让机器学习模型提前适应未来变化的数据分布。
Prospective Learning: Learning for a Dynamic Future
- 将时间作为输入变量，动态调整预测策略。
- 在动态数据下，风险逼近贝叶斯最优水平。
- 适合长期运行、环境持续变化的场景使用。
在现实应用中，数据分布和目标会随时间演变。主流机器学习理论（如可能近似正确，PAC）大多忽略时间因素，导致现有方法在动态环境中表现不佳。本文提出「前瞻性学习」理论框架，专门应对最优假设随时间变化的问题。在传统PAC学习中，经验风险最小化（ERM）是稳定的；本文提出前瞻性ERM，输出一组用于预测未来数据的预测器。在特定随机过程假设下，证明了前瞻性ERM的风险收敛于贝叶斯风险。该方法本质上将时间作为输入，而标准ERM忽略时间，在分布动态时可能完全失效。数值实验表明，前瞻性ERM能有效解决基于MNIST和CIFAR-10构建的合成与视觉识别任务。代码见https://github.com/neurodata/prolearn。
原文摘要 · Abstract (English)
In real-world applications, the distribution of the data, and our goals, evolve over time. The prevailing theoretical framework for studying machine learning, namely probably approximately correct (PAC) learning, largely ignores time. As a consequence, existing strategies to address the dynamic nature of data and goals exhibit poor real-world performance. This paper develops a theoretical framework called "Prospective Learning" that is tailored for situations when the optimal hypothesis changes over time. In PAC learning, empirical risk minimization (ERM) is known to be consistent. We develop a learner called Prospective ERM, which returns a sequence of predictors that make predictions on future data. We prove that the risk of prospective ERM converges to the Bayes risk under certain assumptions on the stochastic process generating the data. Prospective ERM, roughly speaking, incorporates time as an input in addition to the data. We show that standard ERM as done in PAC learning, without incorporating time, can result in failure to learn when distributions are dynamic. Numerical experiments illustrate that prospective ERM can learn synthetic and visual recognition problems constructed from MNIST and CIFAR-10. Code at https://github.com/neurodata/prolearn.
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