| Dynamic Programming is a concept from control theory in which the goal is to optimize a specific type of equation. Here, "programming" doesn't mean the same word as in "computer programming". It's just a carry over word from the field of optimization and mathematical modeling [0]. Goal is to optimize some problem that can be framed as having the following properties: an optimal solution to the overall problem will result in optimal solutions for all "subproblems" and these "subproblems" are not all disjoint. If they are disjoint, then don't need to use DP, but you can use a simpler divide and conquer approach (example: you don't need DP to solve mergesort) Such problems are everywhere. Lots of path planning, shortest path type problems are DP based (high level ex: shortest path from A to C going via B necessarily will imply that the path from A to B is the shortest and B to C is the shortest). In reinforcement learning, similar ideas are crucial. Relatedly, in game theory, these types of problems arise in the form of subgame perfect equilibriums. Thinking graphically, I believe all DPs can be represented as directed acyclical (hyper)graphs. So, the optimal solution on this graph will mean that the subgraphs in the solution also have optimal solutions, and that these subgraphs overlap. In computer science, the optimizations tend to work incrementally as a 'wavefront' from the smallest subgraph (usually some basecases, starting points) -- using the solution to the current subgraph in the larger subgraph, etc. Eventually, the wavefront covers the relevant parts of the graph. This is what people tend to call "bottom up". [0] http://web.mit.edu/15.053/www/AppliedMathematicalProgramming... |