def forward(self, obs: Tensor, act: Tensor) -> Tensor:
obs, act = (nt.vector(x) for x in (obs, act))
state, time = unpack_obs(obs)
tau = nt.vector_to_matrix(torch.cat([state, act], dim="R"))
time = nt.vector_to_scalar(time)
C, c = self._index_parameters(time)
c = nt.vector_to_matrix(c)
cost = nt.transpose(tau) @ C @ tau / 2 + nt.transpose(c) @ tau
reward = nt.matrix_to_scalar(cost.neg())
return nt.where(time.eq(self.horizon), torch.zeros_like(reward),
reward)
def forward(self, obs: Tensor) -> Tensor:
state, time = unpack_obs(obs)
time = nt.vector_to_scalar(time)
quad, linear, const = index_quadratic_parameters(self.quad,
self.linear,
self.const,
time,
max_idx=self.horizon)
state = nt.vector_to_matrix(state)
cost = nt.matrix_to_scalar(
nt.transpose(state) @ quad @ state / 2 +
nt.transpose(nt.vector_to_matrix(linear)) @ state +
nt.scalar_to_matrix(const))
return cost.neg()
def forward(self, rho: lqr.GaussInit, vval: lqr.Quadratic):
"""Expected cost given mean and covariance matrix of the initial state.
https://en.wikipedia.org/wiki/Quadratic_form_(statistics)#Expectation.
"""
# pylint:disable=invalid-name,no-self-use
V, v, c = vval
v = nt.vector_to_matrix(v)
c = nt.scalar_to_matrix(c)
mean, cov = rho
mean = nt.vector_to_matrix(mean)
value = (nt.scalar_to_matrix(nt.trace(cov @ V)) / 2 +
nt.transpose(mean) @ V @ mean / 2 + nt.transpose(v) @ mean +
c)
return nt.matrix_to_scalar(value)
def forward(self, obs: Tensor, action: Tensor) -> Tensor:
state, time = unpack_obs(obs)
time = nt.vector_to_scalar(time)
# noinspection PyTypeChecker
quad, linear, const = index_quadratic_parameters(self.quad,
self.linear,
self.const,
time,
max_idx=self.horizon -
1)
vec = nt.vector_to_matrix(torch.cat([state, action], dim="R"))
cost = nt.matrix_to_scalar(
nt.transpose(vec) @ quad @ vec / 2 +
nt.transpose(nt.vector_to_matrix(linear)) @ vec +
nt.scalar_to_matrix(const))
val = cost.neg()
return nt.where(time.eq(self.horizon), torch.zeros_like(val), val)
def refine_quadratic_output(quadratic: Quadratic):
A, b, c = quadratic
A, b, c = nt.horizon(nt.matrix(A), nt.matrix_to_vector(b),
nt.matrix_to_scalar(c))
return A, b, c