An efficient model selection method for Lotka-Volterra systems based on ABC-PMC and reinforcement learning

This study provides an efficient, adaptive computational framework for Bayesian model selection when likelihood functions are difficult to handle. To address model selection challenges in scenarios where complex model likelihood functions are difficult to handle, this paper proposes an adaptive approximate Bayesian computation with probability-minimizing computation (RL(Softmax)-ABC-PMC) algorithm that integrates a reinforcement learning (RL) Softmax decision mechanism. This method embeds Softmax agents into the standard ABC-PMC framework, dynamically evaluating the historical performance of candidate models to adaptively focus computational resources on potentially optimal models, thereby significantly enhancing selection efficiency. A numerical experiment is provided to select the best model from three Lotka-Volterra (LV) competition models, including a discretized LV model, a randomized LV model, and a fractional-order LV model, where the algorithm effectively distinguishes subtle differences in their fitting ability and yields reliable parameter estimates. Additionally, we further validate the efficiency of the provided algorithm by selecting the best model from three S-shaped growth curve models. Finally, an empirical analysis using Chinese automotive market sales data further validates the practicality and effectiveness of the proposed method in real-world applications, demonstrating that the RL(Softmax)-ABC-PMC algorithm can automatically identify model structures with stronger explanatory power while maintaining high computational efficiency.