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policytree

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A package for learning simple rule-based policies, where the rule takes the form of a shallow decision tree. Applications include settings which require interpretable predictions, such as for example a medical treatment prescription. This package uses doubly robust reward estimates from grf to find a shallow, but globally optimal decision tree.

Some helpful links for getting started:

  • The R package documentation contains usage examples and method references.
  • For community questions and answers around usage, see the GitHub issues page.
  • The package sparse policytree uses an alternate solver that may be faster on large datasets with sparse categorical features.

Installation

The latest release of the package can be installed through CRAN:

install.packages("policytree")

To install the latest development version from source:

devtools::install_github("grf-labs/policytree", subdir = "r-package/policytree")

Installing from source requires a C++ 11 compiler (on Windows Rtools is required as well) together with the R packages Rcpp and BH.

Multi-action policy learning example

library(policytree)
n <- 250
p <- 10
X <- matrix(rnorm(n * p), n, p)
W <- as.factor(sample(c("A", "B", "C"), n, replace = TRUE))
Y <- X[, 1] + X[, 2] * (W == "B") + X[, 3] * (W == "C") + runif(n)
multi.forest <- grf::multi_arm_causal_forest(X, Y, W)

# Compute doubly robust reward estimates.
Gamma.matrix <- double_robust_scores(multi.forest)
head(Gamma.matrix)
#              A          B           C
# 1 -0.002612209 -0.1438422 -0.04243015
# 2  0.417066177  0.4212708  1.04000173
# 3  2.020414370  0.3963890  1.33038496
# 4  1.193587749  1.7862142 -0.05668051
# 5  0.808323778  0.5017521  1.52094053
# 6 -0.045844471 -0.1460745 -1.56055025

# Fit a depth 2 tree on a random training subset.
train <- sample(1:n, 200)
opt.tree <- policy_tree(X[train, ], Gamma.matrix[train, ], depth = 2)
opt.tree
# policy_tree object
# Tree depth:  2
# Actions:  1: A 2: B 3: C
# Variable splits:
# (1) split_variable: X3  split_value: 0.368037
#   (2) split_variable: X2  split_value: -0.098143
#     (4) * action: 1
#     (5) * action: 2
#   (3) split_variable: X2  split_value: 1.25697
#     (6) * action: 3
#     (7) * action: 2

## Predict treatment on held out data
head(predict(opt.tree, X[-train, ]))
#> [1] 2 3 1 2 3 3

Details

policy_tree(): fits a depth k tree by exhaustive search (Nxp features on Nxd actions). The optimal tree maximizes the sum of rewards: let $\Gamma_i \in \mathbb R^d$ be a vector of unit-specific rewards for each action 1 to $d$ and $\pi(X_i) \in \{1, ..., d\}$ a mapping from covariates $X_i$ to action. policy_tree solves the following:

$$ \pi^* = argmax_{\pi \in \Pi} \left[\frac{1}{n} \sum_{i=1}^{n} \Gamma_i(\pi(X_i)) \right], $$

where $\Pi$ is the class of depth-k decision trees. (hybrid_policy_tree() employs a mix between a optimal/greedy approach and can be used to fit deeper trees).

double_robust_scores(): computes doubly robust reward estimates for a subset of grf forest types.

Contributing

Contributions are welcome, please consult the development guide for details.

Funding

Development of policytree is supported by the National Science Foundation, the Sloan Foundation, the Office of Naval Research (Grant N00014-17-1-2131) and Schmidt Futures.

References

Susan Athey and Stefan Wager. Policy Learning With Observational Data. Econometrica 89.1 (2021): 133-161. [paper, arxiv]

Toru Kitagawa and Aleksey Tetenov. Who Should be Treated? Empirical Welfare Maximization Methods for Treatment Choice. Econometrica 86.2 (2018): 591-616. [paper]

Erik Sverdrup, Ayush Kanodia, Zhengyuan Zhou, Susan Athey, and Stefan Wager. policytree: Policy learning via doubly robust empirical welfare maximization over trees. Journal of Open Source Software, 5(50), 2020. [paper]

Zhengyuan Zhou, Susan Athey, and Stefan Wager. Offline Multi-Action Policy Learning: Generalization and Optimization. Operations Research 71.1 (2023). [paper, arxiv]