robustExpDesign

Robust experimental design for combining experimental and external evidence.

robustExpDesign provides tools for planning experiments when observational or other external estimates may be biased. It can choose experiments or moments, allocate a cost-constrained experimental budget, and compute estimator weights that balance variance against sensitivity to misspecification.

The package implements methods from:

Epanomeritakis, A., and Viviano, D. (2026). Learning What to Learn: Experimental Design when Combining Experimental with Observational Evidence. Manuscript, August 4, 2026.

Installation

Install the development version from GitHub:

install.packages("remotes")
remotes::install_github("dviviano/robustExpDesign")

Matrix and rlang are required dependencies and are installed with the package. Install the optional packages needed by the features you plan to use:

install.packages(c("quadprog", "CVXR", "ggplot2"))

The optional Gurobi R interface is required for:

• audience-regret designs;
• designs with n_min > 0;
• the direct experimental-weight formulation obtained with force_gamma_unit_interval = FALSE;
• large mixed-integer problems for which enumerating feasible experiment sets is impractical.

Install the Gurobi optimizer and its R package using the instructions for your local Gurobi installation.

Quick start

The following example uses the non-Gurobi backend. It selects at most two of three experiments and allocates a total cost budget of 500.

library(robustExpDesign)

Sigma_obs <- matrix(
  c(
    0.08, 0.01, 0.00,
    0.01, 0.05, 0.01,
    0.00, 0.01, 0.09
  ),
  nrow = 3,
  byrow = TRUE
)

v2 <- c(direct = 1.00, income = 1.40, wage = 1.10)
omega <- c(direct = 0.40, income = 1.00, wage = -0.70)

fit <- solve_minimax_design(
  Sigma_obs = Sigma_obs,
  v2 = v2,
  n_total = 500,
  omega = omega,
  costs = c(1, 1, 1.5),
  bias_weights = c(1, 1, 1),
  h = 2,
  min_experiments = 1,
  solver = "quadprog"
)

fit
fit$selected
fit$gamma_opt
fit$n_opt
fit$alpha_ratio
fit$beta_ratio
fit$regret

The proportional-regret objective is

max(variance regret, bias regret).

The result includes the selected experiments, effective shrinkage weights, cost-aware allocation, oracle normalizations, variance and bias ratios, and the maximum of those two ratios.

Evaluate a supplied design

Use evaluate_design() when the selection and shrinkage weights are already specified:

evaluated <- evaluate_design(
  Sigma_obs = Sigma_obs,
  v2 = v2,
  n_total = 500,
  omega = omega,
  x = c(1, 1, 0),
  gamma = c(0.8, 0.6, 0),
  costs = c(1, 1, 1.5)
)

evaluated$n_opt
evaluated$alpha
evaluated$beta

Weighted bias radii

bias_weights implements coordinate-specific ambiguity bounds of the form

|b_j| <= bias_weights[j] * B.

A weight of zero treats the corresponding coordinate as not misspecified. The legacy alias k remains available for compatibility.

fit_weighted <- solve_minimax_design(
  Sigma_obs = Sigma_obs,
  v2 = v2,
  n_total = 500,
  omega = omega,
  costs = c(1, 1, 1.5),
  bias_weights = c(1.0, 0.5, 2.0),
  h = 2,
  min_experiments = 1,
  solver = "quadprog"
)

Feasibility restrictions

Experiment menus can be restricted with h, min_experiments, x_max, feasible_sets, or linear constraints on the binary selection vector.

selection_constraints <- list(
  A = matrix(c(1, 1, 0), nrow = 1),
  sense = "<=",
  rhs = 1
)

fit_restricted <- solve_minimax_design(
  Sigma_obs = Sigma_obs,
  v2 = v2,
  n_total = 500,
  omega = omega,
  costs = c(1, 1, 1.5),
  h = 2,
  selection_constraints = selection_constraints,
  min_experiments = 1,
  solver = "quadprog"
)

Use n_min to impose a minimum sample allocation on every selected experiment. Positive n_min currently requires Gurobi, and the same floor is imposed on candidate designs and oracle benchmarks.

Budget sweeps

sweep_n_total() runs the design solvers over budgets and experiment-count limits. It returns arm-level allocation rows, regret rows, fitted objects, and optional ggplot2 plots.

sweep <- sweep_n_total(
  Sigma_obs = Sigma_obs,
  v2 = v2,
  omega = omega,
  n_grid = c(200, 300, 400, 500, 750, 1000),
  h_values = c(1, 2),
  costs = c(1, 1, 1.5),
  experiment_names = c("Direct", "Income", "Wage"),
  include_variance_design = TRUE,
  make_plots = TRUE,
  solver = "quadprog"
)

head(sweep$data$arms)
head(sweep$data$regret)
sweep$plots$allocation
sweep$plots$regret

Moment selection and GMM weights

solve_moment_design() handles general moment-loading problems. With a supplied weighting matrix and optimize_W = FALSE, it evaluates the implied linear GMM estimator. With optimize_W = TRUE, it uses CVXR to optimize over admissible moment sets or weighting-matrix masks.

Lambda <- matrix(
  c(
    1.0, 0.0,
    0.0, 1.0,
    1.0, 0.5,
    0.5, 1.0
  ),
  nrow = 4,
  byrow = TRUE
)

Sigma_mom <- diag(c(0.05, 0.06, 0.10, 0.12))
Omega <- matrix(c(0.4, 1.0), nrow = 1)

fixed_moments <- solve_moment_design(
  Lambda = Lambda,
  Sigma = Sigma_mom,
  Omega = Omega,
  W = diag(4),
  biased_moments = c(3, 4),
  norm = "l2",
  optimize_W = FALSE
)

fixed_moments$alpha
fixed_moments$beta

Audience-regret designs

solve_audience_regret_design() solves the Appendix C.2 objective over a grid of scalarization weights. The transformation is

lambda = B^2 / (1 + B^2),

and the grid must include 0 and 1. The default uses 50 equally spaced points. This solver currently requires Gurobi.

fit_audience <- solve_audience_regret_design(
  Sigma_obs = Sigma_obs,
  v2 = v2,
  n_total = 500,
  omega = omega,
  costs = c(1, 1, 1.5),
  bias_weights = c(1, 1, 1),
  h = 2,
  min_experiments = 1
)

fit_audience$r_opt
fit_audience$risk_by_lambda