arXiv subjects

Ethan X. Fang

Publications and source records attributed to Ethan X. Fang.

At least 37 records · Page 2Linked to original sources

arXiv2026

In-Context Reinforcement Learning From Suboptimal Historical Data

Transformer models have achieved remarkable empirical successes, largely due to their in-context learning capabilities. Inspired by this, we explore training an autoregressive transformer for in-context reinforcement learning (ICRL). In this setting, we initially train a transformer on an offline dataset consisting of trajectories collected from various RL tasks, and then fix and use this transformer to create an action policy for new RL tasks. Notably, we consider the setting where the offline dataset contains trajectories sampled from suboptimal behavioral policies. In this case, standard autoregressive training corresponds to imitation learning and results in suboptimal performance. To address this, we propose the Decision Importance Transformer(DIT) framework, which emulates the actor-critic algorithm in an in-context manner. In particular, we first train a transformer-based value function that estimates the advantage functions of the behavior policies that collected the suboptimal trajectories. Then we train a transformer-based policy via a weighted maximum likelihood estimation loss, where the weights are constructed based on the trained value function to steer the suboptimal policies to the optimal ones. We conduct extensive experiments to test the performance of DIT on both bandit and Markov Decision Process problems. Our results show that DIT achieves superior performance, particularly when the offline dataset contains suboptimal historical data.

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arXiv2025

PASTA: A Unified Framework for Offline Assortment Learning

We study a broad class of assortment optimization problems in an offline and data-driven setting. In such problems, a firm lacks prior knowledge of the underlying choice model, and aims to determine an optimal assortment based on historical customer choice data. The combinatorial nature of assortment optimization often results in insufficient data coverage, posing a significant challenge in designing provably effective solutions. To address this, we introduce a novel Pessimistic Assortment Optimization (PASTA) framework that leverages the principle of pessimism to achieve optimal expected revenue under general choice models. Notably, PASTA requires only that the offline data distribution contains an optimal assortment, rather than providing the full coverage of all feasible assortments. Theoretically, we establish the first finite-sample regret bounds for offline assortment optimization across several widely used choice models, including the multinomial logit and nested logit models. Additionally, we derive a minimax regret lower bound, proving that PASTA is minimax optimal in terms of sample and model complexity. Numerical experiments further demonstrate that our method outperforms existing baseline approaches.

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arXiv2025

Fisher Random Walk: Automatic Debiasing Contextual Preference Inference for Large Language Model Evaluation

Motivated by the need for rigorous and scalable evaluation of large language models, we study contextual preference inference for pairwise comparison functionals of context-dependent preference score functions across domains. Focusing on the contextual Bradley-Terry-Luce model, we develop a semiparametric efficient estimator that automates the debiased estimation through aggregating weighted residual balancing terms across the comparison graph. We show that the efficiency is achieved when the weights are derived from a novel strategy called Fisher random walk. We also propose a computationally feasible method to compute the weights by a potential representation of nuisance weight functions. We show our inference procedure is valid for general score function estimators accommodating the practitioners' need to implement flexible deep learning methods. We extend the procedure to multiple hypothesis testing using a Gaussian multiplier bootstrap that controls familywise error and to distributional shift via a cross-fitted importance-sampling adjustment for target-domain inference. Numerical studies, including language model evaluations under diverse contexts, corroborate the accuracy, efficiency, and practical utility of our method.

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arXiv2025

Stochastic Compositional Optimization with Compositional Constraints

Stochastic compositional optimization (SCO) has attracted considerable attention because of its broad applicability to important real-world problems. However, existing works on SCO assume that the projection within a solution update is simple, which fails to hold for problem instances where the constraints are in the form of expectations, such as empirical conditional value-at-risk constraints. We study a novel model that incorporates single-level expected value and two-level compositional constraints into the current SCO framework. Our model can be applied widely to data-driven optimization and risk management, including risk-averse optimization and high-moment portfolio selection, and can handle multiple constraints. We further propose a class of primal-dual algorithms that generates sequences converging to the optimal solution at the rate of $\cO(\frac{1}{\sqrt{N}})$under both single-level expected value and two-level compositional constraints, where $N$ is the iteration counter, establishing the benchmarks in expected value constrained SCO.

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arXiv2025

Confidence Diagram of Nonparametric Ranking for Uncertainty Assessment in Large Language Models Evaluation

We consider the inference for the ranking of large language models (LLMs). Alignment arises as a significant challenge to mitigate hallucinations in the use of LLMs. Ranking LLMs has proven to be an effective tool to improve alignment based on the best-of-$N$ policy. In this paper, we propose a new inferential framework for hypothesis testing among the ranking for language models. Our framework is based on a nonparametric contextual ranking framework designed to assess large language models' domain-specific expertise, leveraging nonparametric scoring methods to account for their sensitivity to the prompts. To characterize the combinatorial complexity of the ranking, we introduce a novel concept of confidence diagram, which leverages a Hasse diagram to represent the entire confidence set of rankings by a single directed graph. We show the validity of the proposed confidence diagram by advancing the Gaussian multiplier bootstrap theory to accommodate the supremum of independent empirical processes that are not necessarily identically distributed. Extensive numerical experiments conducted on both synthetic and real data demonstrate that our approach offers valuable insight into the evaluation for the performance of different LLMs across various medical domains.

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arXiv2024

Anti-Concentration Inequalities for the Difference of Maxima of Gaussian Random Vectors

We derive novel anti-concentration bounds for the difference between the maximal values of two Gaussian random vectors across various settings. Our bounds are dimension-free, scaling with the dimension of the Gaussian vectors only through the smaller expected maximum of the Gaussian subvectors. In addition, our bounds hold under the degenerate covariance structures, which previous results do not cover. In addition, we show that our conditions are sharp under the homogeneous component-wise variance setting, while we only impose some mild assumptions on the covariance structures under the heterogeneous variance setting. We apply the new anti-concentration bounds to derive the central limit theorem for the maximizers of discrete empirical processes. Finally, we back up our theoretical findings with comprehensive numerical studies.

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arXiv2023

Pivotal Estimation of Linear Discriminant Analysis in High Dimensions

We consider the linear discriminant analysis problem in the high-dimensional settings. In this work, we propose PANDA(PivotAl liNear Discriminant Analysis), a tuning-insensitive method in the sense that it requires very little effort to tune the parameters. Moreover, we prove that PANDA achieves the optimal convergence rate in terms of both the estimation error and misclassification rate. Our theoretical results are backed up by thorough numerical studies using both simulated and real datasets. In comparison with the existing methods, we observe that our proposed PANDA yields equal or better performance, and requires substantially less effort in parameter tuning.

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arXiv2023

Risk-Sensitive Deep RL: Variance-Constrained Actor-Critic Provably Finds Globally Optimal Policy

While deep reinforcement learning has achieved tremendous successes in various applications, most existing works only focus on maximizing the expected value of total return and thus ignore its inherent stochasticity. Such stochasticity is also known as the aleatoric uncertainty and is closely related to the notion of risk. In this work, we make the first attempt to study risk-sensitive deep reinforcement learning under the average reward setting with the variance risk criteria. In particular, we focus on a variance-constrained policy optimization problem where the goal is to find a policy that maximizes the expected value of the long-run average reward, subject to a constraint that the long-run variance of the average reward is upper bounded by a threshold. Utilizing Lagrangian and Fenchel dualities, we transform the original problem into an unconstrained saddle-point policy optimization problem, and propose an actor-critic algorithm that iteratively and efficiently updates the policy, the Lagrange multiplier, and the Fenchel dual variable. When both the value and policy functions are represented by multi-layer overparameterized neural networks, we prove that our actor-critic algorithm generates a sequence of policies that finds a globally optimal policy at a sublinear rate. Further, We provide numerical studies of the proposed method using two real datasets to back up the theoretical results.

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arXiv2023

Implicit Regularization of Bregman Proximal Point Algorithm and Mirror Descent on Separable Data

Bregman proximal point algorithm (BPPA) has witnessed emerging machine learning applications, yet its theoretical understanding has been largely unexplored. We study the computational properties of BPPA through learning linear classifiers with separable data, and demonstrate provable algorithmic regularization of BPPA. For any BPPA instantiated with a fixed Bregman divergence, we provide a lower bound of the margin obtained by BPPA with respect to an arbitrarily chosen norm. The obtained margin lower bound differs from the maximal margin by a multiplicative factor, which inversely depends on the condition number of the distance-generating function measured in the dual norm. We show that the dependence on the condition number is tight, thus demonstrating the importance of divergence in affecting the quality of the learned classifiers. We then extend our findings to mirror descent, for which we establish similar connections between the margin and Bregman divergence, together with a non-asymptotic analysis. Numerical experiments on both synthetic and real-world datasets are provided to support our theoretical findings. To the best of our knowledge, the aforementioned findings appear to be new in the literature of algorithmic regularization.

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arXiv2023

PASTA: Pessimistic Assortment Optimization

We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA for short) designed based on the principle of pessimism, that can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model. We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Numerical studies demonstrate the superiority of the proposed method over the existing baseline method.

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arXiv2021

Lagrangian Inference for Ranking Problems

We propose a novel combinatorial inference framework to conduct general uncertainty quantification in ranking problems. We consider the widely adopted Bradley-Terry-Luce (BTL) model, where each item is assigned a positive preference score that determines the Bernoulli distributions of pairwise comparisons' outcomes. Our proposed method aims to infer general ranking properties of the BTL model. The general ranking properties include the "local" properties such as if an item is preferred over another and the "global" properties such as if an item is among the top $K$-ranked items. We further generalize our inferential framework to multiple testing problems where we control the false discovery rate (FDR), and apply the method to infer the top-$K$ ranked items. We also derive the information-theoretic lower bound to justify the minimax optimality of the proposed method. We conduct extensive numerical studies using both synthetic and real datasets to back up our theory.

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arXiv2020

Nearly Dimension-Independent Sparse Linear Bandit over Small Action Spaces via Best Subset Selection

We consider the stochastic contextual bandit problem under the high dimensional linear model. We focus on the case where the action space is finite and random, with each action associated with a randomly generated contextual covariate. This setting finds essential applications such as personalized recommendation, online advertisement, and personalized medicine. However, it is very challenging as we need to balance exploration and exploitation. We propose doubly growing epochs and estimating the parameter using the best subset selection method, which is easy to implement in practice. This approach achieves $ \tilde{\mathcal{O}}(s\sqrt{T})$ regret with high probability, which is nearly independent in the ``ambient'' regression model dimension $d$. We further attain a sharper $\tilde{\mathcal{O}}(\sqrt{sT})$ regret by using the \textsc{SupLinUCB} framework and match the minimax lower bound of low-dimensional linear stochastic bandit problems. Finally, we conduct extensive numerical experiments to demonstrate the applicability and robustness of our algorithms empirically.

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arXiv2019

High-dimensional Interactions Detection with Sparse Principal Hessian Matrix

In statistical learning framework with regressions, interactions are the contributions to the response variable from the products of the explanatory variables. In high-dimensional problems, detecting interactions is challenging due to combinatorial complexity and limited data information. We consider detecting interactions by exploring their connections with the principal Hessian matrix. Specifically, we propose a one-step synthetic approach for estimating the principal Hessian matrix by a penalized M-estimator. An alternating direction method of multipliers (ADMM) is proposed to efficiently solve the encountered regularized optimization problem. Based on the sparse estimator, we detect the interactions by identifying its nonzero components. Our method directly targets at the interactions, and it requires no structural assumption on the hierarchy of the interaction effects. We show that our estimator is theoretically valid, computationally efficient, and practically useful for detecting the interactions in a broad spectrum of scenarios.

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arXiv2019

Inductive Bias of Gradient Descent based Adversarial Training on Separable Data

Adversarial training is a principled approach for training robust neural networks. Despite of tremendous successes in practice, its theoretical properties still remain largely unexplored. In this paper, we provide new theoretical insights of gradient descent based adversarial training by studying its computational properties, specifically on its inductive bias. We take the binary classification task on linearly separable data as an illustrative example, where the loss asymptotically attains its infimum as the parameter diverges to infinity along certain directions. Specifically, we show that when the adversarial perturbation during training has bounded $\ell_2$-norm, the classifier learned by gradient descent based adversarial training converges in direction to the maximum $\ell_2$-norm margin classifier at the rate of $\tilde{\mathcal{O}}(1/\sqrt{T})$, significantly faster than the rate $\mathcal{O}(1/\log T)$ of training with clean data. In addition, when the adversarial perturbation during training has bounded $\ell_q$-norm for some $q\ge 1$, the resulting classifier converges in direction to a maximum mixed-norm margin classifier, which has a natural interpretation of robustness, as being the maximum $\ell_2$-norm margin classifier under worst-case $\ell_q$-norm perturbation to the data. Our findings provide theoretical backups for adversarial training that it indeed promotes robustness against adversarial perturbation.

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arXiv2018

Multi-Level Stochastic Gradient Methods for Nested Composition Optimization

Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level expectations. In this paper, we consider the multi-level compositional optimization problem that involves compositions of multi-level component functions and nested expectations over a random path. It finds applications in risk-averse optimization and sequential planning. We propose a class of multi-level stochastic gradient methods that are motivated from the method of multi-timescale stochastic approximation. First we propose a basic $T$-level stochastic compositional gradient algorithm, establish its almost sure convergence and obtain an $n$-iteration error bound $O (n^{-1/2^T})$. Then we develop accelerated multi-level stochastic gradient methods by using an extrapolation-interpolation scheme to take advantage of the smoothness of individual component functions. When all component functions are smooth, we show that the convergence rate improves to $O(n^{-4/(7+T)})$ for general objectives and $O (n^{-4/(3+T)})$ for strongly convex objectives. We also provide almost sure convergence and rate of convergence results for nonconvex problems. The proposed methods and theoretical results are validated using numerical experiments.

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arXiv2017

Misspecified Nonconvex Statistical Optimization for Phase Retrieval

Existing nonconvex statistical optimization theory and methods crucially rely on the correct specification of the underlying "true" statistical models. To address this issue, we take a first step towards taming model misspecification by studying the high-dimensional sparse phase retrieval problem with misspecified link functions. In particular, we propose a simple variant of the thresholded Wirtinger flow algorithm that, given a proper initialization, linearly converges to an estimator with optimal statistical accuracy for a broad family of unknown link functions. We further provide extensive numerical experiments to support our theoretical findings.

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arXiv2016

Max-Norm Optimization for Robust Matrix Recovery

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery using a random subset of entries observed with additive noise under general non-uniform and unknown sampling distributions. This method significantly relaxes the uniform sampling assumption imposed for the widely used nuclear-norm penalized approach, and makes low-rank matrix recovery feasible in more practical settings. Theoretically, we prove that the proposed estimator achieves fast rates of convergence under different settings. Computationally, we propose an alternating direction method of multipliers algorithm to efficiently compute the estimator, which bridges a gap between theory and practice of machine learning methods with max-norm regularization. Further, we provide thorough numerical studies to evaluate the proposed method using both simulated and real datasets.

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arXiv2016

Accelerating Stochastic Composition Optimization

Consider the stochastic composition optimization problem where the objective is a composition of two expected-value functions. We propose a new stochastic first-order method, namely the accelerated stochastic compositional proximal gradient (ASC-PG) method, which updates based on queries to the sampling oracle using two different timescales. The ASC-PG is the first proximal gradient method for the stochastic composition problem that can deal with nonsmooth regularization penalty. We show that the ASC-PG exhibits faster convergence than the best known algorithms, and that it achieves the optimal sample-error complexity in several important special cases. We further demonstrate the application of ASC-PG to reinforcement learning and conduct numerical experiments.

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