Risk-Constrained Reinforcement Learning with Percentile Risk Criteria (1512.01629v3)

Abstract: In many sequential decision-making problems one is interested in minimizing an expected cumulative cost while taking into account \emph{risk}, i.e., increased awareness of events of small probability and high consequences. Accordingly, the objective of this paper is to present efficient reinforcement learning algorithms for risk-constrained Markov decision processes (MDPs), where risk is represented via a chance constraint or a constraint on the conditional value-at-risk (CVaR) of the cumulative cost. We collectively refer to such problems as percentile risk-constrained MDPs. Specifically, we first derive a formula for computing the gradient of the Lagrangian function for percentile risk-constrained MDPs. Then, we devise policy gradient and actor-critic algorithms that (1) estimate such gradient, (2) update the policy in the descent direction, and (3) update the Lagrange multiplier in the ascent direction. For these algorithms we prove convergence to locally optimal policies. Finally, we demonstrate the effectiveness of our algorithms in an optimal stopping problem and an online marketing application.

• The paper introduces a formulation for risk-constrained MDPs using CVaR and chance constraints, transforming them into tractable Lagrangian forms.
• The paper develops policy gradient and actor-critic algorithms that update policies and Lagrange multipliers simultaneously, ensuring convergence to locally optimal solutions.
• The paper empirically validates these RL algorithms in optimal stopping and online marketing scenarios, confirming their ability to balance rewards with risk minimization.

Risk-Constrained Reinforcement Learning with Percentile Risk Criteria

The paper presents an investigation into risk-constrained reinforcement learning (RL) within the context of Markov Decision Processes (MDPs), specifically focusing on percentile risk criteria. This exploration is particularly pertinent in applications where risk minimization is critical due to the potential for rare but catastrophic events. The authors propose efficient RL algorithms that incorporate chance constraints and Conditional Value-at-Risk (CVaR) for managing such risks.

Key Contributions

1. Formulation of Risk-Constrained MDPs:
   • The authors articulate two key risk-constrained MDP formulations: one involving a CVaR constraint and the other a chance constraint. For CVaR-constrained optimization, they address both discrete and continuous cost distributions. This formulation involves a Lagrangian approach, transforming the risk constraint into a tractable format.
2. Development of RL Algorithms:
   • The paper introduces both policy gradient and actor-critic algorithms. These algorithms are adept at estimating and updating the gradient of the Lagrangian function while concurrently adjusting the Lagrange multiplier. Notably, the algorithmic framework assures convergence to locally optimal policies. This dual-ascent/descent configuration ensures that both the risk metrics and rewards are balanced.
3. Empirical Validation:
   • The effectiveness of these algorithms is demonstrated through applications such as optimal stopping problems and online marketing scenarios. The empirical results indicate that the algorithms maintain performance while adhering to specified risk constraints, thus confirming their practical viability.

Numerical Results and Assertions

The algorithms were validated through rigorous experiments demonstrating convergence to locally optimal solutions, with empirical evidence showcased in example applications. Notably, the paper provided detailed empirical results in optimal stopping problems, where the algorithms effectively managed cost distributions, and in personalized advertisement recommendations, successfully meeting lower bounds on worst-case revenues.

Theoretical Implications

• Risk Management in RL: This framework expands upon traditional RL by embedding robust risk management strategies. By leveraging CVaR and chance constraints, the approach provides a structured method for incorporating risk-aversion into RL, thus broadening the applicability of RL in high-stakes domains.
• Gradient Estimation in High-Dimensional Spaces: The paper also contributes to existing literature on gradient estimation methods by deploying innovative techniques like simultaneous perturbation stochastic approximation (SPSA), which offers potential improvements in high-dimensional policy spaces.

Future Directions

The paper opens several avenues for further research. The integration of importance sampling techniques to enhance gradient estimations in the tails of the distribution is a promising path, potentially leading to even more accurate risk assessments. Additionally, exploring applications in diverse fields such as finance, supply chain logistics, and autonomous systems could prove beneficial.

In conclusion, the research provides vital insights into risk-aware RL strategies, establishing a foundation for future developments that can accommodate complex, real-world decision-making scenarios under uncertainty. The algorithms developed herein push the boundaries of conventional reinforcement learning by embedding a rigorous risk management paradigm, potentially transforming its application in industry and academia.