  In nature, the behaviors of many complex systems can be described by
parsimonious math equations. Automatically distilling these equations from
limited data is cast as a symbolic regression process which hitherto remains a
grand challenge. Keen efforts in recent years have been placed on tackling this
issue and demonstrated success in symbolic regression. However, there still
exist bottlenecks that current methods struggle to break when the discrete
search space tends toward infinity and especially when the underlying math
formula is intricate. To this end, we propose a novel Reinforcement Symbolic
Regression Machine (RSRM) that masters the capability of uncovering complex
math equations from only scarce data. The RSRM model is composed of three key
modules: (1) a Monte Carlo tree search (MCTS) agent that explores optimal math
expression trees consisting of pre-defined math operators and variables, (2) a
Double Q-learning block that helps reduce the feasible search space of MCTS via
properly understanding the distribution of reward, and (3) a modulated sub-tree
discovery block that heuristically learns and defines new math operators to
improve representation ability of math expression trees. Biding of these
modules yields the state-of-the-art performance of RSRM in symbolic regression
as demonstrated by multiple sets of benchmark examples. The RSRM model shows
clear superiority over several representative baseline models.
