Constraint-Aware Proximal Policy Optimization for Band-Gap Prediction in Inorganic Crystal Datasets

Abstract

A small search space can be obtained for the functional inorganic crystal by a good band-gap prediction; however, traditional regressors may produce chemically inconsistent or poorly calibrated estimates outside the training distribution. This paper introduces a constraint-aware proximal policy optimization algorithm. The algorithm treats predictions as a series of brief potential state-refined actions. A crystal graph encoder initializes the state; a clipped policy selects bounded residual updates; and a supervised value head estimates the band gap along with heteroscedastic uncertainty. Four constraints are imposed via adaptive Lagrange multipliers instead of a fixed penalty: non-negative output, stoichiometric consistency, bounded latent displacement, and uncertainty control. On composition-disjoint benchmark splits with 42,318 crystals, the proposed model achieved a mean absolute error of 0.274 eV and a coefficient of determination of 0.892. It reduced the violation rate from 6.8% for an unconstrained policy to 1.3% and increased the 90% prediction-interval coverage from 82.4% to 89.1%. Under element-holdout transfer, the increase in error was only 18.6%, and it was lower than that for the strongest graph-regression baseline at 31.7%. Ablation results attribute the most reliable gain to adaptive dual updates and uncertainty-aware rewards. Routing of reviews also included difficult predictions and did not discard their estimates for practical two-stage screening. Therefore, by explicitly incorporating physical and statistical constraints during the optimization process, policy-based optimization can enhance the numerical accuracy of the results and the reliability of deployment.