Deep reinforced learning heuristic tested on spin-glass ground states: The larger picture

Abstract

In Changjun Fan et al. [Nature Communications https://doi.org/10.1038/s41467-023-36363-w (2023)], the authors present a deep reinforced learning approach to augment combinatorial optimization heuristics. In particular, they present results for several spin glass ground state problems, for which instances on non-planar networks are generally NP-hard, in comparison with several Monte Carlo based methods, such as simulated annealing (SA) or parallel tempering (PT). Indeed, those results demonstrate that the reinforced learning improves the results over those obtained with SA or PT, or at least allows for reduced runtimes for the heuristics before results of comparable quality have been obtained relative to those other methods. To facilitate the conclusion that their method is ''superior'', the authors pursue two basic strategies: (1) A commercial GUROBI solver is called on to procure a sample of exact ground states as a testbed to compare with, and (2) a head-to-head comparison between the heuristics is given for a sample of larger instances where exact ground states are hard to ascertain. Here, we put these studies into a larger context, showing that the claimed superiority is at best marginal for smaller samples and becomes essentially irrelevant with respect to any sensible approximation of true ground states in the larger samples. For example, this method becomes irrelevant as a means to determine stiffness exponents $\theta$ in $d>2$, as mentioned by the authors, where the problem is not only NP-hard but requires the subtraction of two almost equal ground-state energies and systemic errors in each of $\approx 1\%$ found here are unacceptable. This larger picture on the method arises from a straightforward finite-size corrections study over the spin glass ensembles the authors employ, using data that has been available for decades.