  Optimization problems characterized by both discrete and continuous variables
are common across various disciplines, presenting unique challenges due to
their complex solution landscapes and the difficulty of navigating
mixed-variable spaces effectively. To Address these challenges, we introduce a
hybrid Reinforcement Learning (RL) framework that synergizes RL for discrete
variable selection with Bayesian Optimization for continuous variable
adjustment. This framework stands out by its strategic integration of RL and
continuous optimization techniques, enabling it to dynamically adapt to the
problem's mixed-variable nature. By employing RL for exploring discrete
decision spaces and Bayesian Optimization to refine continuous parameters, our
approach not only demonstrates flexibility but also enhances optimization
performance. Our experiments on synthetic functions and real-world machine
learning hyperparameter tuning tasks reveal that our method consistently
outperforms traditional RL, random search, and standalone Bayesian optimization
in terms of effectiveness and efficiency.
