Mobile Context-Aware Recommender Systems can be naturally modelled as an exploration exploitation trade-off (exr exp) problem, where the system has to choose between maximizing its expected rewards dealing with its current knowledge (exploitation) and learning more about the unknown user's preferences to improve its knowledge (exploration). This problem has been addressed by the reinforcement learning community but they do not consider the risk level of the current user's situation, where it may be dangerous to recommend items the user may not desire in her current situation if the risk level is high. We introduce in this paper an algorithm named R-UCB that considers the risk level of the user's situation to adaptively balance between exr and exp. The detailed analysis of the experimental results reveals several important discoveries in the exr exp behaviour.
Very frequently used in reinforcement learning to study exr exp, the multi-armed bandit problem was originally described by @cite_10 . The @math -greedy is one of the most used strategies to solve this problem. It chooses a random document with @math -frequency, and chooses otherwise the document with the highest estimated mean, the estimation being based on the observed rewards. The @math is chosen by the user in the open interval ]0, 1[.
@cite_10
2949186496 1587673378 2040774021 1516061453
The multi-armed bandit problem is a popular model for studying exploration exploitation trade-off in sequential decision problems. Many algorithms are now available for this well-studied problem. One of the earliest algorithms, given by W. R. Thompson, dates back to 1933. This algorithm, referred to as Thompson Sampling, is a natural Bayesian algorithm. The basic idea is to choose an arm to play according to its probability of being the best arm. Thompson Sampling algorithm has experimentally been shown to be close to optimal. In addition, it is efficient to implement and exhibits several desirable properties such as small regret for delayed feedback. However, theoretical understanding of this algorithm was quite limited. In this paper, for the first time, we show that Thompson Sampling algorithm achieves logarithmic expected regret for the multi-armed bandit problem. More precisely, for the two-armed bandit problem, the expected regret in time @math is @math . And, for the @math -armed bandit problem, the expected regret in time @math is @math . Our bounds are optimal but for the dependence on @math and the constant factors in big-Oh. The multiarmed bandit is often used as an analogy for the tradeoff between exploration and exploitation in search problems. The classic problem involves allocating trials to the arms of a multiarmed slot machine to maximize the expected sum of rewards. We pose a new variation of the multiarmed bandit--the Max K-Armed Bandit--in which trials must be allocated among the arms to maximize the expected best single sample reward of the series of trials. Motivation for the Max K-Armed Bandit is the allocation of restarts among a set of multistart stochastic search algorithms. We present an analysis of this Max K-Armed Bandit showing under certain assumptions that the optimal strategy allocates trials to the observed best arm at a rate increasing double exponentially relative to the other arms. This motivates an exploration strategy that follows a Boltzmann distribution with an exponentially decaying temperature parameter. We compare this exploration policy to policies that allocate trials to the observed best arm at rates faster (and slower) than double exponentially. The results confirm, for two scheduling domains, that the double exponential increase in the rate of allocations to the observed best heuristic outperfonns the other approaches. The restless bandit problem is one of the most well-studied generalizations of the celebrated stochastic multi-armed bandit (MAB) problem in decision theory. In its ultimate generality, the restless bandit problem is known to be PSPACE-Hard to approximate to any nontrivial factor, and little progress has been made on this problem despite its significance in modeling activity allocation under uncertainty. In this article, we consider the Feedback MAB problem, where the reward obtained by playing each of n independent arms varies according to an underlying on off Markov process whose exact state is only revealed when the arm is played. The goal is to design a policy for playing the arms in order to maximize the infinite horizon time average expected reward. This problem is also an instance of a Partially Observable Markov Decision Process (POMDP), and is widely studied in wireless scheduling and unmanned aerial vehicle (UAV) routing. Unlike the stochastic MAB problem, the Feedback MAB problem does not admit to greedy index-based optimal policies. We develop a novel duality-based algorithmic technique that yields a surprisingly simple and intuitive (2+e)-approximate greedy policy to this problem. We show that both in terms of approximation factor and computational efficiency, our policy is closely related to the Whittle index, which is widely used for its simplicity and efficiency of computation. Subsequently we define a multi-state generalization, that we term Monotone bandits, which remains subclass of the restless bandit problem. We show that our policy remains a 2-approximation in this setting, and further, our technique is robust enough to incorporate various side-constraints such as blocking plays, switching costs, and even models where determining the state of an arm is a separate operation from playing it. Our technique is also of independent interest for other restless bandit problems, and we provide an example in nonpreemptive machine replenishment. Interestingly, in this case, our policy provides a constant factor guarantee, whereas the Whittle index is provably polynomially worse. By presenting the first O(1) approximations for nontrivial instances of restless bandits as well as of POMDPs, our work initiates the study of approximation algorithms in both these contexts. The multi-armed bandit problem for a gambler is to decide which arm of a K-slot machine to pull to maximize his total reward in a series of trials. Many real-world learning and optimization problems can be modeled in this way. Several strategies or algorithms have been proposed as a solution to this problem in the last two decades, but, to our knowledge, there has been no common evaluation of these algorithms. This paper provides a preliminary empirical evaluation of several multi-armed bandit algorithms. It also describes and analyzes a new algorithm, Poker (Price Of Knowledge and Estimated Reward) whose performance compares favorably to that of other existing algorithms in several experiments. One remarkable outcome of our experiments is that the most naive approach, the e-greedy strategy, proves to be often hard to beat.