Beyond CVaR: Leveraging Static Spectral Risk Measures for Enhanced Decision-Making in Distributional Reinforcement Learning

In domains such as finance, healthcare, and robotics, managing worst-case scenarios is critical, as failure to do so can lead to catastrophic outcomes. Distributional Reinforcement Learning (DRL) provides a natural framework to incorporate risk sensitivity into decision-making processes. However, existing approaches face two key limitations: (1) the use of fixed risk measures at each decision step often results in overly conservative policies, and (2) the interpretation and theoretical properties of the learned policies remain unclear. While optimizing a static risk measure addresses these issues, its use in the DRL framework has been limited to the simple static CVaR risk measure. In this paper, we present a novel DRL algorithm with convergence guarantees that optimizes for a broader class of static Spectral Risk Measures (SRM). Additionally, we provide a clear interpretation of the learned policy by leveraging the distribution of returns in DRL and the decomposition of static coherent risk measures. Extensive experiments demonstrate that our model learns policies aligned with the SRM objective, and outperforms existing risk-neutral and risk-sensitive DRL models in various settings.

💡 Research Summary

The paper addresses a fundamental tension in risk‑sensitive reinforcement learning (RL): static risk measures provide clear, interpretable objectives but are often applied inconsistently across time steps, while dynamic risk measures maintain time consistency but are difficult to interpret and computationally demanding. Existing distributional RL (DRL) approaches typically embed a fixed risk measure such as Conditional Value‑at‑Risk (CVaR) into each decision step, which can lead to overly conservative policies and time‑inconsistency. Moreover, prior work has largely confined static risk optimization to CVaR because of the computational complexity of more general measures.

To overcome these limitations, the authors propose a novel DRL algorithm—Quantile Regression with Spectral Risk Measures (QR‑SRM)—that optimizes a broad class of static coherent risk measures known as Spectral Risk Measures (SRM). An SRM is defined by a risk spectrum ϕ(u), a non‑increasing, left‑continuous function on