Mathematics 분야 (1): Algorithms; Artificial intelligence; Bandit algorithm

This paper considers the use of a simple posterior sampling algorithm to balance between exploration and exploitation when learning to optimize actions such as in multiarmed bandit problems. The algorithm, also known as Thompson Sampling and as probability matching, offers significant advantages over the popular upper confidence bound (UCB) approach, and can be applied to problems with finite or infinite action spaces and complicated relationships among action rewards. We make two theoretical contributions. The first establishes a connection between posterior sampling and UCB algorithms. This result lets us convert regret bounds developed for UCB algorithms into Bayesian regret bounds for posterior sampling. Our second theoretical contribution is a Bayesian regret bound for posterior sampling that applies broadly and can be specialized to many model classes. This bound depends on a new notion we refer to as the eluder dimension, which measures the degree of dependence among action rewards. Compared to UCB algorithm Bayesian regret bounds for specific model classes, our general bound matches the best available for linear models and is stronger than the best available for generalized linear models. Further, our analysis provides insight into performance advantages of posterior sampling, which are highlighted through simulation results that demonstrate performance surpassing recently proposed UCB algorithms. ©2014 INFORMS.

Classical collaborative filtering, and content-based filtering methods try to learn a static recommendation model given training data. These approaches are far from ideal in highly dynamic recommendation domains such as news recommendation and computational advertisement, where the set of items and users is very fluid. In this work, we investigate an adaptive clustering technique for content recommendation based on exploration-exploitation strategies in contextual multi-armed bandit settings. Our algorithm takes into account the collaborative effects that arise due to the interaction of the users with the items, by dynamically grouping users based on the items under consideration and, at the same time, grouping items based on the similarity of the clusterings induced over the users. The resulting algorithm thus takes advantage of preference patterns in the data in a way akin to collaborative filtering methods. We provide an empirical analysis on medium-size real-world datasets, showing scalability and increased prediction performance (as measured by click-through rate) over state-of-the-art methods for clustering bandits. We also provide a regret analysis within a standard linear stochastic noise setting. © 2016 ACM.

This work covers several aspects of the optimism in the face of uncertainty principle applied to large scale optimization problems under finite numerical budget. The initial motivation for the research reported here originated from the empirical success of the so-called Monte-Carlo Tree Search method popularized in Computer Go and further extended to many other games as well as optimization and planning problems. Our objective is to contribute to the development of theoretical foundations of the field by characterizing the complexity of the underlying optimization problems and designing efficient algorithms with performance guarantees. The main idea presented here is that it is possible to decompose a complex decision making problem (such as an optimization problem in a large search space) into a sequence of elementary decisions, where each decision of the sequence is solved using a (stochastic) multi-armed bandit (simple mathematical model for decision making in stochastic environments). This so-called hierarchical bandit approach (where the reward observed by a bandit in the hierarchy is itself the return of another bandit at a deeper level) possesses the nice feature of starting the exploration by a quasi-uniform sampling of the space and then focusing progressively on the most promising area, at different scales, according to the evaluations observed so far, until eventually performing a local search around the global optima of the function. The performance of the method is assessed in terms of the optimality of the returned solution as a function of the number of function evaluations. Our main contribution to the field of function optimization is a class of hierarchical optimistic algorithms designed for general search spaces (such as metric spaces, trees, graphs, Euclidean spaces) with different algorithmic instantiations depending on whether the evaluations are noisy or noiseless and whether some measure of the "smoothness" of the function is known or unknown. The performance of the algorithms depends on the "local" behavior of the function around its global optima expressed in terms of the quantity of near-optimal states measured with some metric. If this local smoothness of the function is known then one can design very efficient optimization algorithms (with convergence rate independent of the space dimension). When this information is unknown, one can build adaptive techniques which, in some cases, perform almost as well as when it is known. In order to be self-contained, we start with a brief introduction to the stochastic multi-armed bandit problem in Chapter 1 and describe the UCB (Upper Confidence Bound) strategy and several extensions. In Chapter 2 we present the Monte-Carlo Tree Search method applied to Computer Go and show the limitations of previous algorithms such as UCT (UCB applied to Trees). This provides motivation for designing theoretically well-founded optimistic optimization algorithms. The main contributions on hierarchical optimistic optimization are described in Chapters 3 and 4 where the general setting of a semimetric space is introduced and algorithms designed for optimizing a function assumed to be locally smooth (around its maxima) with respect to a semi-metric are presented and analyzed. Chapter 3 considers the case when the semi-metric is known and can be used by the algorithm, whereas Chapter 4 considers the case when it is not known and describes an adaptive technique that does almost as well as when it is known. Finally in Chapter 5 we describe optimistic strategies for a specific structured problem, namely the planning problem in Markov decision processes with infinite horizon discounted rewards. © 2014 R. Munos.

In a multi-armed bandit (MAB) problem, an online algorithm makes a sequence of choices. In each round it chooses from a time-invariant set of alternatives and receives the payoff associated with this alternative. While the case of small strategy sets is by now well-understood, a lot of recent work has focused on MAB problems with exponentially or infinitely large strategy sets, where one needs to assume extra structure in order to make the problem tractable. In particular, recent literature considered information on similarity between arms. We consider similarity information in the setting of contextual bandits, a natural ex-tension of the basic MAB problem where before each round an algorithm is given the context-a hint about the payoffs in this round. Contextual bandits are directly motivated by placing advertisements on web pages, one of the crucial problems in sponsored search. A particularly simple way to represent similarity information in the contextual bandit setting is via a similarity distance between the context-arm pairs which bounds from above the difference between the respective expected payoffs. Prior work on contextual bandits with similarity uses "uniform" partitions of the sim-ilarity space, so that each context-arm pair is approximated by the closest pair in the partition. Algorithms based on "uniform" partitions disregard the structure of the payoffs and the context arrivals, which is potentially wasteful. We present algorithms that are based on adaptive partitions, and take advantage of "benign" payoffs and context arrivals without sacrificing the worst-case performance. The central idea is to maintain a finer partition in high-payoff regions of the similarity space and in popular regions of the context space. Our results apply to several other settings, e.g., MAB with constrained temporal change (Slivkins and Upfal, 2008) and sleeping bandits (Kleinberg et al., 2008a). © 2014 Aleksandrs Slivkins.

We summarize the methodology of the team TOLOLO, which ranked first in the load forecasting and price forecasting tracks of the Global Energy Forecasting Competition 2014. During the competition, we used and tested many different statistical and machine learning methods, such as random forests, gradient boosting machines and generalized additive models. In this paper, we only present the methods that showed the best results. For electric load forecasting, our strategy consists of producing temperature scenarios that we then plug into a probabilistic forecasting load model. Both steps are performed by fitting a quantile generalized additive model (quantGAM). Concerning the electricity price forecasting, we investigate three methods that we used during the competition. The first method follows the spirit of that used for the electric load. The second one is based on combining a set of individual predictors. The last one fits a sparse linear regression to a large set of covariates. We chose to present these three methods in this paper because they perform well and show the potential for improvements in future research. © 2015 International Institute of Forecasters