields (e.g., game), has come at expense of interpretability, reliability, and fundamental understanding. These attributes are of utmost importance in high-stake fields like business and healthcare, where ill-informed decisions can lead to significant financial losses or even loss of human lives. Particularly, the critical aspect of personalized information is often overlooked within traditional RL approaches, with the hope that complex and highly expressive models will somehow glean this information from limited data. In response to these challenges, we propose a personalized kernel embedding RL model to capture the heterogeneity in transition mechanism and reward. Our model is both expressive and interpretable. We develop an algorithm tailored for our personalized reinforcement learning model. We demonstrate the effectiveness of our algorithm through theoretical guarantee and numerical experiments.

MNL model is a traditional model addressing light-weight assortment problem. However, it fails to consider the dynamic nature of customer arrivals, which significantly impacts practical decision-making based on real-time periods like weeks, months, and years. To bridge this gap, we extend the MNL model by incorporating a Poisson distribution, where the arrival rate is dependent on the current assortment and pricing, thus modeling customer arrival patterns over time. The key challenge lies in balancing the popularity of the Poisson model to attract more customers and the profitability in the MNL to increase conversion and revenue for each visit so as to maximize the cumulative reward by a real-time period. We propose an efficient algorithm to jointly solve the Poisson and MNL model. We provide a non-asymptotic bound for regret and show that our algorithm is optimal up to log factors.

The popularity of iterative algorithms and the exploding availability of large data sets make the computational cost, in addition to statistical accuracy, an increasingly important concern in statistics and data science. In this paper, we propose a constructive framework that includes a theoretically solid fully implementable optimization method and gives precise quantification of how the running time influences the statistical accuracy. Our framework takes a new perspective on optimization-error-induced-statistical-error: we focus on approximated optimization problem rather than approximated solution. We show that this is more essential way to characterize optimization-statistical interplay. We showcase the power of our framework in three cases: 1-bit matrix completion and causal inference for panel data, and high-dimensional sparse linear regression. Our framework (a) filling in the blank of both theoretically guaranteed optimization algorithm and precise quantification of running-time’s influence on statistical accuracy for the first two cases; and (b) showing its adaptivity to the degenerate case with simpler setting and stronger assumptions — high-dimensional sparse linear regression. In addition, we provide a sharper statistical rate for the example of causal inference for panel data when the computational resource is assumed to be infinite.

In this paper, we consider optimal estimation and inference for the minimizer and minimum of multivariate additive convex functions under suitable non-asymptotic framework that can characterize the difficulty of the problem at individual functions. We provide sharp minimax lower bounds for both the estimation accuracy and expected volume (length) of confidence hypercube (interval) for the minimizer and minimum. We provide statistically optimal and computationally efficient algorithm for these four tasks.

Estimating heterogeneous treatment effect is an important task in causal inference with wide application fields. It has also attracted increasing attention from machine learning community in recent years. In this work, we reinterpret the heterogeneous treatment effect estimation and propose ways to borrow strength from neural networks. We analyze the strengths and drawbacks of integrating neural networks into heterogeneous treatment effect estimation and clarify the aspects that need to be taken into consideration when designing a specific network. We proposed a specific network under our guidelines. In simulations, we show that our network performs better when the structure of data is complex, and reach a draw under the cases where other methods could be proved to be optimal.