5 accepted papers
We tackle the problem of estimating risk measures of the infinite-horizon discounted cost of 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 $\epsilon$-accura…
We consider an online optimization problem in a bandit setting in which a learner chooses decisions from a continuous decision set at discrete decision epochs, and receives noisy rewards from the environment in response. While the noise samples are assumed to be independent and sub-Gaussian, the…
Barycentric spanners have been used as an efficient exploration basis in online linear optimization problems in a bandit framework. We characterise the barycentric spanner for decision problems in which the cost (or reward) is a polynomial in a single decision variable. Our characterisation of the b…
We consider the problem of estimating a spectral risk measure (SRM) from i.i.d. samples, and propose a novel method that is based on numerical integration. We show that our SRM estimate concentrates exponentially, when the underlying distribution has bounded support. Further, we also consider the ca…
Known finite-sample concentration bounds for the Wasserstein distance between the empirical and true distribution of a random variable are used to derive a two-sided concentration bound for the error between the true conditional value-at-risk (CVaR) of a (possibly unbounded) random variable and a s…