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373 | class DAGEnvironment(BaseVecEnvironment[EnvState, EnvParams]):
def __init__(
self,
reward_module: TRewardModule,
num_variables: int,
) -> None:
super().__init__(reward_module)
self.num_variables = num_variables
self.stop_action = self.num_variables * self.num_variables
if self.is_enumerable:
# Here we construct a helper array to convert an adjacency matrix to an index.
# This is done during initialization to avoid repetitive computations.
self.all_adjacencies_flat_bits = get_all_adjacencies_flat_bits(self.num_variables)
self.all_dags_num = self.all_adjacencies_flat_bits.shape[0]
def get_init_state(self, num_envs: int) -> EnvState:
return EnvState(
adjacency_matrix=jnp.zeros(
(num_envs, self.num_variables, self.num_variables),
dtype=jnp.bool,
),
closure_T=jnp.tile(
jnp.eye(self.num_variables, dtype=jnp.bool),
(num_envs, 1, 1),
),
is_terminal=jnp.zeros((num_envs,), dtype=jnp.bool),
is_initial=jnp.ones((num_envs,), dtype=jnp.bool),
is_pad=jnp.zeros((num_envs,), dtype=jnp.bool),
)
def init(self, rng_key: chex.PRNGKey) -> EnvParams:
dummy_state = self.get_init_state(1)
reward_params = self.reward_module.init(rng_key, dummy_state)
return EnvParams(
num_variables=self.num_variables,
reward_params=reward_params,
)
@property
def max_steps_in_episode(self) -> int:
return (self.num_variables * (self.num_variables - 1)) // 2 + 1
def _single_transition(
self,
state: EnvState,
action: TAction,
env_params: EnvParams,
) -> tuple[EnvState, TDone, dict[Any, Any]]:
is_terminal = state.is_terminal
def get_state_terminal() -> EnvState:
return state.replace(is_pad=True)
def get_state_nonterminal() -> EnvState:
done = action == self.stop_action
source, target = jnp.divmod(action, self.num_variables)
return jax.lax.cond(done, get_state_finished, get_state_inter, source, target)
def get_state_finished(source: chex.Array, target: chex.Array) -> EnvState:
return state.replace(is_terminal=True, is_initial=False)
def get_state_inter(source: chex.Array, target: chex.Array) -> EnvState:
adjacency_matrix = state.adjacency_matrix.at[source, target].set(True)
closure_T = state.closure_T
outer_product = jnp.logical_and(
jnp.expand_dims(closure_T[source], 0),
jnp.expand_dims(closure_T[:, target], 1),
)
closure_T = jnp.logical_or(closure_T, outer_product)
return state.replace(
adjacency_matrix=adjacency_matrix,
closure_T=closure_T,
is_terminal=False,
is_initial=False,
)
next_state = jax.lax.cond(is_terminal, get_state_terminal, get_state_nonterminal)
return next_state, next_state.is_terminal, {}
def _single_source_bfs(self, adjacency_t: chex.Array, start: int) -> chex.Array:
"""
Returns a boolean 1D array 'visited' of shape (d,),
indicating which nodes are reachable from 'start' in adjacency_t.
adjacency_t[i, j] = True means there's an edge i->j in G^T.
"""
d = adjacency_t.shape[0]
visited_init = jnp.zeros(d, dtype=bool).at[start].set(True)
frontier_init = visited_init
def cond_fun(carry):
frontier, _visited = carry
return jnp.any(frontier) # continue while we have newly discovered nodes
def body_fun(carry):
frontier, visited = carry
# adjacency_t & frontier[:, None] marks edges from any node in `frontier`.
# Taking "any(..., axis=0)" merges them into which nodes we can discover next
neighbors = jnp.any(adjacency_t & frontier[:, None], axis=0)
new_frontier = neighbors & jnp.logical_not(visited)
new_visited = visited | new_frontier
return (new_frontier, new_visited)
_, visited_final = jax.lax.while_loop(cond_fun, body_fun, (frontier_init, visited_init))
return visited_final
def _single_compute_closure(self, adjacency: chex.Array) -> chex.Array:
"""
Given the adjacency matrix of G (shape (d, d)),
compute its transitive closure via BFS-from-each-node.
closure[i, j] = True if i can reach j in the graph G.
"""
d = adjacency.shape[0]
closure = jax.vmap(lambda i: self._single_source_bfs(adjacency, i))(jnp.arange(d))
# Force the diagonal True (i can reach i by convention)
return jnp.logical_or(closure, jnp.eye(d, dtype=jnp.bool))
def _single_backward_transition(
self,
state: EnvState,
backward_action: chex.Array,
env_params: EnvParams,
) -> tuple[chex.Array, EnvState, chex.Array, chex.Array, dict[Any, Any]]:
"""Backward transition for DAG environment.
Removing an edge is equivalent to adding a 'phantom' edge.
"""
is_initial = state.is_initial
def get_state_initial() -> EnvState:
return state.replace(is_pad=True)
def get_state_non_initial() -> EnvState:
unterminate = backward_action == self.stop_action
return jax.lax.cond(unterminate, get_state_terminating, get_state_inter)
def get_state_terminating() -> EnvState:
return state.replace(
is_terminal=False,
is_initial=jnp.all(jnp.logical_not(state.adjacency_matrix)),
is_pad=False,
)
def get_state_inter() -> EnvState:
source, target = jnp.divmod(backward_action, self.num_variables)
adjacency_matrix = state.adjacency_matrix.at[source, target].set(False)
closure_T = self._single_compute_closure(adjacency_matrix.T)
return state.replace(
adjacency_matrix=adjacency_matrix,
closure_T=closure_T,
is_terminal=False,
is_initial=jnp.all(jnp.logical_not(adjacency_matrix)),
is_pad=False,
)
prev_state = jax.lax.cond(is_initial, get_state_initial, get_state_non_initial)
return prev_state, prev_state.is_initial, {}
def get_obs(self, state: EnvState, env_params: EnvParams) -> chex.Array:
return state.adjacency_matrix
def get_backward_action(
self,
state: EnvState,
forward_action: chex.Array,
next_state: EnvState,
params: EnvParams,
) -> chex.Array:
return forward_action
def get_forward_action(
self,
state: EnvState,
backward_action: chex.Array,
prev_state: EnvState,
params: EnvParams,
) -> chex.Array:
return backward_action
def get_invalid_mask(self, state: EnvState, env_params: EnvParams) -> chex.Array:
"""Invalid mask for forward actions.
Constructed as a logical or of adjacency matrix and
transitive closure of transposed adjacency matrix.
"""
num_envs = state.is_pad.shape[0]
mask = jnp.logical_or(state.adjacency_matrix, state.closure_T).reshape(num_envs, -1)
return jnp.concatenate(
[mask, jnp.zeros((num_envs, 1), dtype=jnp.bool)], axis=1
) # stop action == last action is always valid
def get_invalid_backward_mask(self, state: EnvState, params: EnvParams) -> chex.Array:
"""Invalid mask for backward actions.
Invert adjacency matrix and allow stop action only for the terminal state.
"""
def _single_get_invalid_backward_mask(state: EnvState) -> chex.Array:
return jax.lax.cond(
state.is_terminal,
lambda: jnp.append(
jnp.ones((self.num_variables**2,), dtype=jnp.bool),
jnp.zeros((1,), dtype=jnp.bool),
),
lambda: jnp.append(
jnp.logical_not(state.adjacency_matrix).reshape(-1),
jnp.ones((1,), dtype=jnp.bool),
),
)
return jax.vmap(_single_get_invalid_backward_mask)(state)
@property
def name(self) -> str:
return f"DAG-{self.num_variables}-v0"
@property
def action_space(self) -> spaces.Discrete:
"""Action space of the environment."""
return spaces.Discrete(self.num_variables * self.num_variables + 1)
@property
def backward_action_space(self) -> spaces.Discrete:
"""Backward action space of the environment."""
return spaces.Discrete(self.num_variables * self.num_variables + 1)
@property
def observation_space(self) -> spaces.Box:
"""Observation space of the environment."""
return spaces.Box(
low=0,
high=1,
shape=(self.num_variables, self.num_variables),
dtype=jnp.bool,
)
@property
def state_space(self) -> spaces.Dict:
"""State space of the environment."""
return spaces.Dict({
"adjacency_matrix": spaces.Box(
low=0,
high=1,
shape=(self.num_variables, self.num_variables),
dtype=jnp.bool,
),
"closure_T": spaces.Box(
low=0,
high=1,
shape=(self.num_variables, self.num_variables),
dtype=jnp.bool,
),
"is_terminal": spaces.Box(low=0, high=1, shape=(), dtype=jnp.bool),
"is_initial": spaces.Box(low=0, high=1, shape=(), dtype=jnp.bool),
"is_pad": spaces.Box(low=0, high=1, shape=(), dtype=jnp.bool),
})
@property
def is_enumerable(self) -> bool:
"""Whether this environment supports enumerable operations."""
return self.num_variables < 6
def state_to_index(self, state: EnvState, env_params: EnvParams) -> chex.Array:
return adj_to_index(state.adjacency_matrix, self.all_adjacencies_flat_bits)
def get_all_states(self, env_params: EnvParams) -> EnvState:
"""Returns all states in the environment in some order."""
all_adjacency_matrices = construct_all_dags(self.num_variables)
sort_idx = jax.vmap(adj_to_index, in_axes=(0, None))(
all_adjacency_matrices, self.all_adjacencies_flat_bits
)
all_adjacency_matrices = all_adjacency_matrices[sort_idx]
return jax.vmap(
lambda x: EnvState(
adjacency_matrix=x,
closure_T=self._single_compute_closure(x.T),
is_terminal=False,
is_initial=False,
is_pad=False,
)
)(all_adjacency_matrices)
def _get_states_rewards(self, env_params: EnvParams) -> chex.Array:
"""
Returns the true distribution of rewards for all states in the DAG environment.
NOTE: The rewards are shifted since log rewards are ~-100.
"""
all_dags = self.get_all_states(env_params)
log_reward = self.reward_module.log_reward(all_dags, env_params)
log_reward = log_reward - jnp.max(log_reward) # softmax trick
return jnp.exp(log_reward)
def get_true_distribution(self, env_params: EnvParams) -> chex.Array:
"""
Returns the true distribution of rewards for all states in the DAG environment.
"""
rewards = self._get_states_rewards(env_params)
return rewards / rewards.sum()
def get_empirical_distribution(self, states: EnvState, env_params: EnvParams) -> chex.Array:
"""
Extracts the empirical distribution from the given states.
"""
sample_idx = jax.vmap(adj_to_index, in_axes=(0, None))(
states.adjacency_matrix, self.all_adjacencies_flat_bits
)
valid_mask = states.is_terminal.astype(jnp.float32)
empirical_dist = jax.ops.segment_sum(
valid_mask, sample_idx, num_segments=self.all_dags_num
)
empirical_dist /= empirical_dist.sum()
return empirical_dist
@property
def is_mean_reward_tractable(self) -> bool:
"""Whether this environment supports mean reward tractability."""
return self.num_variables < 6
def get_mean_reward(self, env_params: EnvParams) -> float:
"""
Returns the mean reward for the DAG environment.
"""
rewards = self._get_states_rewards(env_params)
return jnp.pow(rewards, 2).sum() / rewards.sum()
@property
def is_normalizing_constant_tractable(self) -> bool:
"""Whether this environment supports tractable normalizing constant."""
return self.num_variables < 6
def get_normalizing_constant(self, env_params: EnvParams) -> float:
"""
Returns the normalizing constant for the DAG environment.
The normalizing constant is computed as the sum of rewards.
"""
rewards = self._get_states_rewards(env_params)
return rewards.sum()
|