Stochastic Low-Rank Bandits
Many problems in computer vision and recommender systems involve low-rank matrices. In this work, we study the problem of finding the maximum entry of a stochastic low-rank matrix from sequential observations. At each step, a learning agent chooses pairs of row and column arms, and receives the noisy product of their latent values as a reward. The main challenge is that the latent values are unobserved. We identify a class of non-negative matrices whose maximum entry can be found statistically efficiently and propose an algorithm for finding them, which we call LowRankElim. We derive a $\DeclareMathOperator{\poly}{poly} O((K + L) \poly(d) \Delta^{-1} \log n)$ upper bound on its $n$-step regret, where $K$ is the number of rows, $L$ is the number of columns, $d$ is the rank of the matrix, and $\Delta$ is the minimum gap. The bound depends on other problem-specific constants that clearly do not depend $K L$. To the best of our knowledge, this is the first such result in the literature.
Code (0)
등록된 구현이 없습니다.
Tasks
Recommendation SystemsSimilar Papers 제목 키워드 기반
Solving Bernoulli Rank-One Bandits with Unimodal Thompson Sampling
Stochastic Rank-One Bandits (Katarya et al, (2017a,b)) are a simple framework for regret minimization problems over rank-one matrices of arms. The initially proposed algorithms are proved to have logarithmic regret, but …
Thompson SamplingStochastic Low-rank Tensor Bandits for Multi-dimensional Online Decision Making
Multi-dimensional online decision making plays a crucial role in many real applications such as online recommendation and digital marketing. In these problems, a decision at each time is a combination of choices from dif…
Decision MakingMarketingStochastic Rank-1 Bandits
We propose stochastic rank-$1$ bandits, a class of online learning problems where at each step a learning agent chooses a pair of row and column arms, and receives the product of their values as a reward. The main challe…
Factored Bandits
We introduce the factored bandits model, which is a framework for learning with limited (bandit) feedback, where actions can be decomposed into a Cartesian product of atomic actions. Factored bandits incorporate rank-1 b…
Contextual bandits with concave rewards, and an application to fair ranking
We consider Contextual Bandits with Concave Rewards (CBCR), a multi-objective bandit problem where the desired trade-off between the rewards is defined by a known concave objective function, and the reward vector depends…
FairnessMulti-Armed Bandits