通过协议-目标-资源归约构建学习范式间的关系结构
Structuring Relations Among Learning Paradigms via Protocol--Objective--Resource Reductions
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中文总结 AI 辅助
提出协议-目标-资源框架，通过归约统一监督、迁移、持续和元学习范式，证明复杂度支配性并建立包含关系。
中文摘要 AI 辅助
现代机器学习涵盖监督学习、迁移学习、持续学习、元学习及相关范式，这些范式通常复用相同的假设类别、架构和优化器，但在信息访问、目标、记忆、适应性和样本核算方面存在差异。这使得确定一个范式是真正独特的、另一个范式的特例，还是更广泛结构层级的一部分变得困难。我们引入了一个协议-目标-资源（POR）框架，将表示能力与这些设计选择分离开来。一个范式由环境类别、观察协议、可接受的学习者、性能函数和资源核算规则指定。POR归约结合了环境嵌入、学习者编译器、阈值映射和校准的资源开销。我们的主要定理表明，此类归约意味着在嵌入的比较类别上具有最坏情况复杂度支配性，将上界向前传递，下界向后传递；在标记样本核算下，这产生了样本复杂度支配性。我们还表明，校准的非平凡准确率区间对于避免空洞比较是必要的，并且即使协议和学习者类别不变，强化目标也能严格增加极小极大样本复杂度。将该框架应用于监督学习、迁移学习、持续学习和元学习，产生了典型的特例关系：持续学习包含迁移学习，迁移学习包含监督学习，元学习在对齐的原始样本核算下包含监督学习。我们进一步推导了情景元学习的非精确情景到样本归约，并捕获了范式内细化，如回放记忆和任务标识符。该框架因此为构建学习范式结构及跨范式传递复杂度保证提供了统一语言。
英文摘要
Modern machine learning spans supervised, transfer, continual, meta-learning, and related regimes that often reuse the same hypothesis classes, architectures, and optimizers but differ in information access, objectives, memory, adaptation, and sample accounting. This makes it difficult to determine whether one paradigm is genuinely distinct, a special case of another, or part of a broader structural hierarchy. We introduce a protocol-objective-resource (POR) framework that separates representational capacity from these design choices. A paradigm is specified by an environment class, observation protocol, admissible learners, performance functional, and resource accounting rule. POR reductions combine environment embeddings, learner compilers, threshold maps, and calibrated resource overheads. Our main theorem shows that such reductions imply worst-case complexity domination on embedded comparison classes, transferring upper bounds forward and lower bounds backward; under labeled-example accounting, this yields sample complexity domination. We also show that calibrated nontrivial accuracy regimes are necessary to avoid vacuous comparisons, and that strengthening the objective can strictly increase minimax sample complexity even with unchanged protocols and learner classes. Instantiating the framework for supervised, transfer, continual, and meta-learning yields canonical special-case relations: continual contains transfer, transfer contains supervised, and meta-learning contains supervised under aligned raw-example accounting. We further derive a non-exact episode-to-example reduction for episodic meta-learning and capture within-paradigm refinements such as replay memory and task identifiers. The framework thus provides a unified language for structuring learning paradigms and transferring complexity guarantees across them.
