制定一般的动态规划问题 [英] formulation of general dynamic programming problem
问题描述
我不知道的一般动态规划问题的目标函数总是可以配制成动态规划上维基时，其中目标函数为操作和状态，在每一个阶段的项的总和？或者说只是一个specical情况下，什么是一般的配方？
I wonder if the objective function of a general dynamic programming problem can always be formulated as in dynamic programming on wiki, where the objective function is a sum of items for action and state at every stage? Or that is just a specical case and what is the general formulation?
编辑：
通过动态规划问题，我的意思是可以通过动态规划技术来解决的问题。这样那样的问题具有优化问题和最优结构。
By "dynamic programming problem", I mean a problem that can be solved by dynamic programming technique. Such kind of problems possess the property of optimal problem and optimal structure.
但在租赁我有时不易鉴别这样的问题，也许是因为我还没有习惯于那种口头描述。当我遇到了Bellman方程的wiki页面，我觉得成本函数的数学公式将有助于以某种方式。我怀疑整体成本/增益函数可以总是被重新psented作为来自所有阶段的成本/增益积累$ P $？和积累可以是添加剂或multiplitive还是其他什么东西？
But at lease for me it is sometimes not easy to identify such problems, perhaps because I have not become used to that kind of verbal description. When I came across the WIKI page for Bellman equation, I do feel mathematical formulation of the cost function will help somehow. I suspect the overall cost/gain function can always be represented as accumulation of cost/gain from all the stages? and the accumulation can be additive or multiplitive or something else?
当我张贴了我的问题，我没有意识到这是更恰当的讨论动态规划在一些地方更倾向于数学优化。但也有相当多的在Stackoverflow.com计算机算法的讨论。所以，我不觉得不合适问我的问题在这里无论是。
When I posted my question, I did realize that it is more proper to discuss dynamic programming in some place more oriented to mathematical optimization. But there are quite a lot of discussion of computer algorithms in Stackoverflow.com. So I did not feel improper to ask my question here either.
推荐答案
这不是我会如何描述一个任意优化问题（或者动态规划算法）。具体地，因子β; 吨的看起来像一个电气工程劈，程序员通常不会想要的。更巧妙的是，它看起来像它不会永远是显而易见的是什么功能的 F 的是一个给定的问题。
That's not how I would characterize an arbitrary optimization problem (or a dynamic programming algorithm). In particular, the factor βt looks like an electrical engineering hack that programmers wouldn't usually want. More subtly, it seems like it won't always be obvious what the function F is for a given problem.
但是，是的，设置和测试; 1，并且任意目标函数的可以的制定的方式。通常，目标函数可以是初始状态的任何功能和所采取的所有动作;鉴于这样的功能，可以很容易地定义一个函数的 F 的插入到这个公式。
But yes, set β to 1 and any arbitrary objective function can be formulated that way. Generally the objective function may be any function of the initial state and all the actions taken; given such a function, it's easy to define a function F to plug into that formula.
这是否是一个有益的事情，取决于这个问题，我想。
Whether that's a useful thing to do or not depends on the problem, I suppose.
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