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Backward induction is the process of determining a sequence of optimal choices by reasoning from the endpoint of a problem or situation back to its beginning using individual events or actions. [1] Backward induction involves examining the final point in a series of decisions and identifying the optimal process or action required to arrive at ...
From a dynamic programming point of view, Dijkstra's algorithm for the shortest path problem is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method.
Bellman showed that a dynamic optimization problem in discrete time can be stated in a recursive, step-by-step form known as backward induction by writing down the relationship between the value function in one period and the value function in the next period. The relationship between these two value functions is called the "Bellman equation".
Stochastic dynamic programming deals with problems in which the current period reward and/or the next period state are random, i.e. with multi-stage stochastic systems. The decision maker's goal is to maximise expected (discounted) reward over a given planning horizon.
For example, the dynamic programming algorithms described in the next section require an explicit model, and Monte Carlo tree search requires a generative model (or an episodic simulator that can be copied at any state), whereas most reinforcement learning algorithms require only an episodic simulator.
Backward chaining is implemented in logic programming by SLD resolution. Both rules are based on the modus ponens inference rule. It is one of the two most commonly used methods of reasoning with inference rules and logical implications – the other is forward chaining. Backward chaining systems usually employ a depth-first search strategy, e ...
Typically, a greedy algorithm is used to solve a problem with optimal substructure if it can be proven by induction that this is optimal at each step. [1] Otherwise, provided the problem exhibits overlapping subproblems as well, divide-and-conquer methods or dynamic programming may be used. If there are no appropriate greedy algorithms and the ...
Theories of behavior often assume that players think strategically, meaning that players will base their actions on the probable decisions of other players in a way that will serve their objectives. However, many games, both real and contrived, do not result in the equilibrium predicted by standard analytic methods.