Constraints

Monotonic constraints force predictions to move in a declared direction as a dense feature increases. They are useful when the direction is a modeling requirement, such as price increasing with distance or demand decreasing with travel time.

Interaction constraints restrict which feature combinations may appear together along a tree branch. They are useful when a route, corridor, or lane forecast should allow known families of effects while preventing unsupported cross-family interactions.

Use constraints as scientific assumptions, not as tuning decoration. A constraint should be defensible before training and should survive checks on held-out taxi trips, route groups, and time blocks.

Usage

monotonic_constraints has one entry per dense feature:

Value	Meaning
1	Prediction must be non-decreasing as the feature increases.
-1	Prediction must be non-increasing as the feature increases.
0	Feature is unconstrained.

model = CartoBoostRegressor(
    split_policy="axis_only",
    monotonic_constraints=[1, 0, -1],
)

BoosterConfig.interaction_constraints accepts sorted, deduplicated feature-index groups. During split search, the active branch features plus the candidate split features must fit inside at least one group. Two-feature spatial splitters are checked as a pair. Dense features use their matrix column index; sparse-set columns are addressed after dense columns, so the first sparse-set column is dense_feature_count.

For example, vec![vec![0, 1], vec![2, 3]] allows branch interactions within features 0 and 1 or within features 2 and 3, but blocks a branch that mixes feature 0 with feature 2.

Monotonic constraint support:

• Constant leaves.
• Non-fuzzy training.
• Axis-style splitters, including histogram-axis splitters.
• Dense features only.
• Regression.

Interaction constraints are enforced in the tree split search for axis, histogram-axis, diagonal 2D, Gaussian 2D, periodic, dense sparse-set, and list-valued sparse-set splitters. Groups must be sorted and in range; invalid groups fail before training.

Temporal-Spatial Guidance

Use constraints only when the direction is real, not just visually convenient. Trip distance, elapsed time, toll amount, or known service-level features can be good candidates. Latitude, longitude, zone ID, and similar location IDs usually are not: their relationship to the target is often local, discontinuous, or directional only within a specific market.

For temporal-spatial effects, prefer spatial splitters, periodic splitters, sparse location features, blocked evaluation, and residual diagnostics unless a monotonic rule is part of the problem definition.

Validation

Check more than aggregate RMSE:

• Probe rows that differ only in the constrained feature.
• Check increasing and decreasing constraints separately.
• For interaction groups, inspect trained trees to confirm disallowed feature combinations do not appear on the same branch.
• Include tied or nearly tied feature values.
• Use spatial or temporal holdouts when the constrained feature is correlated with cartography, route, or time.