A two-dimensional experiment measures a business response across settings of two controllable parameters, such as threshold and order_size, then searches for an estimated optimum. In response surface methodology, measurements are aggregated, modeled, optimized, and validated. section 4.2.2
A practical workflow is:
- Measure markout profit repeatedly at parameter settings chosen by a central-composite design, retaining aggregate measurements and standard errors. section 4.2.2
- Fit a quadratic regression with constant, linear, univariate quadratic, and cross terms. section 4.2.2
- Interpolate the fitted surrogate over a parameter grid and select its maximum. section 4.2.2
- Re-measure the proposed optimum and return to design if the result falls outside its 95% confidence bounds. section 4.2.2
Iterative optimization
A first design used threshold values 1, 1.5, and 2 and order sizes 1, 1.5, and 2. A later iteration produced an outlying measurement, violating the near-optimum modeling assumption. A tighter third design yielded an estimated optimum at threshold 1.12 and order_size 3.0, with estimated markout profit 0.41; validation then tested that setting directly. section 4.2.2
Figure 4.16 Measure and analyze a 2D RSM experiment. In the measure stage, you measure the business metric for each of the parameter values chosen in the design stage, just as you did for the 1D RSM. To execute the analyze stage, you need to use a more complex model for interpolation and search more parameter values during optimization.
Use the visual workflow to connect measured parameter settings, surrogate interpolation, and optimization. section 4.2.2
