2.3. Initialize both Q-values at 2 (optimistic). Assume that, as in in the first part, in the first round you get for both actions the reward. Update your Q values once with η = 0.2. Suppose now that in the following rounds, you choose actions a1 and a2 alternatingly and update the Q-values with a very small learning rate (η = 0.001). How many rounds does it take on average, until the maximal Q...

This paper studies the role of ‡uctuations in the aggregate price-earning ratio at di¤erent time scales for predicting stock returns and explore the channels through which returns are predicted. Using U.S. quarterly and international monthly data, we …nd that cycles in the price-earning ratio are strong and better predictors of future returns at short and intermediate horizons than the aggregat...

We present a randomized algorithm sorting n integers in O(n p log logn) expected time and linear space. This improves the previous O(n log logn) bound by Anderson et al. from STOC’95. As an immediate consequence, if the integers are bounded by U , we can sort them in O(n p log logU) expected time. This is the first improvement over the O(n log logU) bound obtained with van Emde Boas’ data struc...

It has been shown previously that sorting n items into n locations with a polynomial number of processors requires (logn= log logn) time. We sidestep this lower bound with the idea of Padded Sorting, or sorting n items into n+o(n) locations. Since many problems do not rely on the exact rank of sorted items, a Padded Sort is often just as useful as an unpadded sort. Our algorithm for Padded Sort...