| projection {pomdp} | R Documentation |
Defining a Belief Space Projection
Description
High dimensional belief spaces can be projected to lower dimension. This is useful for visualization and
to analyze the belief space and value functions. This definition is used by functions like plot_belief_space(),
plot_value_function(), and sample_belief_space().
Usage
projection(x = NULL, model)
Arguments
x |
specification of the projection (see Details section). |
model |
a POMDP. |
Details
The belief space is $n-1$ dimensional, were $n$ is the number of states. Note: it is n-1 dimensional since the probabilities
need to add up to 1. A projection fixes the belief value for a set of states. For example, for a 4-state POMDP
(s1, s2, s3, s4), we can project the belief space on s1 and s2 by holding s3 and s4 constant
which is represented by the vector c(s1 = NA, s2 = NA, s3 = 0, s4 = .1). We use NA to represent that the values are not
fixed and the value that the other dimensions are held constant.
We provide several ways to specify a projection:
A vector with values for all dimensions.
NAs are used for the dimension projected on. This is the canonical form used in this package. Example:c(NA, NA, 0, .1)A named vector with just the dimensions held constant. Example:
c(s3 = 0, s4 = .1)A vector of state names to project on. All other dimensions are held constant at 0. Example:
c("s1", "s2")A vector with indices of the states to project on. All other dimensions are held constant at 0. Example:
c(1, 2)
Value
a canonical description of the projection.
Author(s)
Michael Hahsler
See Also
Other policy:
estimate_belief_for_nodes(),
optimal_action(),
plot_belief_space(),
plot_policy_graph(),
policy(),
policy_graph(),
reward(),
solve_POMDP(),
solve_SARSOP(),
value_function()
Other POMDP:
MDP2POMDP,
POMDP(),
accessors,
actions(),
add_policy(),
plot_belief_space(),
reachable_and_absorbing,
regret(),
sample_belief_space(),
simulate_POMDP(),
solve_POMDP(),
solve_SARSOP(),
transition_graph(),
update_belief(),
value_function(),
write_POMDP()
Examples
model <- POMDP(
states = 4,
actions = 2,
observations = 2,
transition_prob = list("identity","identity"),
observation_prob = list("uniform","uniform"),
reward = rbind(R_(value = 1))
)
projection(NULL, model = model)
projection(1:2, model = model)
projection(c("s2", "s3"), model = model)
projection(c(1,4), model = model)
projection(c(s2 = .4, s3 = .2), model = model)
projection(c(s1 = .1, s2 = NA, s3 = NA, s4 = .3), model = model)