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In this paper, we investigate the impact of diverse user preference on learning under the stochastic multi-armed bandit (MAB) framework. We aim to show that when the user preferences are sufficiently diverse and each arm can be optimal for certain users, the O(log T) regret incurred by exploring the sub-optimal arms under the standard stochastic MAB setting can be reduced to a constant. Our intuition is that to achieve sub-linear regret, the number of times an optimal arm being pulled should scale linearly in time; when all arms are optimal for certain users and pulled frequently, the estimated arm statistics can quickly converge to their true values, thus reducing the need of exploration dramatically. We cast the problem into a stochastic linear bandits model, where both the users preferences and the state of arms are modeled as {independent and identical distributed (i.i.d)} d-dimensional random vectors. After receiving the user preference vector at the beginning of each time slot, the learner pulls an arm and receives a reward as the linear product of the preference vector and the arm state vector. We also assume that the state of the pulled arm is revealed to the learner once its pulled. We propose a Weighted Upper Confidence Bound (W-UCB) algorithm and show that it can achieve a constant regret when the user preferences are sufficiently diverse. The performance of W-UCB under general setups is also completely characterized and validated with synthetic data.
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In this paper, we investigate a new multi-armed bandit (MAB) online learning model that considers real-world phenomena in many recommender systems: (i) the learning agent cannot pull the arms by itself and thus has to offer rewards to users to incentivize arm-pulling indirectly; and (ii) if users with specific arm preferences are well rewarded, they induce a self-reinforcing effect in the sense that they will attract more users of similar arm preferences. Besides addressing the tradeoff of exploration and exploitation, another key feature of this new MAB model is to balance reward and incentivizing payment. The goal of the agent is to maximize the total reward over a fixed time horizon $T$ with a low total payment. Our contributions in this paper are two-fold: (i) We propose a new MAB model with random arm selection that considers the relationship of users self-reinforcing preferences and incentives; and (ii) We leverage the properties of a multi-color Polya urn with nonlinear feedback model to propose two MAB policies termed At-Least-$n$ Explore-Then-Commit and UCB-List. We prove that both policies achieve $O(log T)$ expected regret with $O(log T)$ expected payment over a time horizon $T$. We conduct numerical simulations to demonstrate and verify the performances of these two policies and study their robustness under various settings.
Transfer learning has been demonstrated to be successful and essential in diverse applications, which transfers knowledge from related but different source domains to the target domain. Online transfer learning(OTL) is a more challenging problem where the target data arrive in an online manner. Most OTL methods combine source classifier and target classifier directly by assigning a weight to each classifier, and adjust the weights constantly. However, these methods pay little attention to reducing the distribution discrepancy between domains. In this paper, we propose a novel online transfer learning method which seeks to find a new feature representation, so that the marginal distribution and conditional distribution discrepancy can be online reduced simultaneously. We focus on online transfer learning with multiple source domains and use the Hedge strategy to leverage knowledge from source domains. We analyze the theoretical properties of the proposed algorithm and provide an upper mistake bound. Comprehensive experiments on two real-world datasets show that our method outperforms state-of-the-art methods by a large margin.
Deep learning models are considered to be state-of-the-art in many offline machine learning tasks. However, many of the techniques developed are not suitable for online learning tasks. The problem of using deep learning models with sequential data becomes even harder when several loss functions need to be considered simultaneously, as in many real-world applications. In this paper, we, therefore, propose a novel online deep learning training procedure which can be used regardless of the neural networks architecture, aiming to deal with the multiple objectives case. We demonstrate and show the effectiveness of our algorithm on the Neyman-Pearson classification problem on several benchmark datasets.
This paper deals with bandit online learning problems involving feedback of unknown delay that can emerge in multi-armed bandit (MAB) and bandit convex optimization (BCO) settings. MAB and BCO require only values of the objective function involved that become available through feedback, and are used to estimate the gradient appearing in the corresponding iterative algorithms. Since the challenging case of feedback with emph{unknown} delays prevents one from constructing the sought gradient estimates, existing MAB and BCO algorithms become intractable. For such challenging setups, delayed exploration, exploitation, and exponential (DEXP3) iterations, along with delayed bandit gradient descent (DBGD) iterations are developed for MAB and BCO, respectively. Leveraging a unified analysis framework, it is established that the regret of DEXP3 and DBGD are ${cal O}big( sqrt{Kbar{d}(T+D)} big)$ and ${cal O}big( sqrt{K(T+D)} big)$, respectively, where $bar{d}$ is the maximum delay and $D$ denotes the delay accumulated over $T$ slots. Numerical tests using both synthetic and real data validate the performance of DEXP3 and DBGD.
We aim to design adaptive online learning algorithms that take advantage of any special structure that might be present in the learning task at hand, with as little manual tuning by the user as possible. A fundamental obstacle that comes up in the design of such adaptive algorithms is to calibrate a so-called step-size or learning rate hyperparameter depending on variance, gradient norms, etc. A recent technique promises to overcome this difficulty by maintaining multiple learning rates in parallel. This technique has been applied in the MetaGrad algorithm for online convex optimization and the Squint algorithm for prediction with expert advice. However, in both cases the user still has to provide in advance a Lipschitz hyperparameter that bounds the norm of the gradients. Although this hyperparameter is typically not available in advance, tuning it correctly is crucial: if it is set too small, the methods may fail completely; but if it is taken too large, performance deteriorates significantly. In the present work we remove this Lipschitz hyperparameter by designing n
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