Bandit: Offline Bootstrapped Replay

Policy for the evaluation of policies with offline data through replay with bootstrapping.

Details

The key assumption of the method is that that the original logging policy chose i.i.d. arms uniformly at random.

Take care: if the original logging policy does not change over trials, data may be used more efficiently via propensity scoring (Langford et al., 2008; Strehl et al., 2011) and related techniques like doubly robust estimation (Dudik et al., 2011).

Usage

  bandit <- OfflineBootstrappedReplayBandit(formula,
                                            data, k = NULL, d = NULL,
                                            unique = NULL, shared = NULL,
                                            randomize = TRUE, replacement = TRUE,
                                            jitter = TRUE, arm_multiply = TRUE)

Arguments

formula

formula (required). Format: y.context ~ z.choice | x1.context + x2.xontext + ... By default, adds an intercept to the context model. Exclude the intercept, by adding "0" or "-1" to the list of contextual features, as in: y.context ~ z.choice | x1.context + x2.xontext -1

data

data.table or data.frame; offline data source (required)

k

integer; number of arms (optional). Optionally used to reformat the formula defined x.context vector as a k x d matrix. When making use of such matrix formatted contexts, you need to define custom intercept(s) when and where needed in data.table or data.frame.

d

integer; number of contextual features (optional) Optionally used to reformat the formula defined x.context vector as a k x d matrix. When making use of such matrix formatted contexts, you need to define custom intercept(s) when and where needed in data.table or data.frame.

randomize

logical; randomize rows of data stream per simulation (optional, default: TRUE)

replacement

logical; sample with replacement (optional, default: TRUE)

jitter

logical; add jitter to contextual features (optional, default: TRUE)

arm_multiply

logical; multiply the horizon by the number of arms (optional, default: TRUE)

multiplier

integer; replicate the dataset multiplier times before randomization. When arm_multiply has been set to TRUE, the number of replications is the number of arms times this integer. Can be used when Simulator's policy_time_loop has been set to TRUE, otherwise a simulation might run out of pre-indexed data.

unique

integer vector; index of disjoint features (optional)

shared

integer vector; index of shared features (optional)

Methods

new(formula, data, k = NULL, d = NULL, unique = NULL, shared = NULL, randomize = TRUE, replacement = TRUE, jitter = TRUE, arm_multiply = TRUE)

generates and instantializes a new OfflineBootstrappedReplayBandit 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()

Randomize offline data by shuffling the offline data.table before the start of each individual simulation when self$randomize is TRUE (default)

References

Mary, J., Preux, P., & Nicol, O. (2014, January). Improving offline evaluation of contextual bandit algorithms via bootstrapping techniques. In International Conference on Machine Learning (pp. 172-180).

See also

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

Bandit subclass examples: BasicBernoulliBandit, ContextualLogitBandit, OfflineBootstrappedReplayBandit

Policy subclass examples: EpsilonGreedyPolicy, ContextualLinTSPolicy

Examples

if (FALSE) {

library(contextual)
library(data.table)

# Import personalization data-set

url         <- "http://d1ie9wlkzugsxr.cloudfront.net/data_cmab_basic/dataset.txt"
datafile    <- fread(url)

simulations <- 1
horizon     <- nrow(datafile)

bandit      <- OfflineReplayEvaluatorBandit$new(formula = V2 ~ V1 | . - V1, data = datafile)

# Define agents.
agents      <- list(Agent$new(LinUCBDisjointOptimizedPolicy$new(0.01), bandit, "alpha = 0.01"),
                    Agent$new(LinUCBDisjointOptimizedPolicy$new(0.05), bandit, "alpha = 0.05"),
                    Agent$new(LinUCBDisjointOptimizedPolicy$new(0.1),  bandit, "alpha = 0.1"),
                    Agent$new(LinUCBDisjointOptimizedPolicy$new(1.0),  bandit, "alpha = 1.0"))

# Initialize the simulation.

simulation  <- Simulator$new(agents = agents, simulations = simulations, horizon = horizon,
                             do_parallel = FALSE, save_context = TRUE)

# Run the simulation.
sim  <- simulation$run()

# plot the results
plot(sim, type = "cumulative", regret = FALSE, rate = TRUE,
     legend_position = "bottomright", ylim = c(0,1))


}