Loud eaters and phones nearly spoiled my cinema trip - and it's not just me The cinema lights are low and you're cocooned in your seat, ready for the film to transport you to another world. But just as you settle in, you're jolted back to reality. Audience members around you are scrolling on their phones, talking and munching loudly. Cinemas do clearly ask everyone not to disturb those around them - through the use of adverts, announcements and signs - but is behaviour in getting worse? I experienced disruption a few weeks ago while watching Ryan Gosling's sci-fi movie, Project Hail Mary, at a cinema in London.

We call c(m) the m-step concentrability of a future-state distribution and call Cρ,µ the discountedaverage concentrability coefficient of the future-state distributions. The class of MDPs that satisfies this concentrability assumption is quite large, which is further discussed in Munos and Szepesvári [18]. If Xi, i = 1,...,N is an i.i.d. And when q = 1, N is used instead of N1. From the definition, one can esasily see that Nq,FX1:N N. Lemma A.2. (Single Iteration Error Bound) Let Vk and Vk+1 be the value functions of iteration kand k+1, and Vmax = rmax/(1 γ).

In this section, we provide background information in probability theory, and focus on random processes and concentration of measure inequalities.