Advances — Finite-sum Coupled Compositional Optimization

Coupling reveals depth where composition meets reality!

In this chapter, we study a novel family of stochastic compositional optimization problems namely finite-sum coupled compositional optimization (FCCO), and introduce algorithms for solving them. These algorithms have direct applications in addressing the empirical X-risk minimization challenges discussed in Chapter 2. To ensure broad applicability, we examine various settings of this problem, characterized by different properties of outer and inner functions, including smooth and non-smooth cases, as well as convex, weakly convex, and non-convex scenarios. The results presented here also significantly extend and complement those discussed in Chapter 3.

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