Bandit: ContextualLogitBandit

Samples data from a basic logistic regression model.

Details

ContextualLogitBandit linear predictors are generated from the dot product of a random d dimensional normal weight vector and uniform random d x k dimensional context matrices with equal weights per arm. This product is then inverse-logit transformed to generate k dimensional binary (0/1) reward vectors by randomly sampling from a Bernoulli distribution.

Usage

  bandit <- ContextualLogitBandit$new(k, d, intercept = TRUE)

Arguments

k

integer; number of bandit arms

d

integer; number of contextual features

intercept

logical; if TRUE (default) it adds a constant (1.0) dimension to each context X at the end.

Methods

new(k, d, intercept = TRUE)

generates and instantializes a new ContextualLogitBandit instance.

get_context(t)

argument:

• t: integer, time step t.

returns a named list containing the current d x k dimensional matrix context$X, the number of arms context$k and the number of features context$d.

get_reward(t, context, action)

arguments:

• t: integer, time step t.

• context: list, containing the current context$X (d x k context matrix), context$k (number of arms) and context$d (number of context features) (as set by bandit).

• action: list, containing action$choice (as set by policy).

returns a named list containing reward$reward and, where computable, reward$optimal (used by "oracle" policies and to calculate regret).

post_initialization()

initializes d x k beta matrix.

See also

Core contextual classes: Bandit, Policy, Simulator, Agent, History, Plot

Bandit subclass examples: BasicBernoulliBandit, ContextualLogitBandit, OfflineReplayEvaluatorBandit

Policy subclass examples: EpsilonGreedyPolicy, ContextualLinTSPolicy

Examples

if (FALSE) {

horizon       <- 800L
simulations   <- 30L

bandit        <- ContextualLogitBandit$new(k = 5, d = 5, intercept = TRUE)

agents        <- list(Agent$new(ContextualLinTSPolicy$new(0.1), bandit),
                      Agent$new(EpsilonGreedyPolicy$new(0.1), bandit),
                      Agent$new(LinUCBGeneralPolicy$new(0.6), bandit),
                      Agent$new(ContextualEpochGreedyPolicy$new(8), bandit),
                      Agent$new(LinUCBHybridOptimizedPolicy$new(0.6), bandit),
                      Agent$new(LinUCBDisjointOptimizedPolicy$new(0.6), bandit))

simulation     <- Simulator$new(agents, horizon, simulations)
history        <- simulation$run()

plot(history, type = "cumulative", regret = FALSE,
              rate = TRUE, legend_position = "right")
}