arXiv subjects

Mengge Li

Publications and source records attributed to Mengge Li.

4 recordsLinked to original sources

arXiv2025

Continuous-time reinforcement learning for optimal switching over multiple regimes

This paper studies the continuous-time reinforcement learning (RL) for optimal switching problems across multiple regimes. We consider a type of exploratory formulation under entropy regularization where the agent randomizes both the timing of switches and the selection of regimes through the generator matrix of an associated continuous-time finite-state Markov chain. We establish the well-posedness of the associated system of Hamilton-Jacobi-Bellman (HJB) equations and provide a characterization of the optimal policy. The policy improvement and the convergence of the policy iterations are rigorously established by analyzing the system of equations. We also show that the value function in the exploratory formulation converges to the one in the classical formulation as the temperature parameter vanishes. Finally, a model-free reinforcement learning algorithm is devised and implemented by invoking the policy evaluation based on the martingale characterization. Our numerical examples with financial applications illustrate the effectiveness and efficiency of the proposed RL algorithm.

math.OC↗

arXiv2025

Chemistry-Enhanced Diffusion-Based Framework for Small-to-Large Molecular Conformation Generation

Obtaining 3D conformations of realistic polyatomic molecules at the quantum chemistry level remains challenging, and although recent machine learning advances offer promise, predicting large-molecule structures still requires substantial computational effort. Here, we introduce StoL, a diffusion model-based framework that enables rapid and knowledge-free generation of large molecular structures from small-molecule data. Remarkably, StoL assembles molecules in a LEGO-style fashion from scratch, without seeing the target molecules or any structures of comparable size during training. Given a SMILES input, it decomposes the molecule into chemically valid fragments, generates their 3D structures with a diffusion model trained on small molecules, and assembles them into diverse conformations. This fragment-based strategy eliminates the need for large-molecule training data while maintaining high scalability and transferability. By embedding chemical principles into key steps, StoL ensures faster convergence, chemically rational structures, and broad configurational coverage, as confirmed against DFT calculations.

physics.chem-ph↗

arXiv2024

QCDGE database, Quantum Chemistry Database with Ground- and Excited-state Properties of 450 Kilo Molecules

Due to rapid advancements in deep learning techniques, the demand for large-volume high-quality databases grows significantly in chemical research. We developed a quantum-chemistry database that includes 443,106 small organic molecules with sizes up to 10 heavy atoms including carbon (C), nitrogen (N), oxygen (O), and fluorine (F). Ground-state geometry optimizations and frequency calculations of all compounds were performed at the B3LYP/6-31G* level with the BJD3 dispersion correction, while the excited-state single-point calculations were conducted at the $\omega$B97X-D/6-31G* level. Totally twenty seven molecular properties, such as geometric, thermodynamic, electronic and energetic properties, were gathered from these calculations. Meanwhile, we also established a comprehensive protocol for the construction of a high-volume quantum-chemistry database. Our QCDGE (Quantum Chemistry Database with Ground- and Excited-State Properties) database contains a substantial volume of data, exhibits high chemical diversity, and most importantly includes excited-state information. This database, along with its construction protocol, is expected to have a significant impact on the broad applications of machine learning studies across different fields of chemistry, especially in the area of excited-state research.

physics.chem-ph↗

arXiv2023

Robust Equilibrium Strategy for Mean-Variance Portfolio Selection

The classical mean-variance portfolio selection problem induces time-inconsistent (precommited) strategies (see Zhou and Li (2000)). To overcome this time-inconsistency, Basak and Chabakauri (2010) introduce the game theoretical approach and look for (sub-game perfect Nash) equilibrium strategies, which is solved from the corresponding partial differential equations (PDE) system. In their model, the investor perfectly knows the drift and volatility of the assets. However, in reality investors only have an estimate on them, e.g, a 95% confidence interval. In this case, some literature (e.g., Pham, Wei and Zhou (2022)) derives the optimal precommited strategy under the worst parameters, which is the robust control. The relation between the equilibrium strategy and the PDE system has not been justified when incorporating robust control. In this paper, we consider a general dynamic mean-variance framework and propose a novel definition of the robust equilibrium strategy. Under our definition, a classical solution to the corresponding PDE system implies a robust equilibrium strategy. We then explicitly solve for some special examples.

q-fin.MF↗