A baseline is a fixed point in objective space used as the endpoint of the dominated region. For objectives being maximized, it usually contains the lowest acceptable value for each objective, forming a lower-left bound against which optimization progress is measured. section 11.2
Given a baseline r, dominated hypervolume measures the region between r and the Pareto frontier. A larger region indicates greater progress from the chosen worst-case outcome, so the baseline directly affects the reported hypervolume. section 11.2 section 11.5
Choose a baseline by following these practical rules:
- Use one coordinate for each objective, with coordinates representing the lowest values relevant to the maximization problem. section 11.2
- Keep the baseline fixed while comparing optimization policies, because changing it changes the measured dominated hypervolume. section 11.2
- Pass the baseline together with observed objective values to hypervolume computation, such as BoTorch’s DominatedPartitioning. section 11.5
Two-objective example
For the example objectives, the baseline is [-2.0292, -0.4444]. The first coordinate is the minimum value of the first objective and the second is the minimum value of the second; the resulting hypervolume spans from this point to the Pareto frontier. section 11.2
Airplane-design exercise
The airplane-design optimization uses [-1.5, -2] as the baseline for its two objectives. Hypervolume results from EHVI and alternating EI can then be compared across repeated experiments. section 11.4
