Towards Better Statistical Understanding of Watermarking LLMs

In this paper, we study the problem of watermarking large language models (LLMs). We consider the trade-off between model distortion and detection ability and formulate it as a constrained optimization problem based on the green-red algorithm of Kirchenbauer et al. (2023a). We show that the optimal solution to the optimization problem enjoys a nice analytical property which provides a better understanding and inspires the algorithm design for the watermarking process. We develop an online dual gradient ascent watermarking algorithm in light of this optimization formulation and prove its asymptotic Pareto optimality between model distortion and detection ability. Such a result guarantees an averaged increased green list probability and henceforth detection ability explicitly (in contrast to previous results). Moreover, we provide a systematic discussion on the choice of the model distortion metrics for the watermarking problem. We justify our choice of KL divergence and present issues with the existing criteria of ``distortion-free'' and perplexity. Finally, we empirically evaluate our algorithms on extensive datasets against benchmark algorithms.

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.

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.

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.

When No-Rejection Learning is Optimal for Regression with Rejection

Learning with rejection is a prototypical model for studying the interaction between humans and AI on prediction tasks. The model has two components, a predictor and a rejector. Upon the arrival of a sample, the rejector first decides whether to accept it; if accepted, the predictor fulfills the prediction task, and if rejected, the prediction will be deferred to humans. The learning problem requires learning a predictor and a rejector simultaneously. This changes the structure of the conventional loss function and often results in non-convexity and inconsistency issues. For the classification with rejection problem, several works develop surrogate losses for the jointly learning with provable consistency guarantees; in parallel, there has been less work for the regression counterpart. We study the regression with rejection (RwR) problem and investigate the no-rejection learning strategy which treats the RwR problem as a standard regression task to learn the predictor. We establish that the suboptimality of the no-rejection learning strategy observed in the literature can be mitigated by enlarging the function class of the predictor. Then we introduce the truncated loss to single out the learning for the predictor and we show that a consistent surrogate property can be established for the predictor individually in an easier way than for the predictor and the rejector jointly. Our findings advocate for a two-step learning procedure that first uses all the data to learn the predictor and then calibrates the prediction loss for the rejector. It is better aligned with the common intuition that more data samples will lead to a better predictor and it calls for more efforts on a better design of calibration algorithms for learning the rejector. While our discussions mainly focus on the regression problem, the theoretical results and insights generalize to the classification problem as well.

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.

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.

On Dynamic Pricing with Covariates

We consider the dynamic pricing problem 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 an unknown generalized linear model. 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 a simple pricing algorithm has an $O(d\sqrt{T}\log T)$ regret upper bound without assuming any statistical structure on the covariates $x_t$ (which can even be arbitrarily chosen). The upper bound on the regret matches the lower bound (even under the i.i.d. assumption) up to logarithmic factors. Our paper thus shows 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. Furthermore, we discuss a condition under which a better regret is achievable and how a Thompson sampling algorithm can be applied to give an efficient computation of the prices.