text: We consider a variant of the multi-armed bandit model, which we call multi-armed bandit problem with known trend, where the gambler knows the shape of the reward function of each arm but not its distribution. This new problem is motivated by different online problems like active learning, music and interface recommendation applications, where when an arm is sampled by the model the received reward change according to a known trend. By adapting the standard multi-armed bandit algorithm UCB1 to take advantage of this setting, we propose the new algorithm named A-UCB that assumes a stochastic model. We provide upper bounds of the regret which compare favourably with the ones of UCB1. We also confirm that experimentally with different simulations
  @cite_0: Reinforcement learning policies face the exploration versus exploitation dilemma, i.e. the search for a balance between exploring the environment to find profitable actions while taking the empirically best action as often as possible. A popular measure of a policy's success in addressing this dilemma is the regret, that is the loss due to the fact that the globally optimal policy is not followed all the times. One of the simplest examples of the exploration exploitation dilemma is the multi-armed bandit problem. Lai and Robbins were the first ones to show that the regret for this problem has to grow at least logarithmically in the number of plays. Since then, policies which asymptotically achieve this regret have been devised by Lai and Robbins and many others. In this work we show that the optimal logarithmic regret is also achievable uniformly over time, with simple and efficient policies, and for all reward distributions with bounded support.
  @cite_14: This paper presents a new contextual bandit algorithm, NeuralBandit, which does not need hypothesis on stationarity of contexts and rewards. Several neural networks are trained to modelize the value of rewards knowing the context. Two variants, based on multi-experts approach, are proposed to choose online the parameters of multi-layer perceptrons. The proposed algorithms are successfully tested on a large dataset with and without stationarity of rewards.
summary: Our work is an adaptation of these classes of policies for MAB Problem with known trend reward function. Our work is most related to the study of dynamic versions of the MAB where either the set of arms or their expected reward may change over time. There are several applications, including active learning, music and interface recommendation, where the rewards are far from being stationary random sequences. A solution to cope with non-stationary is to drop the stochastic reward assumption and assume the reward sequences to be chosen by an adversary. Even with this adversarial formulation of the MAB problem, a randomized strategy like EXP3 provides the guarantee of a minimal regret @cite_0 @cite_14 .