We analyze the problem of using Explore-Exploit techniques to improve precision in multi-result ranking systems such as web search, query autocompletion and news recommendation. Adopting an exploration policy directly online, without understanding its impact on the production system, may have unwanted consequences - the system may sustain large losses, create user dissatisfaction, or collect exploration data which does not help improve ranking quality. An offline framework is thus necessary to let us decide what policy and how we should apply in a production environment to ensure positive outcome. Here, we describe such an offline framework. Using the framework, we study a popular exploration policy - Thompson sampling. We show that there are different ways of implementing it in multi-result ranking systems, each having different semantic interpretation and leading to different results in terms of sustained click-through-rate (CTR) loss and expected model improvement. In particular, we demonstrate that Thompson sampling can act as an online learner optimizing CTR, which in some cases can lead to an interesting outcome: lift in CTR during exploration. The observation is important for production systems as it suggests that one can get both valuable exploration data to improve ranking performance on the long run, and at the same time increase CTR while exploration lasts.
The effectiveness of Thompson sampling has been noted previously by @cite_1 @cite_18 @cite_21 and others. Subsequently efforts have focused on understanding better the theoretical properties of the algorithm (e.g., @cite_10 ) leaving aside the important implementation considerations which we raised, namely, that in the context of multi-result ranking there are multiple ways to define the buckets (arms), and that different definitions lead to different semantic interpretation and different results.
@cite_10 @cite_18 @cite_21 @cite_1
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We consider the multi armed bandit problem in non-stationary environments. Based on the Bayesian method, we propose a variant of Thompson Sampling which can be used in both rested and restless bandit scenarios. Applying discounting to the parameters of prior distribution, we describe a way to systematically reduce the effect of past observations. Further, we derive the exact expression for the probability of picking sub-optimal arms. By increasing the exploitative value of Bayes' samples, we also provide an optimistic version of the algorithm. Extensive empirical analysis is conducted under various scenarios to validate the utility of proposed algorithms. A comparison study with various state-of-the-arm algorithms is also included. 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. Thompson Sampling is one of the oldest heuristics for multi-armed bandit problems. It is a randomized algorithm based on Bayesian ideas, and has recently generated significant interest after several studies demonstrated it to have better empirical performance compared to the state-of-the-art methods. However, many questions regarding its theoretical performance remained open. In this paper, we design and analyze a generalization of Thompson Sampling algorithm for the stochastic contextual multi-armed bandit problem with linear payoff functions, when the contexts are provided by an adaptive adversary. This is among the most important and widely studied version of the contextual bandits problem. We prove a high probability regret bound of O(d2 e√T1+e) in time T for any 0 < e < 1, where d is the dimension of each context vector and e is a parameter used by the algorithm. Our results provide the first theoretical guarantees for the contextual version of Thompson Sampling, and are close to the lower bound of Ω(d√T) for this problem. This essentially solves a COLT open problem of Chapelle and Li [COLT 2012]. Thompson Sampling is one of the oldest heuristics for multi-armed bandit problems. It is a randomized algorithm based on Bayesian ideas, and has recently generated significant interest after several studies demonstrated it to have better empirical performance compared to the state-of-the-art methods. However, many questions regarding its theoretical performance remained open. In this paper, we design and analyze a generalization of Thompson Sampling algorithm for the stochastic contextual multi-armed bandit problem with linear payoff functions, when the contexts are provided by an adaptive adversary. This is among the most important and widely studied versions of the contextual bandits problem. We provide the first theoretical guarantees for the contextual version of Thompson Sampling. We prove a high probability regret bound of @math (or @math ), which is the best regret bound achieved by any computationally efficient algorithm available for this problem in the current literature, and is within a factor of @math (or @math ) of the information-theoretic lower bound for this problem.