Specifically, look for:

• Convergence and generalization results for Pareto optimal values
• Multi-objective learning convergence results single-task settings
• Multi-variate objective measures

Multi-Objective SVM

Single-task learning, SVM allow one to optimize multiple objectives. Usually require iterative optimization methods. However, the problem is essentially convex.

Bi03Multi Objective?

• minimize (norm(w) and sum(e))
• Show that this results in a convex Pareto tradeoff surface.
• Iteratively finds the optimal C parameter in C-SVM
• Could be solved with linear programming formulation

Seung Jean06Pareto?

• Extends MPM to show that it solves the bi-criterion problem, maximize TP and TN rates.
• To compute the tradeoff surface, iteratively solve problems with tradeoffs parameterized by a lambda.

Joachims05Support?

• Multi-variate SVM. The performance measure is a function of all examples rather than defined for each individual example.
• Shows that the constraints are exponential in the size of the problem but can be approximated by sparse representations.

Multi-Objective Convergence

Teyaud06How?

• Demonstrates how to do convergence in the Hausdorff distance to the Pareto Front. Basically, this relies on the definition of the max min distance for each direction.
• Lower bounds on fitness comparisons needed to achieve convergence error in Hausdorff distance.
• Applied to multi-objective evolutionary algorithms. No good way to compute empirical Pareto Front as an inductive learning principle.