Look-ahead with mini-bucket heuristics for MPE

The paper investigates the potential of look-ahead in the con-text of AND/OR search in graphical models using the Mini-Bucket heuristic for combinatorial optimization tasks (e.g., MAP/MPE or weighted CSPs). We present and analyze the complexity of computing the residual (a.k.a Bellman update) of the Mini-Bucket heuristic and show how this can be used to identify which parts of the search space are more likely to benefit from look-ahead and how to bound its overhead. We also rephrase the look-ahead computation as a graphical model, to facilitate structure exploiting inference schemes. We demonstrate empirically that augmenting Mini-Bucket heuristics by look-ahead is a cost-effective way of increasing the power of Branch-And-Bound search.Postprint (published version

Limited discrepancy AND/OR search and its application to optimization tasks in graphical models

Many combinatorial problems are solved with a Depth-First search (DFS) guided by a heuristic and it is well-known that this method is very fragile with respect to heuristic mistakes. One standard way to make DFS more robust is to search by increasing number of discrepancies. This approach has been found useful in several domains where the search structure is a height-bounded OR tree. In this paper we investigate the generalization of discrepancy-based search to AND/OR search trees and propose an extension of the Limited Discrepancy Search (LDS) algorithm. We demonstrate the relevance of our proposal in the context of Graphical Models. In these problems, which can be solved with either a standard OR search tree or an AND/OR tree, we show the superiority of our approach. For a fixed number of discrepancies, the search space visited by the AND/OR algorithm strictly contains the search space visited by standard LDS, and many more nodes can be visited due to the multiplicative effect of the AND/OR decomposition. Besides, if the AND/OR tree achieves a significant size reduction with respect to the standard OR tree, the cost of each iteration of the AND/OR algorithm is asymptotically lower than in standard LDS. We report experiments on the minsum problem on different domains and show that the AND/OR version of LDS usually obtains better solutions given the same CPU time.Peer ReviewedPostprint (published version

A Simple Inducement Scheme to Overcome Adoption Externalities

Potential customers of network commodities face coordination problems due to adoption externalities that give rise to multiple, Pareto-ranked equilibria. We investigate the extent to which the coordination problem can be resolved by inducement schemes when agents’ preferences are private information. Specifically, we show that all symmetric “cut-off strategy” profiles (agents adopt if and only if their type is below a threshold) constitute the set of profiles that can be implemented as a unique equilibrium under an inducement scheme. We derive the ex ante cost of implementing each such profile. Furthermore, we fully characterize the set of inducement schemes that I) implement each such profile and ii) have the following simple form: each scheme specifies a fixed fee that every adopter pays, and a fixed gross subsidy/prize to be randomly allocated to (or evenly split among) the adopters. We discuss the implications of these findings on the design of optimal schemes for different network organizers, namely, private entrepreneurs and public entities.adoption externality, coordination, inducement scheme