Solving Stochastic Compositional Optimization is Nearly as Easy as Solving Stochastic Optimization
This work addresses a key bottleneck in applications like reinforcement learning and meta-learning by making compositional optimization nearly as efficient as standard optimization, though it is incremental as it builds on existing methods.
The paper tackles stochastic compositional optimization, a generalization of stochastic optimization involving nested expectations, by introducing the SCSC method, which converges at the same rate as SGD for non-compositional problems and achieves state-of-the-art performance with techniques like Adam.
Stochastic compositional optimization generalizes classic (non-compositional) stochastic optimization to the minimization of compositions of functions. Each composition may introduce an additional expectation. The series of expectations may be nested. Stochastic compositional optimization is gaining popularity in applications such as reinforcement learning and meta learning. This paper presents a new Stochastically Corrected Stochastic Compositional gradient method (SCSC). SCSC runs in a single-time scale with a single loop, uses a fixed batch size, and guarantees to converge at the same rate as the stochastic gradient descent (SGD) method for non-compositional stochastic optimization. This is achieved by making a careful improvement to a popular stochastic compositional gradient method. It is easy to apply SGD-improvement techniques to accelerate SCSC. This helps SCSC achieve state-of-the-art performance for stochastic compositional optimization. In particular, we apply Adam to SCSC, and the exhibited rate of convergence matches that of the original Adam on non-compositional stochastic optimization. We test SCSC using the portfolio management and model-agnostic meta-learning tasks.