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.
RATTL targets runtime safety for agents, including LLM-based systems, acting under uncertainty, and proves a Safety Sandwich: the RATTL value lies between the uninformed robust value and the full- knowledge optimum, with a gap that vanishes as the posterior concentrates.
Exponential Second-Order Expected Utility (SOEU) underlies the entropic approach to model uncertainty. This paper explores in what sense that functional form is essential. In the misspecification-robust Smooth Ambiguity criterion, let a single parameter govern both the model-level robustness and the ambiguity-averse ag...
In this study, we show that a continuous-time risk-sensitive control problem is equivalent to a R\'enyi divergence minimization problem over trajectory path measures. Reformulating stochastic optimal control as probabilistic inference via Kullback-Leibler (KL) divergence minimization avoids the computational intractabi...
Shinji Kataoka, K. Teranishi, Yasumasa Fujisaki· 0 citations
Robust portfolio rules that reconstruct confidence sets after learning need not preserve the evaluator obtained by prior-by-prior Bayesian transport. In the Gaussian model, this discrepancy is summarized by natural-coordinate displacement: inherited transport preserves it whereas fresh reconstruction can replace it. We...
The Schr\"odinger bridge owes its computational power to a single structural fact: by Girsanov's theorem the controlled problem is a Kullback--Leibler (KL) projection onto a fixed reference measure, solvable by alternating projections. This letter shows that the fact does not survive risk sensitivity. When the expected...
We present a solution of the limiting five-expert prediction problem with geometric stopping, based on stochastic calculus and partial differential equations. If $\delta$ is the stopping probability, the minimax expected regret from tied initial scores is $45\pi^2/(512\sqrt{2\delta})+o(\delta^{-1/2})$ as $\delta\downar...
Erhan Bayraktar, Ibrahim Ekren, N. Kolliopoulos· 3 citations
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