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Register a new userDynamic Learning with Frequent New Product Launches: A Sequential Multinomial Logit Bandit Problem
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Motivated by the phenomenon that companies introduce new products to keep abreast with customers rapidly changing tastes, we consider a novel online learning setting where a profit-maximizing seller needs to learn customers preferences through offering recommendations, which may contain existing products and new products that are launched in the middle of a selling period. We propose a sequential multinomial logit (SMNL) model to characterize customers behavior when product recommendations are presented in tiers. For the offline version with known customers preferences, we propose a polynomial-time algorithm and characterize the properties of the optimal tiered product recommendation. For the online problem, we propose a learning algorithm and quantify its regret bound. Moreover, we extend the setting to incorporate a constraint which ensures every new product is learned to a given accuracy. Our results demonstrate the tier structure can be used to mitigate the risks associated with learning new products.
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We study multinomial logit bandit with limited adaptivity, where the algorithms change their exploration actions as infrequently as possible when achieving almost optimal minimax regret. We propose two measures of adaptivity: the assortment switching cost and the more fine-grained item switching cost. We present an anytime algorithm (AT-DUCB) with $O(N log T)$ assortment switches, almost matching the lower bound $Omega(frac{N log T}{ log log T})$. In the fixed-horizon setting, our algorithm FH-DUCB incurs $O(N log log T)$ assortment switches, matching the asymptotic lower bound. We also present the ESUCB algorithm with item switching cost $O(N log^2 T)$.
In this paper, we consider the contextual variant of the MNL-Bandit problem. More specifically, we consider a dynamic set optimization problem, where in every round a decision maker offers a subset (assortment) of products to a consumer, and observes their response. Consumers purchase products so as to maximize their utility. We assume that the products are described by a set of attributes and the mean utility of a product is linear in the values of these attributes. We model consumer choice behavior by means of the widely used Multinomial Logit (MNL) model, and consider the decision makers problem of dynamically learning the model parameters, while optimizing cumulative revenue over the selling horizon $T$. Though this problem has attracted considerable attention in recent times, many existing methods often involve solving an intractable non-convex optimization problem and their theoretical performance guarantees depend on a problem dependent parameter which could be prohibitively large. In particular, existing algorithms for this problem have regret bounded by $O(sqrt{kappa d T})$, where $kappa$ is a problem dependent constant that can have exponential dependency on the number of attributes. In this paper, we propose an optimistic algorithm and show that the regret is bounded by $O(sqrt{dT} + kappa)$, significantly improving the performance over existing methods. Further, we propose a convex relaxation of the optimization step which allows for tractable decision-making while retaining the favourable regret guarantee.
Motivated by the observation that overexposure to unwanted marketing activities leads to customer dissatisfaction, we consider a setting where a platform offers a sequence of messages to its users and is penalized when users abandon the platform due to marketing fatigue. We propose a novel sequential choice model to capture multiple interactions taking place between the platform and its user: Upon receiving a message, a user decides on one of the three actions: accept the message, skip and receive the next message, or abandon the platform. Based on user feedback, the platform dynamically learns users abandonment distribution and their valuations of messages to determine the length of the sequence and the order of the messages, while maximizing the cumulative payoff over a horizon of length T. We refer to this online learning task as the sequential choice bandit problem. For the offline combinatorial optimization problem, we show that an efficient polynomial-time algorithm exists. For the online problem, we propose an algorithm that balances exploration and exploitation, and characterize its regret bound. Lastly, we demonstrate how to extend the model with user contexts to incorporate personalization.
There has been substantial research on sub-linear time approximate algorithms for Maximum Inner Product Search (MIPS). To achieve fast query time, state-of-the-art techniques require significant preprocessing, which can be a burden when the number of subsequent queries is not sufficiently large to amortize the cost. Furthermore, existing methods do not have the ability to directly control the suboptimality of their approximate results with theoretical guarantees. In this paper, we propose the first approximate algorithm for MIPS that does not require any preprocessing, and allows users to control and bound the suboptimality of the results. We cast MIPS as a Best Arm Identification problem, and introduce a new bandit setting that can fully exploit the special structure of MIPS. Our approach outperforms state-of-the-art methods on both synthetic and real-world datasets.
The Thresholding Bandit Problem (TBP) aims to find the set of arms with mean rewards greater than a given threshold. We consider a new setting of TBP, where in addition to pulling arms, one can also emph{duel} two arms and get the arm with a greater mean. In our motivating application from crowdsourcing, dueling two arms can be more cost-effective and time-efficient than direct pulls. We refer to this problem as TBP with Dueling Choices (TBP-DC). This paper provides an algorithm called Rank-Search (RS) for solving TBP-DC by alternating between ranking and binary search. We prove theoretical guarantees for RS, and also give lower bounds to show the optimality of it. Experiments show that RS outperforms previous baseline algorithms that only use pulls or duels.
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