API Reference

Primitive type for node. Alias for Int.

Chance node type.

Examples

c = ChanceNode(3, [1, 2])

Decision node type.

Examples

d = DecisionNode(2, [1])

Value node type.

Examples

v = ValueNode(4, [1, 3])

Primitive type for the number of states. Alias for Int.

States type. Works like Vector{State}.

Examples

S = States([2, 3, 2, 4])

Construct states from vector of (state, nodes) tuples.

Examples

julia> S = States([(2, [1, 3]), (3, [2, 4, 5])])
States([2, 3, 2, 3, 3])

Validate influence diagram.

Path type. Alias for NTuple{N, State} where N.

Iterate over paths in lexicographical order.

Examples

julia> states = States([2, 3])
julia> vec(collect(paths(states)))
[(1, 1), (2, 1), (1, 2), (2, 2), (1, 3), (2, 3)]

Iterate over paths with fixed states in lexicographical order.

Examples

julia> states = States([2, 3])
julia> vec(collect(paths(states, Dict(1=>2))))
[(2, 1), (2, 2), (2, 3)]

Construct and validate stage probabilities.

Examples

julia> data = [0.5 0.5 ; 0.2 0.8]
julia> X = Probabilities(2, data)
julia> s = (1, 2)
julia> X(s)
0.5

Abstract path probability type.

Examples

struct PathProbability <: AbstractPathProbability
    C::Vector{ChanceNode}
    # ...
end

(U::PathProbability)(s::Path) = ...

Path probability.

Examples

P = DefaultPathProbability(C, X)
s = (1, 2)
P(s)

State utilities.

Examples

julia> vals = [1.0 -2.0; 3.0 4.0]
julia> Y = Consequences(3, vals)
julia> s = (1, 2)
julia> Y(s)
-2.0

Abstract path utility type.

Examples

struct PathUtility <: AbstractPathUtility
    V::Vector{ValueNode}
    # ...
end

(U::PathUtility)(s::Path) = ...

Default path utility.

Examples

U = DefaultPathUtility(V, Y)
s = (1, 2)
U(s)

Local decision strategy type.

Examples

Z = LocalDecisionStrategy(1, data)
Z(s_I)

Decision strategy type.

Create decision variables and constraints.

Examples

z = DecisionVariables(model, S, D)

Create path probability variables and constraints.

Examples

π_s = PathProbabilityVariables(model, z, S, P)
π_s = PathProbabilityVariables(model, z, S, P; hard_lower_bound=false))

Adds a probability cut to the model as a lazy constraint.

Examples

probability_cut(model, π_s, P)

Adds a active paths cut to the model as a lazy constraint.

Examples

atol = 0.9  # Tolerance to trigger the creation of the lazy cut
active_paths_cut(model, π_s, S, P; atol=atol)

Positive affine transformation of path utility. Always evaluates positive values.

Examples

julia> U⁺ = PositivePathUtility(S, U)
julia> all(U⁺(s) > 0 for s in paths(S))
true

Create an expected value objective.

Examples

EV = expected_value(model, π_s, U)

Create a conditional value-at-risk (CVaR) objective.

Examples

α = 0.05  # Parameter such that 0 ≤ α ≤ 1
CVaR = conditional_value_at_risk(model, π_s, U, α)

Construct decision strategy from variable refs.

Extract values for decision variables from solved decision model.

Examples

Z = DecisionStrategy(z)

Interface for iterating over active paths given influence diagram and decision strategy.

1. Initialize path s of length n
2. Fill chance states s[C] by generating subpaths paths(C)
3. Fill decision states s[D] by decision strategy Z and path s

Examples

for s in CompatiblePaths(S, C, Z)
    ...
end

UtilityDistribution type.

Constructs the probability mass function for path utilities on active paths.

Examples

UtilityDistribution(S, P, U, Z)

StateProbabilities type.

Associates each node with array of probabilities for each of its states occuring in active paths.

Examples

StateProbabilities(S, P, Z)

Associates each node with array of conditional probabilities for each of its states occuring in active paths given fixed states and prior probability.

Examples

# Prior probabilities
prev = StateProbabilities(S, P, Z)

# Select node and fix its state
node = 1
state = 2
StateProbabilities(S, P, Z, node, state, prev)

Value-at-risk.

Conditional value-at-risk.

Print decision strategy.

Examples

print_decision_strategy(S, Z)

Print utility distribution

Examples

udist = UtilityDistribution(S, P, U, Z)
print_utility_distribution(udist)

Print state probabilities with fixed states.

Examples

sprobs = StateProbabilities(S, P, U, Z)
print_state_probabilities(sprobs, [c.j for c in C])
print_state_probabilities(sprobs, [d.j for d in D])

Print statistics.

Print risk measures.

Generate random decision diagram with n_C chance nodes, n_D decision nodes, and n_V value nodes. Parameter m_C and m_D are the upper bounds for the size of the information set.

Examples

rng = MersenneTwister(3)
random_diagram(rng, 5, 2, 3, 2)

Generate n random states from states.

Examples

rng = MersenneTwister(3)
S = States(rng, [2, 3], 10)

Generate random probabilities for chance node c with S states.

Examples

rng = MersenneTwister(3)
c = ChanceNode(2, [1])
S = States([2, 2])
Probabilities(rng, c, S)

Generate random consequences between low and high for value node v with S states.

Examples

rng = MersenneTwister(3)
v = ValueNode(3, [1])
S = States([2, 2])
Consequences(rng, v, S; low=-1.0, high=1.0)

Generate random decision strategy for decision node d with S states.

Examples

rng = MersenneTwister(3)
d = DecisionNode(2, [1])
S = States([2, 2])
LocalDecisionStrategy(rng, d, S)