Mathematical Optimization and Advanced Algorithms for Few-Shot and Zero-Shot Visual Learning: An Optimization-Centered Review

Few-shot learning (FSL) and zero-shot learning (ZSL) are usually studied as separate problems, yet both require prediction when class-specific evidence is absent or scarce. This review analyzes their shared difficulty from an optimization perspective. Instead of grouping studies only by architecture, it tracks four common coordinates: the information available to the learner, the variables estimated from that information, the objectives and constraints, and the numerical solvers. These coordinates support a unified comparison of attribute-based ZSL, episodic meta-learning, metric and prototype estimators, graph and optimal-transport inference, generative any-shot models, and adaptation of vision–language models. The synthesis exposes recurring trade-offs rather than a universally preferable family: flexible updates increase estimator variance; tractable task-time solvers inherit representation bias; query batches can improve inference while changing the protocol; and strong pretrained priors reduce target-data requirements while making the origin of task evidence harder to audit. Canonical objectives are distinguished from simplified review formulations and prospective research targets. The framework also clarifies the progression from explicit semantic mappings to local adaptation around pretrained image–text representations. Three priorities emerge: model selection without extra validation labels, safe use of uncertain pretrained knowledge, and stable parameter-efficient adaptation. Under this view, FSL and ZSL are connected structured-estimation problems rather than an inventory of unrelated algorithms.