R/policy_mab_ucb1.R

In contextual: Simulation and Analysis of Contextual Multi-Armed Bandit Policies

#' @export
UCB1Policy <- R6::R6Class(
  portable = FALSE,
  class = FALSE,
  inherit = Policy,
  public = list(
    class_name = "UCB1Policy",
    initialize = function() {
      super$initialize()
    },
    set_parameters = function(context_params) {
      self$theta_to_arms <- list('n' = 0, 'mean' = 0)
    },
    get_action = function(t, context) {
      n_zero_arms <- which(self$theta$n == 0)
      if (length(n_zero_arms) > 0) {
        action$choice <- sample_one_of(n_zero_arms)
        return(action)
      }
      expected_rewards <- rep(0.0, context$k)
      total_n          <- sum_of(self$theta$n)
      for (arm in 1:context$k) {
        variance <- sqrt((2*log(total_n)) / self$theta$n[[arm]])
        expected_rewards[arm] <- self$theta$mean[[arm]] + variance
      }
      action$choice <- which_max_tied(expected_rewards)
      action
    },
    set_reward = function(t, context, action, reward) {
      arm <- action$choice
      reward <- reward$reward
      inc(self$theta$n[[arm]]) <- 1
      inc(self$theta$mean[[arm]]) <- (reward - self$theta$mean[[arm]]) / self$theta$n[[arm]]
      self$theta
    }
  )
)

#' Policy: UCB1
#'
#' UCB policy for bounded bandits with a Chernoff-Hoeffding Bound
#'
#' \code{UCB1Policy} constructs an optimistic estimate in the form of an Upper Confidence Bound to
#' create an estimate of the expected payoff of each action, and picks the action with the highest estimate.
#' If the guess is wrong, the optimistic guess quickly decreases, till another action has
#' the higher estimate.
#'
#' @name UCB1Policy
#'
#'
#' @section Usage:
#' \preformatted{
#' policy <- UCB1Policy()
#' }
#'
#'
#' @section Methods:
#'
#' \describe{
#'   \item{\code{new()}}{ Generates a new \code{UCB1Policy} object.}
#' }
#'
#' \describe{
#'   \item{\code{set_parameters()}}{each policy needs to assign the parameters it wants to keep track of
#'   to list \code{self$theta_to_arms} that has to be defined in \code{set_parameters()}'s body.
#'   The parameters defined here can later be accessed by arm index in the following way:
#'   \code{theta[[index_of_arm]]$parameter_name}
#'   }
#' }
#'
#' \describe{
#'   \item{\code{get_action(context)}}{
#'     here, a policy decides which arm to choose, based on the current values
#'     of its parameters and, potentially, the current context.
#'    }
#'   }
#'
#'  \describe{
#'   \item{\code{set_reward(reward, context)}}{
#'     in \code{set_reward(reward, context)}, a policy updates its parameter values
#'     based on the reward received, and, potentially, the current context.
#'    }
#'   }
#'
#' @references
#'
#' Lai, T. L., & Robbins, H. (1985). Asymptotically efficient adaptive allocation rules. Advances in applied
#' mathematics, 6(1), 4-22.
#'
#' @seealso
#'
#' Core contextual classes: \code{\link{Bandit}}, \code{\link{Policy}}, \code{\link{Simulator}},
#' \code{\link{Agent}}, \code{\link{History}}, \code{\link{Plot}}
#'
#' Bandit subclass examples: \code{\link{BasicBernoulliBandit}}, \code{\link{ContextualLogitBandit}},
#' \code{\link{OfflineReplayEvaluatorBandit}}
#'
#' Policy subclass examples: \code{\link{EpsilonGreedyPolicy}}, \code{\link{ContextualLinTSPolicy}}
#'
#' @examples
#' \dontrun{
#'
#' horizon            <- 100L
#' simulations        <- 100L
#' weights            <- c(0.9, 0.1, 0.1)
#'
#' policy             <- UCB1Policy$new()
#' bandit             <- BasicBernoulliBandit$new(weights = weights)
#' agent              <- Agent$new(policy, bandit)
#'
#' history            <- Simulator$new(agent, horizon, simulations, do_parallel = FALSE)$run()
#'
#' plot(history, type = "cumulative")
#'
#' plot(history, type = "arms")
#'
#' }
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