Although there has been a lot of effort in theoretical work produced on comparative preference formalisms in recent years, including award winning papers (Boutilier et al. 2004a, Koriche & Zanuttini 2009), development towards applications has lagged behind. On the other hand, RSs are gaining momentum in the e-commerce applica- tions market to face the “information overload” problem. This progressively reveals an increasing need to enable those RSs with suitable preference dominance engines that are capable of efficient preference handling that support users in expressing their preferences with a minimum of burden during an automated process that in- cludes user-system interaction.
In this chapter, we define a formalism for preference elicitation based on compar- ative preferences and integrate it into a conversational RS. To our knowledge, this type of comparative preference is deployed for the first time with RSs. We conduct different experiments and perform a comparative study between a first approach based on a sum of weights-based dominance relation and a second approach based on comparative preference theories dominance relation. Comparative preference theories were able to give freedom and flexibility to the system to handle the user’s preferences by allowing the system to capture preference nuances and various forms of preferences without giving up the attractive computational properties of the pref- erence dominance. The dominance algorithm described in Section 3.5 in Chapter 3 is proven to work efficiently for a range of comparative preference statements when checking dominance between two outcomes α and β.
The suitability and attractiveness of the comparative preference theories-based approach for RSs were verified and validated through several experiments that in- clude repeated scenarios with simulated users represented by models that are based on different semantics (e.g., weights vector vs cp-tree).
5
Constrained Optimisation for
Comparative Preferences
5.1
Introduction
Constrained optimisation looks for (feasible) solutions, regarding the constraints, that best meet the user’s preferences. One goal is to assist users with cognitive tasks like configuring products for an online shopper, or scheduling a meeting for a busy executive. In such situations, the automated agent needs to balance the user’s desires with hard and externally imposed constraints.
On the one hand, in daily life, people’s expectations from decision support sys- tems (DSSs) are getting higher and higher; they hope for more personalized and fo- cused query handling. On the other hand, the preference representation approaches and preference reasoning engines are progressing towards more intuitiveness and compactness. Therefore, the integration of newly developed preference languages and reasoning approaches in DSSs paves the way for effective and intuitive infor- mation streams required by users. It will build the bridge between users and today’s systems.
A decoupled approach that combines CSPs and conditional preference theories, for which a preference reasoning engine was developed, seems to be worth studying particularly when the user’s preferences over an assignment to some subset of vari- ables of the problem is usually conditioned on the assignments to other subsets of
variables. Then, we intend to develop decoupled COP approaches, using conditional preference theories (i.e., cp-theories), and taking a similar approach to (Boutilier et al. 2004b), in the sense that they are able to: 1) find the first non-dominated so- lution fast as the first solution met in the preference-based search tree is considered optimal and 2) find optimal solutions in anytime-working mode algorithm as the algorithm can stop at any point and returns the set of optimal solutions found so far. The solution set generated at that point will be a subset of the set of all optimal solutions.
In B&B, the bounding rule typically requires, at each node of the search tree, a test that checks some necessary conditions for the newly created branch to achieve an optimality level not worse than the so far best obtained level. In this chapter, in order to bound the horizon of the search space, we define pruning rules that check conditions, at each node of the search tree, to see whether the newly created sub- problem no longer contributes to the solution of the global optimisation problem and hence can be discarded. In other words, the conditions check whether the partial as- signment constructed so far at the current node cannot be extended to an optimal (i.e., non-dominated) solution. Optimality is referring to a (partially ordered) pref- erence relation represented by a cp-theory described in Section 3.3.1 in Chapter 3. We are thus extending B&B for cp-theories. In Sections 5.3 and 5.4 we develop a first group of sufficient conditions that help the constrained optimisation algorithm prune the search space. Such pruning will certainly aid the search for optimal solu- tions, without jeopardizing any potentially meritorious solutions. One of the main advantages of pruning away subspaces from the search space is the reduction of the number of pairwise comparisons performed during the search.
Another way of avoiding uninteresting comparisons is to avoid involving any optimal solution that is unable to better (i.e., dominate) any extension (complete assignment) in a sub-space. In other words, an optimal solution α, which was already found, might be unable to dominate any outcome that extends the partial assignment obtained so far in the search. If we prove that this is the case then we do not need to involve α in any dominance check below the current node. This can be performed by our second category of pruning rules presented in Section 5.5 and which temporarily disengage any subset of optimal solutions below some node of the search tree from playing a role in the comparisons performed in the sub-space newly created. This pruning rule checks whether any optimal solution already found is unable to better any other possible assignment in the sub-space. If the condition is confirmed for a solution α, then α is no longer involved in eventual comparisons below the current node in the search tree.
Section 5.6 discusses an example of computer configuration which illustrates as- pects of the cp-theories-based constrained optimisation. Issues encountered during