hybrid_policy_tree {policytree}

Hybrid tree search

Description

Finds a depth k tree by looking ahead l steps.

Usage

hybrid_policy_tree(
  X,
  Gamma,
  depth = 3,
  search.depth = 2,
  split.step = 1,
  min.node.size = 1,
  verbose = TRUE
)

Arguments

X

The covariates used. Dimension N*p where p is the number of features.

Gamma

The rewards for each action. Dimension N*d where d is the number of actions.

depth

The depth of the fitted tree. Default is 3.

search.depth

Depth to look ahead when splitting. Default is 2.

split.step

An optional approximation parameter, the number of possible splits to consider when performing tree search. split.step = 1 (default) considers every possible split, split.step = 10 considers splitting at every 10'th sample and may yield a substantial speedup for dense features. Manually rounding or re-encoding continuous covariates with very high cardinality in a problem specific manner allows for finer-grained control of the accuracy/runtime tradeoff and may in some cases be the preferred approach.

min.node.size

An integer indicating the smallest terminal node size permitted. Default is 1.

verbose

Give verbose output. Default is TRUE.

Details

Builds deeper trees by iteratively using exact tree search to look ahead l splits. For example, with depth = 3 and search.depth = 2, the root split is determined by a depth 2 exact tree, and two new depth 2 trees are fit in the two immediate children using exact tree search, leading to a total depth of 3 (the resulting tree may be shallower than the specified depth depending on whether leaf nodes were pruned or not). This algorithm scales with some coefficient multiple of the runtime of a search.depth policy_tree, which means that for this approach to be feasible it needs an (n, p, d) configuration in which a search.depth policy_tree runs in reasonable time.

The algorithm: desired depth is given by depth. Each node is split using exact tree search with depth = search.depth. When we reach a node where the current level + search.depth is equal to depth, we stop and attach the search.depth subtree to this node. We also stop if the best search.depth split yielded a leaf node.

Value

A policy_tree object.

Examples

# Fit a depth three tree on doubly robust treatment effect estimates from a causal forest.
n <- 1500
p <- 5
X <- round(matrix(rnorm(n * p), n, p), 2)
W <- rbinom(n, 1, 1 / (1 + exp(X[, 3])))
tau <- 1 / (1 + exp((X[, 1] + X[, 2]) / 2)) - 0.5
Y <- X[, 3] + W * tau + rnorm(n)
c.forest <- grf::causal_forest(X, Y, W)
dr.scores <- double_robust_scores(c.forest)

tree <- hybrid_policy_tree(X, dr.scores, depth = 3)

# Predict treatment assignment.
predicted <- predict(tree, X)