A Re-solving Heuristic for Dynamic Assortment Optimization with Knapsack Constraints

In this paper, we consider a multi-stage dynamic assortment optimization problem with multi-nomial choice modeling (MNL) under resource knapsack constraints. Given the current resource inventory levels, the retailer makes an assortment decision at each period, and the goal of the retailer is to maximize the total profit from purchases. With the exact optimal dynamic assortment solution being computationally intractable, a practical strategy is to adopt the re-solving technique that periodically re-optimizes deterministic linear programs (LP) arising from fluid approximation. However, the fractional structure of MNL makes the fluid approximation in assortment optimization highly non-linear, which brings new technical challenges. To address this challenge, we propose a new epoch-based re-solving algorithm that effectively transforms the denominator of the objective into the constraint. Theoretically, we prove that the regret (i.e., the gap between the resolving policy and the optimal objective of the fluid approximation) scales logarithmically with the length of time horizon and resource capacities.

Research on Autonomous Robots Navigation based on Reinforcement Learning

Reinforcement learning continuously optimizes decision-making based on real-time feedback reward signals through continuous interaction with the environment, demonstrating strong adaptive and self-learning capabilities. In recent years, it has become one of the key methods to achieve autonomous navigation of robots. In this work, an autonomous robot navigation method based on reinforcement learning is introduced. We use the Deep Q Network (DQN) and Proximal Policy Optimization (PPO) models to optimize the path planning and decision-making process through the continuous interaction between the robot and the environment, and the reward signals with real-time feedback. By combining the Q-value function with the deep neural network, deep Q network can handle high-dimensional state space, so as to realize path planning in complex environments. Proximal policy optimization is a strategy gradient-based method, which enables robots to explore and utilize environmental information more efficiently by optimizing policy functions. These methods not only improve the robot's navigation ability in the unknown environment, but also enhance its adaptive and self-learning capabilities. Through multiple training and simulation experiments, we have verified the effectiveness and robustness of these models in various complex scenarios.

Stochastic Zeroth-Order Optimization under Strongly Convexity and Lipschitz Hessian: Minimax Sample Complexity

Optimization of convex functions under stochastic zeroth-order feedback has been a major and challenging question in online learning. In this work, we consider the problem of optimizing second-order smooth and strongly convex functions where the algorithm is only accessible to noisy evaluations of the objective function it queries. We provide the first tight characterization for the rate of the minimax simple regret by developing matching upper and lower bounds. We propose an algorithm that features a combination of a bootstrapping stage and a mirror-descent stage. Our main technical innovation consists of a sharp characterization for the spherical-sampling gradient estimator under higher-order smoothness conditions, which allows the algorithm to optimally balance the bias-variance tradeoff, and a new iterative method for the bootstrapping stage, which maintains the performance for unbounded Hessian.

Navigate Beyond Shortcuts: Debiased Learning through the Lens of Neural Collapse

Recent studies have noted an intriguing phenomenon termed Neural Collapse, that is, when the neural networks establish the right correlation between feature spaces and the training targets, their last-layer features, together with the classifier weights, will collapse into a stable and symmetric structure. In this paper, we extend the investigation of Neural Collapse to the biased datasets with imbalanced attributes. We observe that models will easily fall into the pitfall of shortcut learning and form a biased, non-collapsed feature space at the early period of training, which is hard to reverse and limits the generalization capability. To tackle the root cause of biased classification, we follow the recent inspiration of prime training, and propose an avoid-shortcut learning framework without additional training complexity. With well-designed shortcut primes based on Neural Collapse structure, the models are encouraged to skip the pursuit of simple shortcuts and naturally capture the intrinsic correlations. Experimental results demonstrate that our method induces better convergence properties during training, and achieves state-of-the-art generalization performance on both synthetic and real-world biased datasets.

On the Optimal Regret of Locally Private Linear Contextual Bandit

Contextual bandit with linear reward functions is among one of the most extensively studied models in bandit and online learning research. Recently, there has been increasing interest in designing \emph{locally private} linear contextual bandit algorithms, where sensitive information contained in contexts and rewards is protected against leakage to the general public. While the classical linear contextual bandit algorithm admits cumulative regret upper bounds of $\tilde O(\sqrt{T})$ via multiple alternative methods, it has remained open whether such regret bounds are attainable in the presence of local privacy constraints, with the state-of-the-art result being $\tilde O(T^{3/4})$. In this paper, we show that it is indeed possible to achieve an $\tilde O(\sqrt{T})$ regret upper bound for locally private linear contextual bandit. Our solution relies on several new algorithmic and analytical ideas, such as the analysis of mean absolute deviation errors and layered principal component regression in order to achieve small mean absolute deviation errors.

Demand Balancing in Primal-Dual Optimization for Blind Network Revenue Management

This paper proposes a practically efficient algorithm with optimal theoretical regret which solves the classical network revenue management (NRM) problem with unknown, nonparametric demand. Over a time horizon of length $T$, in each time period the retailer needs to decide prices of $N$ types of products which are produced based on $M$ types of resources with unreplenishable initial inventory. When demand is nonparametric with some mild assumptions, Miao and Wang (2021) is the first paper which proposes an algorithm with $O(\text{poly}(N,M,\ln(T))\sqrt{T})$ type of regret (in particular, $\tilde O(N^{3.5}\sqrt{T})$ plus additional high-order terms that are $o(\sqrt{T})$ with sufficiently large $T\gg N$). In this paper, we improve the previous result by proposing a primal-dual optimization algorithm which is not only more practical, but also with an improved regret of $\tilde O(N^{3.25}\sqrt{T})$ free from additional high-order terms. A key technical contribution of the proposed algorithm is the so-called demand balancing, which pairs the primal solution (i.e., the price) in each time period with another price to offset the violation of complementary slackness on resource inventory constraints. Numerical experiments compared with several benchmark algorithms further illustrate the effectiveness of our algorithm.

Gender Bias in Large Language Models across Multiple Languages

With the growing deployment of large language models (LLMs) across various applications, assessing the influence of gender biases embedded in LLMs becomes crucial. The topic of gender bias within the realm of natural language processing (NLP) has gained considerable focus, particularly in the context of English. Nonetheless, the investigation of gender bias in languages other than English is still relatively under-explored and insufficiently analyzed. In this work, We examine gender bias in LLMs-generated outputs for different languages. We use three measurements: 1) gender bias in selecting descriptive words given the gender-related context. 2) gender bias in selecting gender-related pronouns (she/he) given the descriptive words. 3) gender bias in the topics of LLM-generated dialogues. We investigate the outputs of the GPT series of LLMs in various languages using our three measurement methods. Our findings revealed significant gender biases across all the languages we examined.

The Da Vinci Code of Large Pre-trained Language Models: Deciphering Degenerate Knowledge Neurons

This study explores the mechanism of factual knowledge storage in pre-trained language models (PLMs). Previous research suggests that factual knowledge is stored within multi-layer perceptron weights, and some storage units exhibit degeneracy, referred to as Degenerate Knowledge Neurons (DKNs). This paper provides a comprehensive definition of DKNs that covers both structural and functional aspects, pioneering the study of structures in PLMs' factual knowledge storage units. Based on this, we introduce the Neurological Topology Clustering method, which allows the formation of DKNs in any numbers and structures, leading to a more accurate DKN acquisition. Furthermore, we introduce the Neuro-Degeneracy Analytic Analysis Framework, which uniquely integrates model robustness, evolvability, and complexity for a holistic assessment of PLMs. Within this framework, our execution of 34 experiments across 2 PLMs, 4 datasets, and 6 settings highlights the critical role of DKNs. The code will be available soon.

Utility Fairness in Contextual Dynamic Pricing with Demand Learning

This paper introduces a novel contextual bandit algorithm for personalized pricing under utility fairness constraints in scenarios with uncertain demand, achieving an optimal regret upper bound. Our approach, which incorporates dynamic pricing and demand learning, addresses the critical challenge of fairness in pricing strategies. We first delve into the static full-information setting to formulate an optimal pricing policy as a constrained optimization problem. Here, we propose an approximation algorithm for efficiently and approximately computing the ideal policy. We also use mathematical analysis and computational studies to characterize the structures of optimal contextual pricing policies subject to fairness constraints, deriving simplified policies which lays the foundations of more in-depth research and extensions. Further, we extend our study to dynamic pricing problems with demand learning, establishing a non-standard regret lower bound that highlights the complexity added by fairness constraints. Our research offers a comprehensive analysis of the cost of fairness and its impact on the balance between utility and revenue maximization. This work represents a step towards integrating ethical considerations into algorithmic efficiency in data-driven dynamic pricing.

Automatic Coronary Artery Plaque Quantification and CAD-RADS Prediction using Mesh Priors

Coronary artery disease (CAD) remains the leading cause of death worldwide. Patients with suspected CAD undergo coronary CT angiography (CCTA) to evaluate the risk of cardiovascular events and determine the treatment. Clinical analysis of coronary arteries in CCTA comprises the identification of atherosclerotic plaque, as well as the grading of any coronary artery stenosis typically obtained through the CAD-Reporting and Data System (CAD-RADS). This requires analysis of the coronary lumen and plaque. While voxel-wise segmentation is a commonly used approach in various segmentation tasks, it does not guarantee topologically plausible shapes. To address this, in this work, we propose to directly infer surface meshes for coronary artery lumen and plaque based on a centerline prior and use it in the downstream task of CAD-RADS scoring. The method is developed and evaluated using a total of 2407 CCTA scans. Our method achieved lesion-wise volume intraclass correlation coefficients of 0.98, 0.79, and 0.85 for calcified, non-calcified, and total plaque volume respectively. Patient-level CAD-RADS categorization was evaluated on a representative hold-out test set of 300 scans, for which the achieved linearly weighted kappa ($\kappa$) was 0.75. CAD-RADS categorization on the set of 658 scans from another hospital and scanner led to a $\kappa$ of 0.71. The results demonstrate that direct inference of coronary artery meshes for lumen and plaque is feasible, and allows for the automated prediction of routinely performed CAD-RADS categorization.