Novel Algorithms to Approximate the Future Consequence of Sequential Decisions

商业、医疗和交通中出现的许多复杂问题可以建模为不确定情况下的连续决策问题，这意味着决策者必须定期做出决策，而一些随机事件会随着时间的推移而展开。例如，一家航空公司在不知道未来实际需求的情况下，动态改变城市网络上不同航班的票价，试图最大化收入，同时管理未售出座位的风险。这些问题可以方便地用动态规划的形式建模，动态规划是一种通过最大化当前回报和预期未来回报的总和来寻找最佳决策的方法。不幸的是，对于许多实际问题，为了计算预期的未来回报函数，人们应该考虑的未来情景的数量是指数级的，这使得准确计算这个函数变得困难。为了克服这一问题，人们发展了近似动态规划(ADP)方法来寻找近似最优解。

Many complex problems arising in business, health care, and transportation can be modelled as sequential decision making problems under uncertainty, meaning that a decision maker has to make decisions periodically while some random events unfold over time. For instance, an airline dynamically changes the fare for different flights over a network of cities without knowing the actual future demand, trying to maximize its revenue while managing the risk of unsold seats. These problems can be conveniently modelled in the form of dynamic programs, a method that finds the best decision by maximizing the sum of immediate reward and the expected future reward. Unfortunately, for many practical problems, the number of future scenarios that one should consider in order to calculate the expected future reward function is exponentially large, making exact calculation of this function intractable. In order to overcome this issue, approximate dynamic programming (ADP) methods have been developed to find an approximate optimal solution.