Risk-sensitive Reinforcement Learning (1311.2097v3)

Abstract: We derive a family of risk-sensitive reinforcement learning methods for agents, who face sequential decision-making tasks in uncertain environments. By applying a utility function to the temporal difference (TD) error, nonlinear transformations are effectively applied not only to the received rewards but also to the true transition probabilities of the underlying Markov decision process. When appropriate utility functions are chosen, the agents' behaviors express key features of human behavior as predicted by prospect theory (Kahneman and Tversky, 1979), for example different risk-preferences for gains and losses as well as the shape of subjective probability curves. We derive a risk-sensitive Q-learning algorithm, which is necessary for modeling human behavior when transition probabilities are unknown, and prove its convergence. As a proof of principle for the applicability of the new framework we apply it to quantify human behavior in a sequential investment task. We find, that the risk-sensitive variant provides a significantly better fit to the behavioral data and that it leads to an interpretation of the subject's responses which is indeed consistent with prospect theory. The analysis of simultaneously measured fMRI signals show a significant correlation of the risk-sensitive TD error with BOLD signal change in the ventral striatum. In addition we find a significant correlation of the risk-sensitive Q-values with neural activity in the striatum, cingulate cortex and insula, which is not present if standard Q-values are used.

• The paper proposes a novel utility-based framework that transforms temporal difference errors using risk-sensitive utility functions from prospect theory.
• It introduces a risk-sensitive Q-learning algorithm with rigorous convergence analysis, aligning decision outcomes with observed human behavior.
• Empirical validation, including fMRI correlations, demonstrates the model’s practical impact in finance, robotics, and decision-making under uncertainty.

Analysis of Risk-Sensitive Reinforcement Learning

The paper "Risk-sensitive Reinforcement Learning" presents an extension to traditional reinforcement learning by incorporating risk preferences into the decision-making process. The authors propose a novel framework that integrates principles from decision theory, specifically prospect theory, with reinforcement learning. This model enables agents to exhibit varying risk preferences in uncertain environments, akin to human behavior in decision-making tasks.

Key Contributions and Methodology

1. Utility-Based Framework: The paper introduces risk-sensitive reinforcement learning methods where agents apply utility functions to temporal difference (TD) errors. This transformation affects both the rewards and transition probabilities within a Markov decision process (MDP), aligning agent behavior with the non-linear probability weighting described in prospect theory.
2. Risk-Sensitive Q-Learning Algorithm: The authors propose a risk-sensitive variant of Q-learning, characterized by a utility function-transforming TD errors. They ensure this algorithm's convergence rigorously, providing a solid theoretical foundation for analyzing risk in a reinforcement learning context.
3. Empirical Validation: The framework is validated through an experiment involving a sequential investment task. The risk-sensitive model is shown to fit human behavioral data significantly better than traditional models.
4. Neuroscientific Correlation: The paper associates the risk-sensitive TD errors with BOLD signal changes observed in fMRI scans, demonstrating neural correlates of the proposed model with activity in the ventral striatum, among other regions. Such neural alignment endorses the biological plausibility of the framework.

Theoretical and Practical Implications

Theoretically, this work enriches the reinforcement learning field by integrating risk sensitivity through behavioral economics principles. The modified reward signal enables modeling of intricate human-like decision patterns, such as varying attitudes towards risks associated with potential gains and losses. The convergence proofs further solidify the robustness of the proposed methods, facilitating the design of algorithms that better predict decision outcomes under uncertainty.

Practically, incorporating risk sensitivity has promising applications in fields where decision-making under uncertainty is critical—such as finance, robotics, and autonomous systems. By mirroring human risk preferences, the framework enhances the decision quality of AI systems in volatile environments, paving the way for more sophisticated adaptation strategies that account for both agent and human interaction scenarios.

Conclusion and Future Directions

This paper advances reinforcement learning by bridging economic behavior theories with computational models, offering a novel avenue to emulate complex human decision-making processes. A potential future direction involves extending this framework to encompass continuous state-action spaces, applying function approximation techniques to scalability challenges. Additionally, exploring different utility functions and their impact on multi-agent environments could provide deeper insights into collective risk-sensitive behavior. The integration of additional neuroscientific data could further substantiate the biological underpinnings of risk-sensitive learning, making the model increasingly relevant for cognitive and neuroscience-driven AI research.