Parameter-dependent self-learning optimization

Abstract

Manually developing optimization algorithms is a time-consuming task requiring expert knowledge. Therefore, it makes a lot of sense to automate the design process of such algorithms. Additionally, learned optimization algorithms reduce the number of a priori assumptions made about the characteristics of the underlying objective function. Numerous works discuss possibilities for learning optimization algorithms. This field of study is called learn-to-optimize. In this bachelor’s thesis, we concentrate on the reinforcement learning perspective. Consequently, optimization algorithms are represented as policies. The comparison of learned algorithms to current state-of-the-art algorithms for particular applications reveals that learned algorithms manage to perform better concerning convergence speed and final objective function value. However, most existing approaches only consider fixed sets of parameters to be optimized. Because of this, it is challenging to adapt the learned optimization algorithm to other objective functions. More importantly, it is impossible to optimize when explicit constraints on so-called “free” optimization parameters are given. We investigated the learn-to-optimize approach under various optimization parameter sets and conditions on “free” parameters to solve this problem. Furthermore, we studied the performance of learned optimizers in high-dimensional setups.