Novel Algorithms to Approximate the Future Consequence of Sequential Decisions

在商业、医疗和交通中出现的许多复杂问题都可以建模为不确定性下的顺序决策问题，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，动态地改变城市网络上不同航班的票价，试图在管理未售出座位风险的同时最大化收入。这些问题可以很方便地以动态规划的形式进行建模，这种方法通过最大化即时回报和预期未来回报之和来找到最佳决策。不幸的是，对于许多实际问题，为了计算预期的未来奖励函数，应该考虑的未来场景的数量是指数级的，使得该函数的精确计算变得困难。为了克服这个问题，近似动态规划（ADP）方法已被开发，以找到一个近似的最优解。

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.