What question did this study set out to answer?

To formulate and solve a Bayesian adaptive optimal stochastic control problem where cost functionals depend nonlinearly on the entire posterior distribution of a hidden static signal.

August 14, 2026SIAM Journal on Control and OptimizationOpen Access

A Measure-Valued HJB Perspective on Bayesian Optimal Adaptive Control

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Authors

ACAlexander M. G. CoxUniversity of Bath SKSigrid KällbladKTH Royal Institute of Technology

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Implication

Mathematical analysis characterizes optimal Bayesian adaptive control via measure-valued Hamilton-Jacobi-Bellman viscosity solutions, establishing near-optimal controls for hidden signal tracking.

Key Points

To formulate and solve a Bayesian adaptive optimal stochastic control problem where cost functionals depend nonlinearly on the entire posterior distribution of a hidden static signal.
Embedded the filtering dynamics into an infinite-dimensional stochastic control framework utilizing measure-valued martingales in the observation filtration.
Employed viscosity solution theory and approximation arguments to characterize the associated measure-valued Hamilton-Jacobi-Bellman (HJB) equation.
Demonstrated equivalence to a weak formulation and established the optimal value as the unique continuous viscosity solution of the infinite-dimensional HJB equation.
Constructed a piecewise constant control strategy that achieves arbitrarily close performance to the theoretical optimum.
Derived a novel stability result for a general class of measure-valued stochastic differential equations.

Cite This Study

Cox et al. (2026) studied this question.

synapsesocial.com/papers/6a7ec69fb70b84ec8b912b7b https://doi.org/10.1137/25m1735081

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Implication

Mathematical analysis characterizes optimal Bayesian adaptive control via measure-valued Hamilton-Jacobi-Bellman viscosity solutions, establishing near-optimal controls for hidden signal tracking.

A Measure-Valued HJB Perspective on Bayesian Optimal Adaptive Control

Discussion

Member takes

Implication

Key Points

Cite This Study

A Measure-Valued HJB Perspective on Bayesian Optimal Adaptive Control

Discussion

Member takes

Implication

Key Points

Cite This Study

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