Finding the Ground State of Spin Hamiltonians with Reinforcement Learning

By Kyle Mills, Pooya Ronagh, & Isaac Tamblyn
Reinforcement learning (RL) has become a proven method for optimizing a procedure for which success has been defined, but the specific actions needed to achieve it have not. Using a method we call “controlled online optimization learning” (COOL), we apply the so-called “black box” method of RL to simulated annealing (SA), demonstrating that an RL agent based on proximal policy optimization can, through experience alone, arrive at a temperature schedule that surpasses the performance of standard heuristic temperature schedules for two classes of Hamiltonians. When the system is initialized at a cool temperature, the RL agent learns to heat the system to “melt” it and then slowly cool it in an effort to anneal to the ground state; if the system is initialized at a high temperature, the algorithm immediately cools the system. We investigate the performance of our RL-driven SA agent in generalizing to all Hamiltonians of a specific class. When trained on random Hamiltonians of nearest-neighbour spin glasses, the RL agent is able to control the SA process for other Hamiltonians, reaching the ground state with a higher probability than a simple linear annealing schedule. Furthermore, the scaling performance (with respect to system size) of the RL approach is far more favourable, achieving a performance improvement of almost two orders of magnitude on L = 14² systems. We demonstrate the robustness of the RL approach when the system operates in a “destructive observation” mode, an allusion to a quantum system where measurements destroy the state of the system. The success of the RL agent could have far-reaching impacts, from classical optimization, to quantum annealing and to the simulation of physical systems.

Journal reference:  Mills, K., Ronagh, P., & Tamblyn, I. Finding the ground state of spin Hamiltonians with reinforcement learning. Nat Mach Intell 2, 509–517 (2020).

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