The exploration–exploitation trade-off is a fundamental concept in single-state reinforcement learning, particularly for the \(L_{KN, K}\) family of learning automaton (LA). The depth parameter (N) in the \(L_{KN, K}\) determines the balance between exploration and exploitation, and an inappropriate value can disrupt this balance, especially in unknown environments. To address this issue, we introduce SVDHLA, a novel hybrid learning automaton that self-adaptively adjusts the depth parameter. This is the first model to combine \(L_{KN, K}\) with a single variable action set learning automaton, allowing for intelligent depth configuration. Through extensive simulations in both stationary and non-stationary environments, we compare SVDHLA’s performance against the state-of-the-art model, demonstrating its superiority in terms of cumulative reward and cumulative regret. To further illustrate the practical utility of our model, we apply the SVDHLA to develop a learning automaton-based dropout mechanism for neural networks, aimed at preventing overfitting and improving performance. The results demonstrate its superiority over previous LA-based dropout methods.
