Peng Zeng

Peng Zeng, Xiaotian Song, Andrew Lensen et al.

Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the dominator in solving SR problems. However, as the scale of SR problems increases, GP often poorly demonstrates and cannot effectively address the real-world high-dimensional problems. This limitation is mainly caused by the stochastic evolutionary nature of traditional GP in constructing the trees. In this paper, we propose a differentiable approach named DGP to construct GP trees towards high-dimensional SR for the first time. Specifically, a new data structure called differentiable symbolic tree is proposed to relax the discrete structure to be continuous, thus a gradient-based optimizer can be presented for the efficient optimization. In addition, a sampling method is proposed to eliminate the discrepancy caused by the above relaxation for valid symbolic expressions. Furthermore, a diversification mechanism is introduced to promote the optimizer escaping from local optima for globally better solutions. With these designs, the proposed DGP method can efficiently search for the GP trees with higher performance, thus being capable of dealing with high-dimensional SR. To demonstrate the effectiveness of DGP, we conducted various experiments against the state of the arts based on both GP and deep neural networks. The experiment results reveal that DGP can outperform these chosen peer competitors on high-dimensional regression benchmarks with dimensions varying from tens to thousands. In addition, on the synthetic SR problems, the proposed DGP method can also achieve the best recovery rate even with different noisy levels. It is believed this work can facilitate SR being a powerful alternative to interpretable ML for a broader range of real-world problems.

Guangxi Wan, Peng Zeng, Xiaoting Dong et al.

Cyber-physical systems (CPS) require the joint optimization of discrete cyber actions and continuous physical parameters under stringent safety logic constraints. However, existing hierarchical approaches often compromise global optimality, whereas reinforcement learning (RL) in hybrid action spaces often relies on brittle reward penalties, masking, or shielding and struggles to guarantee constraint satisfaction. We present logic-informed reinforcement learning (LIRL), which equips standard policy-gradient algorithms with projection that maps a low-dimensional latent action onto the admissible hybrid manifold defined on-the-fly by first-order logic. This guarantees feasibility of every exploratory step without penalty tuning. Experimental evaluations have been conducted across multiple scenarios, including industrial manufacturing, electric vehicle charging stations, and traffic signal control, in all of which the proposed method outperforms existing hierarchical optimization approaches. Taking a robotic reducer assembly system in industrial manufacturing as an example, LIRL achieves a 36.47\% to 44.33\% reduction at most in the combined makespan-energy objective compared to conventional industrial hierarchical scheduling methods. Meanwhile, it consistently maintains zero constraint violations and significantly surpasses state-of-the-art hybrid-action reinforcement learning baselines. Thanks to its declarative logic-based constraint formulation, the framework can be seamlessly transferred to other domains such as smart transportation and smart grid, thereby paving the way for safe and real-time optimization in large-scale CPS.

Hanwen Huang, Peng Zeng

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of regularized convex classifiers in the high-dimensional limit, where both the sample size $n$ and the dimension $p$ approach infinity while their ratio $α=n/p$ remains fixed. Our focus is on the generalization error and variable selection properties of the estimators. Specifically, based on the distributional limit of the classifier, we construct a de-biased estimator to perform variable selection through an appropriate hypothesis testing procedure. Using $L_1$-regularized logistic regression as an example, we conducted extensive computational experiments to confirm that our analytical findings are consistent with numerical simulations in finite-sized systems. We also explore the influence of the covariance structure on the performance of the de-biased estimator.