30,191 research outputs found
Unifying Two Views on Multiple Mean-Payoff Objectives in Markov Decision Processes
We consider Markov decision processes (MDPs) with multiple limit-average (or
mean-payoff) objectives. There exist two different views: (i) the expectation
semantics, where the goal is to optimize the expected mean-payoff objective,
and (ii) the satisfaction semantics, where the goal is to maximize the
probability of runs such that the mean-payoff value stays above a given vector.
We consider optimization with respect to both objectives at once, thus unifying
the existing semantics. Precisely, the goal is to optimize the expectation
while ensuring the satisfaction constraint. Our problem captures the notion of
optimization with respect to strategies that are risk-averse (i.e., ensure
certain probabilistic guarantee). Our main results are as follows: First, we
present algorithms for the decision problems which are always polynomial in the
size of the MDP. We also show that an approximation of the Pareto-curve can be
computed in time polynomial in the size of the MDP, and the approximation
factor, but exponential in the number of dimensions. Second, we present a
complete characterization of the strategy complexity (in terms of memory bounds
and randomization) required to solve our problem.Comment: Extended journal version of the LICS'15 pape
Yang-Baxter Equations, Computational Methods and Applications
Computational methods are an important tool for solving the Yang-Baxter
equations(in small dimensions), for classifying (unifying) structures, and for
solving related problems. This paper is an account of some of the latest
developments on the Yang-Baxter equation, its set-theoretical version, and its
applications. We construct new set-theoretical solutions for the Yang-Baxter
equation. Unification theories and other results are proposed or proved.Comment: 12 page
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