pomdp (version 1.2.4)

plot_belief_space: Plot a 2D or 3D Projection of the Belief Space

Description

Plots the optimal action, the node in the policy graph or the reward for a given set of belief points on a line (2D) or on a ternary plot (3D). If no points are given, points are sampled using a regular arrangement or randomly from the (projected) belief space.

Usage

plot_belief_space(
  model,
  projection = NULL,
  epoch = 1,
  sample = "regular",
  n = 100,
  what = c("action", "pg_node", "reward"),
  legend = TRUE,
  pch = 20,
  col = NULL,
  jitter = 0,
  oneD = TRUE,
  ...
)

Value

Returns invisibly the sampled points.

Arguments

model

a solved POMDP.

projection

Sample in a projected belief space. See projection() for details.

epoch

display this epoch.

sample

a matrix with belief points as rows or a character string specifying the method used for sample_belief_space().

n

number of points sampled.

what

what to plot.

legend

logical; add a legend? If the legend is covered by the plot then you need to increase the plotting region of the plotting device.

pch

plotting symbols.

col

plotting colors.

jitter

jitter amount for 2D belief spaces (good values are between 0 and 1, while using ylim = c(0,1)).

oneD

plot projections on two states in one dimension.

...

additional arguments are passed on to plot for 2D or TerneryPlot for 3D.

Author

Michael Hahsler

See Also

Other policy: estimate_belief_for_nodes(), optimal_action(), plot_policy_graph(), policy(), policy_graph(), projection(), reward(), solve_POMDP(), solve_SARSOP(), value_function()

Other POMDP: MDP2POMDP, POMDP(), accessors, actions(), add_policy(), projection(), reachable_and_absorbing, regret(), sample_belief_space(), simulate_POMDP(), solve_POMDP(), solve_SARSOP(), transition_graph(), update_belief(), value_function(), write_POMDP()

Examples

# two-state POMDP
data("Tiger")
sol <- solve_POMDP(Tiger)

plot_belief_space(sol)
plot_belief_space(sol, oneD = FALSE)
plot_belief_space(sol, n = 10)
plot_belief_space(sol, n = 100, sample = "random")

# plot the belief points used by the grid-based solver
plot_belief_space(sol, sample = sol $solution$belief_points_solver)

# plot different measures
plot_belief_space(sol, what = "pg_node")
plot_belief_space(sol, what = "reward")

# three-state POMDP
# Note: If the plotting region is too small then the legend might run into the plot
data("Three_doors")
sol <- solve_POMDP(Three_doors)
sol

# plotting needs the suggested package Ternary
if ("Ternary" %in% installed.packages()) {
plot_belief_space(sol)
plot_belief_space(sol, n = 10000)
plot_belief_space(sol, what = "reward", sample = "random", n = 1000)
plot_belief_space(sol, what = "pg_node", n = 10000)

# holding tiger-left constant at .5 follows this line in the ternary plot 
Ternary::TernaryLines(list(c(.5, 0, .5), c(.5, .5, 0)), col = "black", lty = 2)
# we can plot the projection for this line 
plot_belief_space(sol, what = "pg_node", n = 1000, projection = c("tiger-left" = .5))

# plot the belief points used by the grid-based solver
plot_belief_space(sol, sample = sol$solution$belief_points_solver, what = "pg_node")

# plot the belief points obtained using simulated trajectories with an epsilon-greedy policy.
# Note that we only use n = 50 to save time.
plot_belief_space(sol, 
  sample = simulate_POMDP(sol, n = 50, horizon = 100,
    epsilon = 0.1, return_beliefs = TRUE)$belief_states)
}

# plot a 3-state belief space using ggtern (ggplot2)
if (FALSE) {
library(ggtern)
samp <- sample_belief_space(sol, n = 1000)
df <- cbind(as.data.frame(samp), reward_node_action(sol, belief = samp))
df$pg_node <- factor(df$pg_node)

ggtern(df, aes(x = `tiger-left`, y = `tiger-center`, z = `tiger-right`)) +
  geom_point(aes(color = pg_node), size = 2)

ggtern(df, aes(x = `tiger-left`, y = `tiger-center`, z = `tiger-right`)) +
  geom_point(aes(color = action), size = 2)

ggtern(df, aes(x = `tiger-left`, y = `tiger-center`, z = `tiger-right`)) +
  geom_point(aes(color = reward), size = 2)
}