pomdp (version 1.0.2)

update_belief: Belief Update

Description

Update the belief given a taken action and observation.

Usage

update_belief(
  model,
  belief = NULL,
  action = NULL,
  observation = NULL,
  episode = 1,
  digits = 7,
  drop = TRUE
)

Arguments

model

a POMDP object.

belief

the current belief state. Defaults to the start belief state specified in the model or "uniform".

action

the taken action. Can also be a vector of multiple actions or, if missing, then all actions are evaluated.

observation

the received observation. Can also be a vector of multiple observations or, if missing, then all observations are evaluated.

episode

Use transition and observation matrices for the given episode for time-dependent POMDPs (see POMDP).

digits

round decimals.

drop

logical; drop the result to a vector if only a single belief state is returned.

Value

returns the updated belief state as a named vector. If action or observations is a vector with multiple elements ot missing, then a matrix with all resulting belief states is returned.

Details

Update the belief state \(b\) (belief) with an action \(a\) and observation \(o\). The new belief state \(b'\) is:

$$b'(s') = \eta O(o | s',a) \sum_{s \in S} T(s' | s,a) b(s)$$

where \(\eta = 1/ \sum_{s' \in S}[ O(o | s',a) \sum_{s \in S} T(s' | s,a) b(s)]\) normalizes the new belief state so the probabilities add up to one.

See Also

Other POMDP: POMDP(), plot_belief_space(), sample_belief_space(), simulate_POMDP(), solve_POMDP(), solve_SARSOP(), transition_matrix(), write_POMDP()

Examples

# NOT RUN {
data(Tiger)

update_belief(c(.5,.5), model = Tiger)
update_belief(c(.5,.5), action = "listen", observation = "tiger-left", model = Tiger)
update_belief(c(.15,.85), action = "listen", observation = "tiger-right", model = Tiger)

# }