Risk Estimation in a Markov Cost Process: Lower and Upper Bounds

arXiv:2310.11389v2 Announce Type: replace
Abstract: We tackle the problem of estimating risk measures of the infinite-horizon discounted cost within a Markov cost process. The risk measures we study include variance, Value-at-Risk (VaR), and Conditional Value-at-Risk (CVaR). First, we show that estimating any of these risk measures with $\epsilon$-accuracy, either in expected or high-probability sense, requires at least $\Omega(1/\epsilon^2)$ samples. Then, using a truncation scheme, we derive an upper bound for the CVaR and variance estimation. This bound matches our lower …

abstract accuracy arxiv cost cs.lg epsilon horizon markov process risk show stat.ml study type value variance