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Register a new userMNL-Bandit: A Dynamic Learning Approach to Assortment Selection
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Added by
Vashist Avadhanula
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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We consider a dynamic assortment selection problem, where in every round the retailer offers a subset (assortment) of $N$ substitutable products to a consumer, who selects one of these products according to a multinomial logit (MNL) choice model. The retailer observes this choice and the objective is to dynamically learn the model parameters, while optimizing cumulative revenues over a selling horizon of length $T$. We refer to this exploration-exploitation formulation as the MNL-Bandit problem. Existing methods for this problem follow an explore-then-exploit approach, which estimate parameters to a desired accuracy and then, treating these estimates as if they are the correct parameter values, offers the optimal assortment based on these estimates. These approaches require certain a priori knowledge of separability, determined by the true parameters of the underlying MNL model, and this in turn is critical in determining the length of the exploration period. (Separability refers to the distinguishability of the true optimal assortment from the other sub-optimal alternatives.) In this paper, we give an efficient algorithm that simultaneously explores and exploits, achieving performance independent of the underlying parameters. The algorithm can be implemented in a fully online manner, without knowledge of the horizon length $T$. Furthermore, the algorithm is adaptive in the sense that its performance is near-optimal in both the well separated case, as well as the general parameter setting where this separation need not hold.
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We consider a sequential subset selection problem under parameter uncertainty, where at each time step, the decision maker selects a subset of cardinality $K$ from $N$ possible items (arms), and observes a (bandit) feedback in the form of the index of one of the items in said subset, or none. Each item in the index set is ascribed a certain value (reward), and the feedback is governed by a Multinomial Logit (MNL) choice model whose parameters are a priori unknown. The objective of the decision maker is to maximize the expected cumulative rewards over a finite horizon $T$, or alternatively, minimize the regret relative to an oracle that knows the MNL parameters. We refer to this as the MNL-Bandit problem. This problem is representative of a larger family of exploration-exploitation problems that involve a combinatorial objective, and arise in several important application domains. We present an approach to adapt Thompson Sampling to this problem and show that it achieves near-optimal regret as well as attractive numerical performance.
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Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While recent approaches use Bayesian optimization to adaptively select configurations, we focus on speeding up random search through adaptive resource allocation and early-stopping. We formulate hyperparameter optimization as a pure-exploration non-stochastic infinite-armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations. We introduce a novel algorithm, Hyperband, for this framework and analyze its theoretical properties, providing several desirable guarantees. Furthermore, we compare Hyperband with popular Bayesian optimization methods on a suite of hyperparameter optimization problems. We observe that Hyperband can provide over an order-of-magnitude speedup over our competitor set on a variety of deep-learning and kernel-based learning problems.
Encoder-decoder-based recurrent neural network (RNN) has made significant progress in sequence-to-sequence learning tasks such as machine translation and conversational models. Recent works have shown the advantage of this type of network in dealing with various time series forecasting tasks. The present paper focuses on the problem of multi-horizon short-term load forecasting, which plays a key role in the power systems planning and operation. Leveraging the encoder-decoder RNN, we develop an attention model to select the relevant features and similar temporal information adaptively. First, input features are assigned with different weights by a feature selection attention layer, while the updated historical features are encoded by a bi-directional long short-term memory (BiLSTM) layer. Then, a decoder with hierarchical temporal attention enables a similar day selection, which re-evaluates the importance of historical information at each time step. Numerical results tested on the dataset of the global energy forecasting competition 2014 show that our proposed model significantly outperforms some existing forecasting schemes.
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