Robustness of Dynamical Quantities of Interest via Goal-Oriented Information Theory
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Variational-principle-based methods that relate expectations of a quantity of interest to information-theoretic divergences have proven to be effective tools for obtaining robustness bounds under both parametric and non-parametric model-form uncertainty. Here, we extend these ideas to utilize information divergences that are specifically targeted at the quantity-of-interest being investigated; leveraging this specificity results in tighter robustness bounds and expands the class of problems that can be treated. We find the method especially useful for problems involving unbounded time-horizons, a case where established information-theoretic methods only produce trivial bounds. General problem types that can be treated within this framework include the expected value and distribution of a stopping time, time averages, and exponentially discounted observables. We illustrate these results with several examples, including option pricing, stochastic control, semi-Markov processes, and expectations and distributions of hitting times.
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