arXiv subjects

Xiaocheng Li

Publications and source records attributed to Xiaocheng Li.

At least 37 records · Page 2Linked to original sources

arXiv2024

Uncertainty Estimation and Quantification for LLMs: A Simple Supervised Approach

In this paper, we study the problem of uncertainty estimation and calibration for LLMs. We begin by formulating the uncertainty estimation problem, a relevant yet underexplored area in existing literature. We then propose a supervised approach that leverages labeled datasets to estimate the uncertainty in LLMs' responses. Based on the formulation, we illustrate the difference between the uncertainty estimation for LLMs and that for standard ML models and explain why the hidden neurons of the LLMs may contain uncertainty information. Our designed approach demonstrates the benefits of utilizing hidden activations to enhance uncertainty estimation across various tasks and shows robust transferability in out-of-distribution settings. We distinguish the uncertainty estimation task from the uncertainty calibration task and show that better uncertainty estimation leads to better calibration performance. Furthermore, our method is easy to implement and adaptable to different levels of model accessibility including black box, grey box, and white box.

cs.LG↗

arXiv2024

Understanding the Training and Generalization of Pretrained Transformer for Sequential Decision Making

In this paper, we consider the supervised pre-trained transformer for a class of sequential decision-making problems. The class of considered problems is a subset of the general formulation of reinforcement learning in that there is no transition probability matrix; though seemingly restrictive, the subset class of problems covers bandits, dynamic pricing, and newsvendor problems as special cases. Such a structure enables the use of optimal actions/decisions in the pre-training phase, and the usage also provides new insights for the training and generalization of the pre-trained transformer. We first note the training of the transformer model can be viewed as a performative prediction problem, and the existing methods and theories largely ignore or cannot resolve an out-of-distribution issue. We propose a natural solution that includes the transformer-generated action sequences in the training procedure, and it enjoys better properties both numerically and theoretically. The availability of the optimal actions in the considered tasks also allows us to analyze the properties of the pre-trained transformer as an algorithm and explains why it may lack exploration and how this can be automatically resolved. Numerically, we categorize the advantages of pre-trained transformers over the structured algorithms such as UCB and Thompson sampling into three cases: (i) it better utilizes the prior knowledge in the pre-training data; (ii) it can elegantly handle the misspecification issue suffered by the structured algorithms; (iii) for short time horizon such as $T\le50$, it behaves more greedy and enjoys much better regret than the structured algorithms designed for asymptotic optimality.

cs.LG↗

arXiv2024

Facilitating Battery Swapping Services for Freight Trucks with Spatial-Temporal Demand Prediction

Electrifying heavy-duty trucks offers a substantial opportunity to curtail carbon emissions, advancing toward a carbon-neutral future. However, the inherent challenges of limited battery energy and the sheer weight of heavy-duty trucks lead to reduced mileage and prolonged charging durations. Consequently, battery-swapping services emerge as an attractive solution for these trucks. This paper employs a two-fold approach to investigate the potential and enhance the efficacy of such services. Firstly, spatial-temporal demand prediction models are adopted to predict the traffic patterns for the upcoming hours. Subsequently, the prediction guides an optimization module for efficient battery allocation and deployment. Analyzing the heavy-duty truck data on a highway network spanning over 2,500 miles, our model and analysis underscore the value of prediction/machine learning in facilitating future decision-makings. In particular, we find that the initial phase of implementing battery-swapping services favors mobile battery-swapping stations, but as the system matures, fixed-location stations are preferred.

eess.SY↗

arXiv2024

Towards Better Understanding of In-Context Learning Ability from In-Context Uncertainty Quantification

Predicting simple function classes has been widely used as a testbed for developing theory and understanding of the trained Transformer's in-context learning (ICL) ability. In this paper, we revisit the training of Transformers on linear regression tasks, and different from all the existing literature, we consider a bi-objective prediction task of predicting both the conditional expectation $\mathbb{E}[Y|X]$ and the conditional variance Var$(Y|X)$. This additional uncertainty quantification objective provides a handle to (i) better design out-of-distribution experiments to distinguish ICL from in-weight learning (IWL) and (ii) make a better separation between the algorithms with and without using the prior information of the training distribution. Theoretically, we show that the trained Transformer reaches near Bayes-optimum, suggesting the usage of the information of the training distribution. Our method can be extended to other cases. Specifically, with the Transformer's context window $S$, we prove a generalization bound of $\tilde{\mathcal{O}}(\sqrt{\min\{S, T\}/(n T)})$ on $n$ tasks with sequences of length $T$, providing sharper analysis compared to previous results of $\tilde{\mathcal{O}}(\sqrt{1/n})$. Empirically, we illustrate that while the trained Transformer behaves as the Bayes-optimal solution as a natural consequence of supervised training in distribution, it does not necessarily perform a Bayesian inference when facing task shifts, in contrast to the \textit{equivalence} between these two proposed in many existing literature. We also demonstrate the trained Transformer's ICL ability over covariates shift and prompt-length shift and interpret them as a generalization over a meta distribution.

cs.LG↗

arXiv2024

Predict-then-Calibrate: A New Perspective of Robust Contextual LP

Contextual optimization, also known as predict-then-optimize or prescriptive analytics, considers an optimization problem with the presence of covariates (context or side information). The goal is to learn a prediction model (from the training data) that predicts the objective function from the covariates, and then in the test phase, solve the optimization problem with the covariates but without the observation of the objective function. In this paper, we consider a risk-sensitive version of the problem and propose a generic algorithm design paradigm called predict-then-calibrate. The idea is to first develop a prediction model without concern for the downstream risk profile or robustness guarantee, and then utilize calibration (or recalibration) methods to quantify the uncertainty of the prediction. While the existing methods suffer from either a restricted choice of the prediction model or strong assumptions on the underlying data, we show the disentangling of the prediction model and the calibration/uncertainty quantification has several advantages. First, it imposes no restriction on the prediction model and thus fully unleashes the potential of off-the-shelf machine learning methods. Second, the derivation of the risk and robustness guarantee can be made independent of the choice of the prediction model through a data-splitting idea. Third, our paradigm of predict-then-calibrate applies to both (risk-sensitive) robust and (risk-neutral) distributionally robust optimization (DRO) formulations. Theoretically, it gives new generalization bounds for the contextual LP problem and sheds light on the existing results of DRO for contextual LP. Numerical experiments further reinforce the advantage of the predict-then-calibrate paradigm in that an improvement on either the prediction model or the calibration model will lead to a better final performance.

math.OC↗

arXiv2024

When No-Rejection Learning is Consistent for Regression with Rejection

Learning with rejection has been a prototypical model for studying the human-AI interaction on prediction tasks. Upon the arrival of a sample instance, the model first uses a rejector to decide whether to accept and use the AI predictor to make a prediction or reject and defer the sample to humans. Learning such a model changes the structure of the original loss function and often results in undesirable non-convexity and inconsistency issues. For the classification with rejection problem, several works develop consistent surrogate losses for the joint learning of the predictor and the rejector, while there have been fewer works for the regression counterpart. This paper studies the regression with rejection (RwR) problem and investigates a no-rejection learning strategy that uses all the data to learn the predictor. We first establish the consistency for such a strategy under the weak realizability condition. Then for the case without the weak realizability, we show that the excessive risk can also be upper bounded with the sum of two parts: prediction error and calibration error. Lastly, we demonstrate the advantage of such a proposed learning strategy with empirical evidence.

cs.LG↗

arXiv2024

Learning to Make Adherence-Aware Advice

As artificial intelligence (AI) systems play an increasingly prominent role in human decision-making, challenges surface in the realm of human-AI interactions. One challenge arises from the suboptimal AI policies due to the inadequate consideration of humans disregarding AI recommendations, as well as the need for AI to provide advice selectively when it is most pertinent. This paper presents a sequential decision-making model that (i) takes into account the human's adherence level (the probability that the human follows/rejects machine advice) and (ii) incorporates a defer option so that the machine can temporarily refrain from making advice. We provide learning algorithms that learn the optimal advice policy and make advice only at critical time stamps. Compared to problem-agnostic reinforcement learning algorithms, our specialized learning algorithms not only enjoy better theoretical convergence properties but also show strong empirical performance.

stat.ML↗

arXiv2023

On Dynamic Pricing with Covariates

We consider dynamic pricing with covariates under a generalized linear demand model: a seller can dynamically adjust the price of a product over a horizon of $T$ time periods, and at each time period $t$, the demand of the product is jointly determined by the price and an observable covariate vector $x_t\in\mathbb{R}^d$ through a generalized linear model with unknown co-efficients. Most of the existing literature assumes the covariate vectors $x_t$'s are independently and identically distributed (i.i.d.); the few papers that relax this assumption either sacrifice model generality or yield sub-optimal regret bounds. In this paper, we show that UCB and Thompson sampling-based pricing algorithms can achieve an $O(d\sqrt{T}\log T)$ regret upper bound without assuming any statistical structure on the covariates $x_t$. Our upper bound on the regret matches the lower bound up to logarithmic factors. We thus show that (i) the i.i.d. assumption is not necessary for obtaining low regret, and (ii) the regret bound can be independent of the (inverse) minimum eigenvalue of the covariance matrix of the $x_t$'s, a quantity present in previous bounds. Moreover, we consider a constrained setting of the dynamic pricing problem where there is a limited and unreplenishable inventory and we develop theoretical results that relate the best achievable algorithm performance to a variation measure with respect to the temporal distribution shift of the covariates. We also discuss conditions under which a better regret is achievable and demonstrate the proposed algorithms' performance with numerical experiments.

cs.LG↗

arXiv2023

Distribution-Free Model-Agnostic Regression Calibration via Nonparametric Methods

In this paper, we consider the uncertainty quantification problem for regression models. Specifically, we consider an individual calibration objective for characterizing the quantiles of the prediction model. While such an objective is well-motivated from downstream tasks such as newsvendor cost, the existing methods have been largely heuristic and lack of statistical guarantee in terms of individual calibration. We show via simple examples that the existing methods focusing on population-level calibration guarantees such as average calibration or sharpness can lead to harmful and unexpected results. We propose simple nonparametric calibration methods that are agnostic of the underlying prediction model and enjoy both computational efficiency and statistical consistency. Our approach enables a better understanding of the possibility of individual calibration, and we establish matching upper and lower bounds for the calibration error of our proposed methods. Technically, our analysis combines the nonparametric analysis with a covering number argument for parametric analysis, which advances the existing theoretical analyses in the literature of nonparametric density estimation and quantile bandit problems. Importantly, the nonparametric perspective sheds new theoretical insights into regression calibration in terms of the curse of dimensionality and reconciles the existing results on the impossibility of individual calibration. To our knowledge, we make the first effort to reach both individual calibration and finite-sample guarantee with minimal assumptions in terms of conformal prediction. Numerical experiments show the advantage of such a simple approach under various metrics, and also under covariates shift. We hope our work provides a simple benchmark and a starting point of theoretical ground for future research on regression calibration.

cs.LG↗

arXiv2023

Transformer Choice Net: A Transformer Neural Network for Choice Prediction

Discrete-choice models, such as Multinomial Logit, Probit, or Mixed-Logit, are widely used in Marketing, Economics, and Operations Research: given a set of alternatives, the customer is modeled as choosing one of the alternatives to maximize a (latent) utility function. However, extending such models to situations where the customer chooses more than one item (such as in e-commerce shopping) has proven problematic. While one can construct reasonable models of the customer's behavior, estimating such models becomes very challenging because of the combinatorial explosion in the number of possible subsets of items. In this paper we develop a transformer neural network architecture, the Transformer Choice Net, that is suitable for predicting multiple choices. Transformer networks turn out to be especially suitable for this task as they take into account not only the features of the customer and the items but also the context, which in this case could be the assortment as well as the customer's past choices. On a range of benchmark datasets, our architecture shows uniformly superior out-of-sample prediction performance compared to the leading models in the literature, without requiring any custom modeling or tuning for each instance.

cs.LG↗

arXiv2023

A Neural Network Based Choice Model for Assortment Optimization

Discrete-choice models are used in economics, marketing and revenue management to predict customer purchase probabilities, say as a function of prices and other features of the offered assortment. While they have been shown to be expressive, capturing customer heterogeneity and behaviour, they are also hard to estimate, often based on many unobservables like utilities; and moreover, they still fail to capture many salient features of customer behaviour. A natural question then, given their success in other contexts, is if neural networks can eliminate the necessity of carefully building a context-dependent customer behaviour model and hand-coding and tuning the estimation. It is unclear however how one would incorporate assortment effects into such a neural network, and also how one would optimize the assortment with such a black-box generative model of choice probabilities. In this paper we investigate first whether a single neural network architecture can predict purchase probabilities for datasets from various contexts and generated under various models and assumptions. Next, we develop an assortment optimization formulation that is solvable by off-the-shelf integer programming solvers. We compare against a variety of benchmark discrete-choice models on simulated as well as real-world datasets, developing training tricks along the way to make the neural network prediction and subsequent optimization robust and comparable in performance to the alternates.

cs.AI↗

arXiv2023

Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming

In this paper, we study the predict-then-optimize problem where the output of a machine learning prediction task is used as the input of some downstream optimization problem, say, the objective coefficient vector of a linear program. The problem is also known as predictive analytics or contextual linear programming. The existing approaches largely suffer from either (i) optimization intractability (a non-convex objective function)/statistical inefficiency (a suboptimal generalization bound) or (ii) requiring strong condition(s) such as no constraint or loss calibration. We develop a new approach to the problem called \textit{maximum optimality margin} which designs the machine learning loss function by the optimality condition of the downstream optimization. The max-margin formulation enjoys both computational efficiency and good theoretical properties for the learning procedure. More importantly, our new approach only needs the observations of the optimal solution in the training data rather than the objective function, which makes it a new and natural approach to the inverse linear programming problem under both contextual and context-free settings; we also analyze the proposed method under both offline and online settings, and demonstrate its performance using numerical experiments.

cs.LG↗

arXiv2022

Non-stationary Bandits with Knapsacks

In this paper, we study the problem of bandits with knapsacks (BwK) in a non-stationary environment. The BwK problem generalizes the multi-arm bandit (MAB) problem to model the resource consumption associated with playing each arm. At each time, the decision maker/player chooses to play an arm, and s/he will receive a reward and consume certain amount of resource from each of the multiple resource types. The objective is to maximize the cumulative reward over a finite horizon subject to some knapsack constraints on the resources. Existing works study the BwK problem under either a stochastic or adversarial environment. Our paper considers a non-stationary environment which continuously interpolates between these two extremes. We first show that the traditional notion of variation budget is insufficient to characterize the non-stationarity of the BwK problem for a sublinear regret due to the presence of the constraints, and then we propose a new notion of global non-stationarity measure. We employ both non-stationarity measures to derive upper and lower bounds for the problem. Our results are based on a primal-dual analysis of the underlying linear programs and highlight the interplay between the constraints and the non-stationarity. Finally, we also extend the non-stationarity measure to the problem of online convex optimization with constraints and obtain new regret bounds accordingly.

cs.LG↗

arXiv2022

Deep Learning for Choice Modeling

Choice modeling has been a central topic in the study of individual preference or utility across many fields including economics, marketing, operations research, and psychology. While the vast majority of the literature on choice models has been devoted to the analytical properties that lead to managerial and policy-making insights, the existing methods to learn a choice model from empirical data are often either computationally intractable or sample inefficient. In this paper, we develop deep learning-based choice models under two settings of choice modeling: (i) feature-free and (ii) feature-based. Our model captures both the intrinsic utility for each candidate choice and the effect that the assortment has on the choice probability. Synthetic and real data experiments demonstrate the performances of proposed models in terms of the recovery of the existing choice models, sample complexity, assortment effect, architecture design, and model interpretation.

stat.ML↗

arXiv2022

A Unified Image Preprocessing Framework For Image Compression

With the development of streaming media technology, increasing communication relies on sound and visual information, which puts a massive burden on online media. Data compression becomes increasingly important to reduce the volume of data transmission and storage. To further improve the efficiency of image compression, researchers utilize various image processing methods to compensate for the limitations of conventional codecs and advanced learning-based compression methods. Instead of modifying the image compression oriented approaches, we propose a unified image compression preprocessing framework, called Kuchen, which aims to further improve the performance of existing codecs. The framework consists of a hybrid data labeling system along with a learning-based backbone to simulate personalized preprocessing. As far as we know, this is the first exploration of setting a unified preprocessing benchmark in image compression tasks. Results demonstrate that the modern codecs optimized by our unified preprocessing framework constantly improve the efficiency of the state-of-the-art compression.

cs.CV↗

arXiv2022

Online Stochastic Optimization with Wasserstein Based Non-stationarity

We consider a general online stochastic optimization problem with multiple budget constraints over a horizon of finite time periods. In each time period, a reward function and multiple cost functions are revealed, and the decision maker needs to specify an action from a convex and compact action set to collect the reward and consume the budget. Each cost function corresponds to the consumption of one budget. In each period, the reward and cost functions are drawn from an unknown distribution, which is non-stationary across time. The objective of the decision maker is to maximize the cumulative reward subject to the budget constraints. This formulation captures a wide range of applications including online linear programming and network revenue management, among others. In this paper, we consider two settings: (i) a data-driven setting where the true distribution is unknown but a prior estimate (possibly inaccurate) is available; (ii) an uninformative setting where the true distribution is completely unknown. We propose a unified Wasserstein-distance based measure to quantify the inaccuracy of the prior estimate in setting (i) and the non-stationarity of the system in setting (ii). We show that the proposed measure leads to a necessary and sufficient condition for the attainability of a sublinear regret in both settings. For setting (i), we propose a new algorithm, which takes a primal-dual perspective and integrates the prior information of the underlying distributions into an online gradient descent procedure in the dual space. The algorithm also naturally extends to the uninformative setting (ii). Under both settings, we show the corresponding algorithm achieves a regret of optimal order. In numerical experiments, we demonstrate how the proposed algorithms can be naturally integrated with the re-solving technique to further boost the empirical performance.

cs.LG↗

arXiv2022

Learning to Sell a Focal-ancillary Combination

A number of products are sold in the following sequence: First a focal product is shown, and if the customer purchases, one or more ancillary products are displayed for purchase. A prominent example is the sale of an airline ticket, where first the flight is shown, and when chosen, a number of ancillaries such as cabin or hold bag options, seat selection, insurance etc. are presented. The firm has to decide on a sale format -- whether to sell them in sequence unbundled, or together as a bundle -- and how to price the focal and ancillary products, separately or as a bundle. Since the ancillary is considered by the customer only after the purchase of the focal product, the sale strategy chosen by the firm creates an information and learning dependency between the products: for instance, offering only a bundle would preclude learning customers' valuation for the focal and ancillary products individually. In this paper we study learning strategies for such focal and ancillary item combinations under the following scenarios: (a) pure unbundling to all customers, (b) personalized mechanism, where, depending on some observed features of the customers, the two products are presented and priced as a bundle or in sequence, (c) initially unbundling (for all customers), and switch to bundling (if more profitable) permanently once during the horizon. We design pricing and decisions algorithms for all three scenarios, with regret upper bounded by $O(d \sqrt{T} \log T)$, and an optimal switching time for the third scenario.

cs.LG↗

arXiv2022

An estimate for spherical functions on $\mathrm{SL}(3,\mathbb{R})$

We prove an estimate for spherical functions $φ_λ(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $λ$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $λ$ and $a$ vary.

math.RT↗