Automatic adjustment of replica exchange

One or more non-transitory computer-readable storage media configured to store instructions that, in response to being executed, cause a system to perform operations, the operations comprising:

• obtaining a first fixed temperature of a replica exchange Markov Chain Monte Carlo (MCMC) process used to solve an optimization problem associated with a system;
• obtaining a second fixed temperature of the replica exchange MCMC process;
• obtaining a plurality of replicas of the system to use in the replica exchange MCMC process;
• assigning each replica of the plurality of replicas to a different corresponding temperature of a set of temperatures of the replica exchange MCMC process, the set of temperatures including the first fixed temperature, the second fixed temperature, and a plurality of variable temperatures that are numerically ordered between the first fixed temperature and the second fixed temperature;
• obtaining a target swap acceptance probability with respect to swapping, during the replica exchange MCMC process, between replicas that correspond to adjacently ordered variable temperatures of the plurality of variable temperatures;
• determining a respective average swap acceptance probability with respect to one or more respective adjacent pairs of the plurality of variable temperatures, each respective swap acceptance probability being with respect to swaps between replicas assigned to the one or more respective adjacent pairs;
• adjusting, during the replica exchange MCMC process while maintaining the first fixed temperature and the second fixed temperature, one or more of the variable temperatures based on a relationship between the target swap acceptance probability and each of one or more of the respective swap acceptance probabilities;
• adjusting, during the replica exchange MCMC process, a number of replicas used during the MCMC process, the adjusting of the number of replicas being based on a difference between the second fixed temperature and a particular variable temperature that is ordered adjacently to the second fixed temperature;
• and
• identifying, based on an output of the replica exchange MCMC process, a particular state of the system as a solution to the optimization problem associated with the system.

A system comprising:

• hardware configured to perform operations, the operations comprising:
• obtaining a first fixed temperature of a replica exchange Markov Chain Monte Carlo (MCMC) process used to solve an optimization problem associated with a system;
• obtaining a second fixed temperature of the replica exchange MCMC process;
• obtaining a plurality of replicas of the system to use in the replica exchange MCMC process;
• assigning each replica of the plurality of replicas to a different corresponding temperature of a set of temperatures of the replica exchange MCMC process, the set of temperatures including the first fixed temperature, the second fixed temperature, and a plurality of variable temperatures that are numerically ordered between the first fixed temperature and the second fixed temperature;
• obtaining a target swap acceptance probability with respect to swapping, during the replica exchange MCMC process, between replicas that correspond to adjacently ordered variable temperatures of the plurality of variable temperatures;
• determining a respective average swap acceptance probability with respect to one or more respective adjacent pairs of the plurality of variable temperatures, each respective swap acceptance probability being with respect to swaps between replicas assigned to the one or more respective adjacent pairs;
• adjusting, during the replica exchange MCMC process while maintaining the first fixed temperature and the second fixed temperature, one or more of the variable temperatures based on a relationship between the target swap acceptance probability and each of one or more of the respective swap acceptance probabilities;
• and
• identifying, based on an output of the replica exchange MCMC process, a particular state of the system as a solution to the optimization problem associated with the system.