Risk-Sensitive Control and an Abstract Collatz-Wielandt Formula

Abstract

The "value" of infinite horizon risk-sensitive control is the principal eigenvalue of a certain positive operator. This facilitates the use of Chang's extension of the Collatz-Wielandt formula to derive a variational characterization thereof. For the uncontrolled case, this reduces to the Donsker-Varadhan functional.

Cited by in corpus (6)

• Markov Decision Processes with Risk-Sensitive Criteria: An Overview
• A counterexample to a nonlinear version of the Krein-Rutman theorem by R. Mahadevan
• A variational characterization of the risk-sensitive average reward for controlled diffusions on ${\mathbb{R}}^d$
• A variational formula for risk-sensitive control of diffusions in ${\mathbb{R}}^d$
• Global algorithms for maximal eigenpair
• Asymptotics of impulse control problem with multiplicative reward