Optimization on a Budget: A Reinforcement Learning Approach

Many popular optimization algorithms, like the Levenberg-Marquardt algorithm (LMA), use heuristic-based “controllers” that modulate the behavior of the optimizer during the optimization process. For example, in the LMA a damping parameter λ is dynamically modified based on a set of rules that were developed using heuristic arguments. Reinforcement learning (RL) is a machine learning approach to learn optimal controllers from examples and thus is an obvious candidate to improve the heuristic-based controllers implicit in the most popular and heavily used optimization algorithms. Improving the performance of off-the-shelf optimizers is particularly important for time-constrained optimization problems. For example the LMA algorithm has become popular for many real-time computer vision problems, including object tracking from video, where only a small amount of time can be allocated to the optimizer on each incoming video frame. Here we show that a popular modern reinforcement learning technique using a very simple state space can dramatically improve the performance of general purpose optimizers, like the LMA. Surprisingly the controllers learned for a particular domain also work well in very different optimization domains. For example we used RL methods to train a new controller for the damping parameter of the LMA. This controller was trained on a collection of classic, relatively small, non-linear regression problems. The modified LMA performed better than the standard LMA on these problems. This controller also dramatically outperformed the standard LMA on a difficult computer vision problem for which it had not been trained. Thus the controller appeared to have extracted control rules that were not just domain specific but generalized across a range of optimization domains.