The insights and techniques developed in the paper, such as the martingale characterization of the optimal q-function and the risk-sensitive q-learning algorithm, can be extended to other types of risk-sensitive objectives beyond the exponential form. By understanding the fundamental principles of risk-sensitive reinforcement learning and the role of risk sensitivity coefficients, these techniques can be adapted to different objective functions that capture various risk preferences.
For objectives like CVaR or certainty-equivalency, the martingale perspective and q-learning algorithms can still be applied by modifying the loss functions and constraints to align with the specific form of the risk-sensitive objective. The key lies in formulating the objective function and constraints in a way that reflects the desired risk-awareness criteria while maintaining the principles of reinforcement learning.
Furthermore, the concept of entropy regularization and exploration can be generalized to different risk-sensitive objectives to encourage learning policies that balance between exploration and exploitation under uncertainty. By adapting the algorithms and methodologies developed in this paper, researchers can explore a wide range of risk-sensitive objectives and enhance the applicability of risk-sensitive reinforcement learning in various domains.