def admits_ri(cid: CID, decision: str, node: str) -> bool:
"""
Return True if cid admits a response incentive on node.
- A CID G admits a response incentive on X ∈ V \ {D} if
and only if the reduced graph G* min has a directed path X --> D.
("Agent Incentives: a Causal Perspective" by Everitt, Carey, Langlois, Ortega, and Legg, 2020)
"""
if len(cid.agents) > 1:
raise Exception(
f"This CID has {len(cid.agents)} agents. This incentive is currently only \
valid for CIDs with one agent.")
if node not in cid.nodes:
raise Exception(f"{node} is not present in the cid")
if decision not in cid.nodes:
raise Exception(f"{decision} is not present in the cid")
if not cid.sufficient_recall():
raise Exception("Voi only implemented graphs with sufficient recall")
if node == decision:
return False
req_graph = requisite_graph(cid)
if find_all_dir_paths(req_graph, node, decision):
return True
return False
def admits_dir_voc(cid: CID, decision: str, node: str) -> bool:
"""
Return True if a single-decision cid admits direct positive value of control for node.
- A single-decision CID G admits positive value of control for a node X ∈ V \ {D} if and
only if there is a directed path X --> U in the reduced graph G∗.
- The path X --> U may or may not pass through D.
- The agent has a direct value of control incentive on D if the path does not pass through D.
- The agent has an indirect value of control incentive on D if the path does pass through D
and there is also a backdoor path X--U that begins backwards from X (...<- X) and is
active when conditioning on Fa_D \ {X}
"""
if node not in cid.nodes:
raise Exception(f"{node} is not present in the cid")
if decision not in cid.nodes:
raise Exception(f"{decision} is not present in the cid")
agent_utilities = cid.all_utility_nodes
req_graph = requisite_graph(cid)
if not admits_voc(cid, decision, node):
return False
for util in agent_utilities:
if node == util or util in nx.descendants(req_graph, node):
x_u_paths = find_all_dir_paths(req_graph, node, util)
if any([decision not in path for path in x_u_paths]):
return True
return False
def _effective_dir_path_exists(mb: MACIDBase, start: str, finish: str,
effective_set: List[str]) -> bool:
"""
checks whether an effective directed path exists
"""
start_finish_paths = find_all_dir_paths(mb, start, finish)
for path in start_finish_paths:
if _path_is_effective(mb, path, effective_set):
return True
else:
return False
def _directed_effective_path_not_through_set_y(mb: MACIDBase,
start: str,
finish: str,
effective_set: List[str],
y: List[str] = []) -> bool:
"""
checks whether a directed effective path exists that doesn't pass through any of the nodes in the set y.
"""
start_finish_paths = find_all_dir_paths(mb, start, finish)
for path in start_finish_paths:
path_not_through_y = set(y).isdisjoint(set(path))
if _path_is_effective(mb, path, effective_set) and path_not_through_y:
return True
else:
return False
def admits_ri(cid: CID, decision: str, node: str) -> bool:
"""
Return True if a single-decision cid admits a response incentive on node.
- A single decision CID G admits a response incentive on X ∈ V \ {D} if
and only if the reduced graph G* min has a directed path X --> D.
("Agent Incentives: a Causal Perspective" by Everitt, Carey, Langlois, Ortega, and Legg, 2020)
"""
if node not in cid.nodes:
raise Exception(f"{node} is not present in the cid")
if decision not in cid.nodes:
raise Exception(f"{decision} is not present in the cid")
if node == decision:
return False
req_graph = requisite_graph(cid)
if find_all_dir_paths(req_graph, node, decision):
return True
return False
def test_find_all_dir_paths(self) -> None:
example = MACID([
('A', 'B'),
('B', 'C'),
('C', 'D'),
('D', 'E'),
('B', 'F'),
('F', 'E')],
{1: {'D': ['D'], 'U': ['E']}})
self.assertEqual(find_all_dir_paths(example, 'A', 'E'), [['A', 'B', 'C', 'D', 'E'], ['A', 'B', 'F', 'E']])
self.assertEqual(find_all_dir_paths(example, 'C', 'E'), [['C', 'D', 'E']])
self.assertFalse(find_all_dir_paths(example, 'F', 'A'))
self.assertTrue(len(find_all_dir_paths(example, 'B', 'E')) == 2)
with self.assertRaises(Exception):
find_all_dir_paths(example, 'U2', 'A')
def admits_ici(cid: CID, decision: str, node: str) -> bool:
"""
Return True if a single-decision cid admits an instrumental control incentive on node.
- A single-decision CID G admits an instrumental control incentive on X ∈ V
if and only if G has a directed path from the decision D to a utility node U ∈ U that passes through X,
i.e. a directed path D --> X --> U.
"""
if node not in cid.nodes:
raise Exception(f"{node} is not present in the cid")
if decision not in cid.nodes:
raise Exception(f"{decision} is not present in the cid")
agent_utilities = cid.all_utility_nodes
d_u_paths = [
path for util in agent_utilities
for path in find_all_dir_paths(cid, decision, util)
]
if any(node in path for path in d_u_paths):
return True
return False
