Synthetic Minority Oversampling Technique (SMOTE) is a common rebalancing
strategy for handling imbalanced data sets. Asymptotically, we prove that SMOTE
(with default parameter) regenerates the original distribution by simply
copying the original minority samples. We also prove that SMOTE density
vanishes near the boundary of the support of the minority distribution,
therefore justifying the common BorderLine SMOTE strategy. Then we introduce
two new SMOTE-related strategies, and compare them with state-of-the-art
rebalancing procedures. We show that rebalancing strategies are only required
when the data set is highly imbalanced. For such data sets, SMOTE, our
proposals, or undersampling procedures are the best strategies.

SMOTE 是处理不平衡数据集的常见重平衡策略，它能通过复制原始少数样本来重新生成原始分布，同时在少数分布边界附近 SMOTE 密度消失，验证了常见的边界 SMOTE 策略。我们还介绍了两种新的 SMOTE 相关策略，并将其与最先进的重平衡程序进行比较。我们表明，只有在数据集高度不平衡时才需要重平衡策略，对于这样的数据集，SMOTE、我们的提议或欠采样程序是最佳策略。

SMOTE 的理论和实验研究：再平衡策略的限制和比较

Theoretical and experimental study of SMOTE: limitations and comparisons  of rebalancing strategies

Bike-Sharing Systems provide eco-friendly urban mobility, contributing to the
alleviation of traffic congestion and to healthier lifestyles. Efficiently
operating such systems and maintaining high customer satisfaction is
challenging due to the stochastic nature of trip demand, leading to full or
empty stations. Devising effective rebalancing strategies using vehicles to
redistribute bikes among stations is therefore of uttermost importance for
operators. As a promising alternative to classical mathematical optimization,
reinforcement learning is gaining ground to solve sequential decision-making
problems. This paper introduces a spatio-temporal reinforcement learning
algorithm for the dynamic rebalancing problem with multiple vehicles. We first
formulate the problem as a Multi-agent Markov Decision Process in a continuous
time framework. This allows for independent and cooperative vehicle
rebalancing, eliminating the impractical restriction of time-discretized models
where vehicle departures are synchronized. A comprehensive simulator under the
first-arrive-first-serve rule is then developed to facilitate the learning
process by computing immediate rewards under diverse demand scenarios. To
estimate the value function and learn the rebalancing policy, various Deep
Q-Network configurations are tested, minimizing the lost demand. Experiments
are carried out on various datasets generated from historical data, affected by
both temporal and weather factors. The proposed algorithms outperform
benchmarks, including a multi-period Mixed-Integer Programming model, in terms
of lost demand. Once trained, it yields immediate decisions, making it suitable
for real-time applications. Our work offers practical insights for operators
and enriches the integration of reinforcement learning into dynamic rebalancing
problems, paving the way for more intelligent and robust urban mobility
solutions.

骑行共享系统是提供生态友好的城市出行方式，有助于减轻交通拥堵和改善健康生活方式。本研究提出一种基于时空强化学习算法的动态均衡问题解决方案，在多种数据集上的实验证明其在减少需求损失方面优于传统模型，为城市出行提供更智能、强大的解决方案。