# Solving Limited Memory Influence Diagrams Using Branch-and-Bound Search

@article{Khaled2012SolvingLM, title={Solving Limited Memory Influence Diagrams Using Branch-and-Bound Search}, author={Arindam Khaled and Changhe Yuan and Eric A. Hansen}, journal={ArXiv}, year={2012}, volume={abs/1309.6839} }

A limited-memory influence diagram (LIMID) generalizes a traditional influence diagram by relaxing the assumptions of regularity and no-forgetting, allowing a wider range of decision problems to be modeled. Algorithms for solving traditional influence diagrams are not easily generalized to solve LIMIDs, however, and only recently have exact algorithms for solving LIMIDs been developed. In this paper, we introduce an exact algorithm for solving LIMIDs that is based on branch-and-bound search…

## 6 Citations

### Speeding Up k-Neighborhood Local Search in Limited Memory Influence Diagrams

- Computer ScienceProbabilistic Graphical Models
- 2014

This paper investigates algorithms for k-neighborhood local search and develops fast schema to perform approximate k-local search; experiments show that the methods improve on current local search algorithms both with respect to time and to accuracy.

### Fast local search methods for solving limited memory influence diagrams

- Computer ScienceInt. J. Approx. Reason.
- 2016

### Equivalences between maximum a posteriori inference in Bayesian networks and maximum expected utility computation in influence diagrams

- Computer ScienceInt. J. Approx. Reason.
- 2014

This work shows constructively that these two problems are equivalent in the sense that any algorithm designed for one problem can be used to solve the other with small overhead, and shows a polynomial-time reduction from MAP to MEU that preserves the boundedness of treewidth.

### Generalized Dual Decomposition for Bounding Maximum Expected Utility of Influence Diagrams with Perfect Recall

- Computer ScienceAAAI Workshops
- 2018

This work presents a gradient based local search algorithm in which the outer loop controls the randomization of the initial configurations and the inner loop tightens the upper-bound based on block coordinate descent with gradients perturbed by a random noise.

### Integer Programming on the Junction Tree Polytope for Influence Diagrams

- Computer Science
- 2019

This work presents a mixed integer linear formulation for solving an ID, as well as valid inequalities, which lead to a computationally efficient algorithm and shows that the linear relaxation yields an optimal integer solution for instances that can be solved by the "single policy update", the default algorithm for addressing IDs.

### Mathematical programming for influence diagrams

- Computer Science
- 2019

This work presents a mixed integer linear formulation for solving an ID, as well as valid inequalities, which lead to a computationally efficient algorithm and shows that the linear relaxation yields an optimal integer solution for instances that can be solved by the "single policy update", the default algorithm for addressing IDs.

## References

SHOWING 1-10 OF 27 REFERENCES

### Solving Limited Memory Influence Diagrams

- Computer ScienceJ. Artif. Intell. Res.
- 2012

A new algorithm for exactly solving decision making problems represented as influence diagrams that does not require the usual assumptions of no forgetting and regularity and is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables and 1064 solutions.

### Solving Multistage Influence Diagrams using Branch-and-Bound Search

- Business, Computer ScienceUAI
- 2010

A practical implementation of depth-first branch-and-bound search for influence diagram evaluation that outperforms existing methods for solving influence diagrams with multiple stages is developed.

### Solving Influence Diagrams using HUGIN, Shafer-Shenoy and Lazy Propagation

- Computer ScienceUAI
- 2001

This paper shows how the obtained savings is considerably increased when the computations are performed according to the LP scheme.

### Solving Decision Problems with Limited Information

- Computer ScienceNIPS
- 2011

A new algorithm for exactly solving decision-making problems represented as an influence diagram is presented, which is empirically shown to outperform a state-of-the-art algorithm in randomly generated problems of up to 150 variables and 1064 strategies.

### Strategy Selection in Influence Diagrams using Imprecise Probabilities

- Computer ScienceUAI
- 2008

A new algorithm to solve the decision making problem in Influence Diagrams based on algorithms for credal networks and a reformulation is introduced that finds the global maximum strategy with respect to the expected utility.

### Representing and Solving Decision Problems with Limited Information

- Computer ScienceManag. Sci.
- 2001

An algorithm for improving any given strategy by local computation of single policy updates and investigate conditions for the resulting strategy to be optimal is given.

### Memory-Bounded Dynamic Programming for DEC-POMDPs

- Computer ScienceIJCAI
- 2007

This work presents the first memory-bounded dynamic programming algorithm for finite-horizon decentralized POMDPs, which can handle horizons that are multiple orders of magnitude larger than what was previously possible, while achieving the same or better solution quality.

### A New Approach to Influence Diagrams Evaluation

- Computer ScienceSGAI Conf.
- 2009

This paper presents a new algorithm for maximizing the expected utility over a set of policies by traversing an AND/OR search space associated with an influence diagram that exploits the deterministic information encoded by the influence diagram and avoids redundant computations for infeasible decision choices.

### Evaluating Influence Diagrams

- Computer ScienceOper. Res.
- 1986

An algorithm is developed that can evaluate any well-formed influence diagram and determine the optimal policy for its decisions and can be performed using the decision maker's perspective on the problem.