Deep metric learning (DML) aims to minimize empirical expected loss of the pairwise intra-/inter- class proximity violations in the embedding space. We relate DML to feasibility problem of finite chance constraints. We show that minimizer of proxy-based DML satisfies certain chance constraints, and that the worst case generalization performance of the proxy-based methods can be characterized by the radius of the smallest ball around a class proxy to cover the entire domain of the corresponding class samples, suggesting multiple proxies per class helps performance. To provide a scalable algorithm as well as exploiting more proxies, we consider the chance constraints implied by the minimizers of proxy-based DML instances and reformulate DML as finding a feasible point in intersection of such constraints, resulting in a problem to be approximately solved by iterative projections. Simply put, we repeatedly train a regularized proxy-based loss and re-initialize the proxies with the embeddings of the deliberately selected new samples. We applied our method with 4 well-accepted DML losses and show the effectiveness with extensive evaluations on 4 popular DML benchmarks. Code is available at: https://github.com/yetigurbuz/ccp-dml

翻译：深度度量学习（DML）旨在最小化嵌入空间中成对内/跨类邻近度违反的期望经验损失。我们将DML与有限机会约束的可行性问题相关联。研究表明，基于代理的DML的最小化器满足特定的机会约束，且基于代理方法的最坏情况泛化性能可由覆盖相应类别样本完整定义域的最小球半径来表征，这提示每个类别使用多个代理有助于提升性能。为了提供可扩展算法并利用更多代理，我们考虑由基于代理的DML实例的最小化器隐含的机会约束，并将DML重新表述为在这些约束的交集中寻找可行点，从而形成可通过迭代投影近似求解的问题。简言之，我们重复训练正则化的基于代理的损失，并用精心选择的新样本的嵌入重新初始化代理。我们将所提方法应用于4种广泛接受的DML损失函数，并在4个主流DML基准上通过大量评估验证了其有效性。代码地址：https://github.com/yetigurbuz/ccp-dml