Bounded Approximations for Linear Multi−Objective Planning under Uncertainty
Diederik Roijers‚ Joris Scharpff‚ Matthijs Spaan‚ Frans Oliehoek‚ Mathijs De Weerdt and Shimon Whiteson
Planning under uncertainty poses a complex problem in which multiple objectives often need to be balanced. In maintaining road networks traffic hindrance and maintenance costs need to be balanced, for example. When dealing with multiple objectives, it is often assumed that the relative importance of the objectives is known a priori. However, in practice human decision makers often find it hard to specify such preferences, and would prefer a decision support system that presents a range of possible alternatives. We propose two algorithms for computing these alternatives for the case of linearly weighted objectives. First, we propose an anytime method, approximate optimistic linear support (AOLS), that incrementally builds up a complete set of epsilon-optimal plans, exploiting the piecewise linear and convex shape of the value function. Second, we propose an approximate anytime method, scalarised sample incremental improve (SSII), that employs weight sampling to focus on the most interesting regions in weight space, as suggested by a prior over preferences. We show empirically that our methods are able to produce (near-)optimal alternative sets orders of magnitude faster than existing techniques, thereby demonstrating that our method provides sensible approximations in realistic multi-objective, numerical, stochastic planning domains.