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Optimal Activation of Halting Multi-Armed Bandit Models
We study new types of dynamic allocation problems the {\sl Halting Bandit} models.
Accelerating the Computation of UCB and Related Indices for Reinforcement Learning
In this paper we derive an efficient method for computing the indices associated with an asymptotically optimal upper confidence bound algorithm (MDP-UCB) of Burnetas and Katehakis (1997) that only requires solving a system of two non-linear equations with two unknowns, irrespective of the cardinality of the state space of the Markovian decision process (MDP).
Reinforcement Learning: a Comparison of UCB Versus Alternative Adaptive Policies
In this paper we consider the basic version of Reinforcement Learning (RL) that involves computing optimal data driven (adaptive) policies for Markovian decision process with unknown transition probabilities.
Asymptotically Optimal Sequential Experimentation Under Generalized Ranking
We consider the \mnk{classical} problem of a controller activating (or sampling) sequentially from a finite number of $N \geq 2$ populations, specified by unknown distributions.
Asymptotic Behavior of Minimal-Exploration Allocation Policies: Almost Sure, Arbitrarily Slow Growing Regret
The purpose of this paper is to provide further understanding into the structure of the sequential allocation ("stochastic multi-armed bandit", or MAB) problem by establishing probability one finite horizon bounds and convergence rates for the sample (or "pseudo") regret associated with two simple classes of allocation policies $\pi$.
An Asymptotically Optimal Policy for Uniform Bandits of Unknown Support
The objective is to have a policy $\pi$ for deciding, based on available data, from which of the $N$ populations to sample from at any time $n=1, 2,\ldots$ so as to maximize the expected sum of outcomes of $n$ samples or equivalently to minimize the regret due to lack on information of the parameters $\{ a_i \}$ and $\{ b_i \}$.
Normal Bandits of Unknown Means and Variances: Asymptotic Optimality, Finite Horizon Regret Bounds, and a Solution to an Open Problem
Consider the problem of sampling sequentially from a finite number of $N \geq 2$ populations, specified by random variables $X^i_k$, $ i = 1,\ldots , N,$ and $k = 1, 2, \ldots$; where $X^i_k$ denotes the outcome from population $i$ the $k^{th}$ time it is sampled.
