When Gravity Fails: Local Search Topology

When Gravity Fails: Local Search Topology

Local search algorithms for combinatorial search problems frequently encounter a sequence of states in which it is impossible to improve the value of the objective function; moves through these regions, called plateau moves, dominate the time spent in local search. We analyze and characterize plateaus for three di erent classes of randomly generated Boolean Satis ability problems. We identify s...

Local Search Topology: Implications for Planner Performance

Hoffmann’s topological analysis of the h and h F state spaces explained why Fast Forward dominated the performance on early planning domains (Hoffmann 2004). His taxonomy segmented domains according to the presence/size of local minima and dead-end class. Surprisingly, the taxonomy has not been used to explain the performance of other planners that use similar heuristics. In this paper, we exte...

When Bellman's Principle Fails

We present several examples which show that the well known statements about Markov Decision Processes can fail if the loss function is not bounded.

When Sharing Fails

When Abstraction Fails

Reasoning about programs is mostly deduction: the reasoning from the abstract model to the concrete run. Deduction is useful because it allows us to predict properties of future runs—up to the point that a program will never fail its specification. However, even such a 100% correct program may still show a problem: the specification itself may be problematic, or deduction required us to abstrac...