关于马尔可夫决策过程中多个均值-收益目标的两种观点的统一
Unifying Two Views on Multiple Mean-Payoff Objectives in Markov Decision Processes
摘要：
我们考虑马尔可夫决策过程（MDP）与多个极限平均（或平均值支付）的目标。存在两种不同的观点：（i）期望语义，其目标是优化预期的平均收益目标，以及（ii）满意语义，其目标是最大化运行的概率，使得平均收益值保持在给定向量之上。我们考虑优化这两个目标，从而统一现有的语义。准确地说，目标是在确保满足约束的同时优化期望。我们的问题抓住了关于风险规避策略的优化概念（即，保证一定概率）。我们的主要结果如下：首先，我们提出的算法的决策问题，总是多项式的大小MDP。我们还表明，近似的帕累托曲线可以计算在时间多项式的大小的MDP，和近似因子，但指数的维数。其次，我们提出了一个完整的表征的策略复杂性（在内存边界和随机化），需要解决我们的问题。
英文摘要：
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.
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