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 Problem Solving


A Divide-and-Conquer Approach for Solving Interval Algebra Networks

AAAI Conferences

Deciding consistency of constraint networks is a fundamental problem in qualitative spatial and temporal reasoning. In this paper we introduce a divide-and-conquer method that recursively partitions a given problem into smaller sub-problems in deciding consistency. We identify a key theoretical property of a qualitative calculus that ensures the soundness and completeness of this method, and show that it is satisfied by the Interval Algebra (IA) and the Point Algebra (PA). We develop a new encoding scheme for IA networks based on a combination of our divide-and-conquer method with an existing encoding of IA networks into SAT. We empirically show that our new encoding scheme scales to much larger problems and exhibits a consistent and significant improvement in efficiency over state-of-the-art solvers on the most difficult instances.


Planning with Partial Preference Models

AAAI Conferences

In many real-world planning scenarios, the users are interested in optimizing multiple objectives (such as makespan and execution cost), but are unable to express their exact tradeoff between those objectives. When a planner encounters such partial preference models, rather than look for a single optimal plan, it needs to present the pareto set of plans and let the user choose from them. This idea of presenting the full pareto set is fraught with both computational and user-interface challenges. To make it practical, we propose the approach of finding a representative subset of the pareto set. We measure the quality of this representative set using the Integrated Convex Preference (ICP) model, originally developed in the OR community. We implement several heuristic approaches based on the Metric-LPG planner to find a good solution set according to this measure. We present empirical results demonstrating the promise of our approach.


Plausible Repairs for Inconsistent Requirements

AAAI Conferences

Knowledge-based recommenders support users in the identification of interesting items from large and potentially complex assortments. In cases where no recommendation could be found for a given set of requirements, such systems propose explanations that indicate minimal sets of faulty requirements. Unfortunately, such explanations are not personalized and do not include repair proposals which triggers a low degree of satisfaction and frequent cancellations of recommendation sessions. In this paper we present a personalized repair approach that integrates the calculation of explanations with collaborative problem solving techniques. In order to demonstrate the applicability of our approach, we present the results of an empirical study that show significant improvements in the accuracy of predictions for interesting repairs.


Fast Recommendations using GAI Models

AAAI Conferences

This paper deals with Decision-Making in the context of multiattribute utility theory and, more precisely, with the problem of efficiently determining the best alternative w.r.t. an agent's preferences (choice problem). We assume that alternatives are elements of a product set of attributes and that the agent's preferences are represented by a generalized additive decomposable (GAI) utility on this set. Such a function allows an efficient representation of interactions between attributes while preserving some decomposability of the model. GAI utilities can be compiled into graphical structures called GAI networks that can be exploited to solve choice problems using collect/distribute schemes essentially similar to those used in Bayesian networks. In this paper, rather than directly using this scheme on the GAI network for determining the most preferred alternative, we propose to work with another GAI function, acting as an upper-bound on utility values and enhancing the model's decomposability. This method still provides the exact optimal solution but speeds up significantly the search. It proves to be particularly useful when dealing with choice and ranking under constraints and within collective Decision-Making, where GAI nets tend to have a large size. We present an efficient algorithm for determining this new GAI function and provide experimental results highlighting the practical efficiency of our procedure.


Discovering Theorems in Game Theory: Two-Person Games with Unique Pure Nash Equilibrium Payoffs

AAAI Conferences

We consider all possible games that have unique PNE payoffs. Our starting point is the classes of games that can be expressed by a conjunction class of two-person strictly competitive games. We first formulate of two binary clauses, and our program rediscovered the notions of games, strictly competitive games and Kats and Thisse's class of weakly unilaterally PNEs in first-order logic. Under our formulation, a class of competitive two-person games, and came games corresponds to a first-order sentence. In particular, the up with several other classes of games that have sentence that corresponds to the class of strictly competitive unique pure Nash equilibrium payoffs. It also came games is a conjunction of two binary clauses with all variables up with new classes of strict games that have unique universally quantified. So we implemented a program pure Nash equilibria, where a game is strict if for that examines all these universally quantified conjunctions of both player different profiles have different payoffs.


On the Tip of My Thought: Playing the Guillotine Game

AAAI Conferences

In this paper we propose a system to solve a language game, called Guillotine, which requires a player with a strong cultural and linguistic background knowledge. The player observes a set of five words, generally unrelated to each other, and in one minute she has to provide a sixth word, semantically connected to the others. Several knowledge sources, such as a dictionaryย  and a set of proverbs, have been modeled and integrated in order to realize a knowledge infusion process into the system. The main motivation for designing an artificial player for Guillotine is the challenge of providing the machine with the cultural and linguistic background knowledge which makes it similar to a human being, with the ability of interpreting natural language documents and reasoning on their content. Experiments carried out showed promising results, and both the knowledge source modeling and the reasoning mechanismsย  (implementingย  a spreading activation algorithm to find out the solution) seem to be appropriate. We are convinced that the approach has a great potential for other more practical applications besides solving a language game, such as semantic search.


Goal-Driven Learning in the GILA Integrated Intelligence Architecture

AAAI Conferences

Goal Driven Learning (GDL) focuses on systems that determine by themselves what has to be learnt and how to learn it. Typically GDL systems use meta-reasoning capabilities over a base {\em reasoner}, identifying learning goals and devising strategies. In this paper we present a novel GDL technique to deal with complex AI systems where the meta-reasoning module has to analyze the reasoning trace of multiple components with potentially different learning paradigms. Our approach works by distributing the generation of learning strategies among the different modules instead of centralizing it in the meta-reasoner. We implemented our technique in the GILA system, that works in the airspace task orders domain, showing an increase in performance.


Solving 8x8 Hex

AAAI Conferences

A conservative estimate of the latter number is the number of distinct board Using efficient methods that reduce the search states in which the board is at most half full. This estimate space, we design an algorithm strong enough to includes some invalid states: those in which one player already solve all 8 8 Hex openings.


A New d-DNNF-Based Bound Computation Algorithm for Functional E-MAJSAT

AAAI Conferences

We present a new algorithm for computing upper bounds for an optimization version of the EMAJSAT problem called functional E-MAJSAT. The algorithm utilizes the compilation language d- DNNF which underlies several state-of-the-art algorithms for solving related problems. This bound computation can be used in a branch-and-bound solver for solving functional E-MAJSAT. We then present a technique for pruning values from the branch-and-bound search tree based on the information available after each bound computation. We evaluated the proposed techniques in a MAP solver and a probabilistic conformant planner. In both cases, our experiments showed that the new techniques improved the efficiency of state-of-the-art solvers by orders of magnitude.


Expressive Power-Based Resource Allocation for Data Centers

AAAI Conferences

As data-center energy consumption continues to rise, efficient power management is becoming increasingly important. In this work, we examine the use of a novel market mechanism for finding the right balance between power and performance. The market enables a separation between a `buyer side' that strives to maximize performance and a 'seller side' that strives to minimize power and other costs. A concise and scalable description language is defined for agent preferences that admits a mixed-integer program for computing optimal allocations. Experimental results demonstrate the robustness, flexibility, practicality and scalability of the architecture.