Quantifying Risk Under Evolving Uncertainty: Belief-Dependent Robustness for Safe Sequential Decision Making

An agent still learning its environment should be cautious while ignorant and bold once confident. The entropic value-at-risk captures this through a robust-optimization identity---a confidence level fixes the radius of a relative-entropy ball of alternative models---but that ball cannot reach catastrophes the nominal deems impossible, precisely what a safe agent must hedge. We instead use an optimal-transport ball and study the coherent risk measure it induces, the Wasserstein entropic value-at-risk. It has a variational dual mirroring the entropic formula (an inverse temperature becomes a transport price), occupies a definite place in the risk hierarchy, and provably accounts for the reachable catastrophes the entropic measure ignores; we verify both dualities numerically. Driving the transport radius by belief entropy then yields a closed-form robust dynamic-programming operator whose caution contracts as the belief sharpens, with a certified safety sandwich and a sharp safety switch.

Deploying reinforcement learning in safety critical domains, from autonomous vehicles to medical decision support, is constrained by failures arising when systems encounter unfamiliar conditions. We argue that the fundamental bottleneck is not individual challenges like changing dynamics or incomplete observations, but their synergistic interaction, which we term the Epistemic Trap: agents cannot estimate their state without knowing system dynamics, nor learn dynamics without accurate state information. Proof-of-concept experiments in simulated locomotion reveal that combining these uncertainties causes failures far worse than either challenge alone, a 77% observed degradation against the 46% additive prediction, demonstrating that compounding failure modes can emerge and, when they do, far exceed what additive reasoning would predict. Conventional approaches typically adopt a passive epistemic stance that cannot resolve this coupled uncertainty. We propose reframing safety as an information problem. We introduce an Adaptive Safety Architecture built around three contributions. First, the Compound Uncertainty Coefficient ($κ$), a mutual-information based metric that quantifies how tightly state and dynamics uncertainties are coupled. Second, information-seeking policies governed by a MaxInfoRL objective that actively probe system dynamics rather than waiting for the environment to reveal itself passively. Third, regime adaptive safety constraints that tighten automatically as epistemic coupling rises. Together, these constitute a paradigm shift from passive robustness to active perception, offering a principled path toward decision making systems that operate under uncertainty, recognize their own ignorance, and act strategically to resolve it.

Modern decision systems increasingly rely on learned components whose outputs may be confident yet wrong, exposing downstream actions to costly errors. We introduce Risk-Aware Causal Gating (RACG), a framework that decides whether to act on, defer, or abstain from a model's prediction by combining causal effect estimation with calibrated risk control. RACG models the causal pathway from candidate actions to outcomes and gates each decision according to an estimated counterfactual risk rather than raw predictive confidence. To make gating reliable, we derive distribution-free bounds on the probability of acting under high-risk conditions and show how these bounds translate into operating thresholds that satisfy user-specified safety constraints. We further propose an adaptive gating policy that adjusts to distribution shift by monitoring discrepancies between predicted and realized outcomes, tightening the gate when causal assumptions appear violated. Across simulated interventions and real-world decision benchmarks, RACG reduces high-cost errors substantially while preserving most of the utility of an ungated policy, and it outperforms confidence-based and selective-prediction baselines at matched abstention rates. Our results indicate that explicitly separating causal risk from predictive uncertainty yields decision systems that are both safer and more transparent, offering a principled mechanism for trustworthy automation in high-stakes settings.