In a data-driven approach, the risk sensitivity coefficient can be determined through iterative optimization methods that aim to find the optimal value for the coefficient based on the observed data and the performance of the RL algorithm. One common method is to use reinforcement learning techniques to learn the risk sensitivity coefficient along with the policy. This can be achieved by incorporating the risk sensitivity coefficient as a parameter in the policy and updating it during the learning process.
One approach is to frame the determination of the risk sensitivity coefficient as a hyperparameter optimization problem. By treating the risk sensitivity coefficient as a hyperparameter, techniques such as grid search, random search, or more advanced optimization algorithms like Bayesian optimization or evolutionary strategies can be employed to find the optimal value that maximizes the performance of the RL algorithm.
Another method is to use model-based reinforcement learning techniques to estimate the risk sensitivity coefficient. By building a model of the environment and simulating different scenarios with varying risk sensitivity coefficients, the algorithm can learn the impact of different coefficients on the performance and adjust accordingly.
Overall, by integrating the determination of the risk sensitivity coefficient into the learning process of the RL algorithm, it can be optimized endogenously based on the data and the task at hand.