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Register a new userRandomized Exploration in Generalized Linear Bandits
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We study two randomized algorithms for generalized linear bandits, GLM-TSL and GLM-FPL. GLM-TSL samples a generalized linear model (GLM) from the Laplace approximation to the posterior distribution. GLM-FPL fits a GLM to a randomly perturbed history of past rewards. We prove $tilde{O}(d sqrt{n log K})$ bounds on the $n$-round regret of GLM-TSL and GLM-FPL, where $d$ is the number of features and $K$ is the number of arms. The regret bound of GLM-TSL improves upon prior work and the regret bound of GLM-FPL is the first of its kind. We apply both GLM-TSL and GLM-FPL to logistic and neural network bandits, and show that they perform well empirically. In more complex models, GLM-FPL is significantly faster. Our results showcase the role of randomization, beyond sampling from the posterior, in exploration.
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We propose a new online algorithm for minimizing the cumulative regret in stochastic linear bandits. The key idea is to build a perturbed history, which mixes the history of observed rewards with a pseudo-history of randomly generated i.i.d. pseudo-rewards. Our algorithm, perturbed-history exploration in a linear bandit (LinPHE), estimates a linear model from its perturbed history and pulls the arm with the highest value under that model. We prove a $tilde{O}(d sqrt{n})$ gap-free bound on the expected $n$-round regret of LinPHE, where $d$ is the number of features. Our analysis relies on novel concentration and anti-concentration bounds on the weighted sum of Bernoulli random variables. To show the generality of our design, we extend LinPHE to a logistic reward model. We evaluate both algorithms empirically and show that they are practical.
In this paper, we consider online learning in generalized linear contextual bandits where rewards are not immediately observed. Instead, rewards are available to the decision-maker only after some delay, which is unknown and stochastic. We study the performance of two well-known algorithms adapted to this delayed setting: one based on upper confidence bounds, and the other based on Thompson sampling. We describe modifications on how these two algorithms should be adapted to handle delays and give regret characterizations for both algorithms. Our results contribute to the broad landscape of contextual bandits literature by establishing that both algorithms can be made to be robust to delays, thereby helping clarify and reaffirm the empirical success of these two algorithms, which are widely deployed in modern recommendation engines.
We study the problem of incentivizing exploration for myopic users in linear bandits, where the users tend to exploit arm with the highest predicted reward instead of exploring. In order to maximize the long-term reward, the system offers compensation to incentivize the users to pull the exploratory arms, with the goal of balancing the trade-off among exploitation, exploration and compensation. We consider a new and practically motivated setting where the context features observed by the user are more informative than those used by the system, e.g., features based on users private information are not accessible by the system. We propose a new method to incentivize exploration under such information gap, and prove that the method achieves both sublinear regret and sublinear compensation. We theoretical and empirically analyze the added compensation due to the information gap, compared with the case that the system has access to the same context features as the user, i.e., without information gap. We also provide a compensation lower bound of our problem.
We propose an online algorithm for cumulative regret minimization in a stochastic multi-armed bandit. The algorithm adds $O(t)$ i.i.d. pseudo-rewards to its history in round $t$ and then pulls the arm with the highest average reward in its perturbed history. Therefore, we call it perturbed-history exploration (PHE). The pseudo-rewards are carefully designed to offset potentially underestimated mean rewards of arms with a high probability. We derive near-optimal gap-dependent and gap-free bounds on the $n$-round regret of PHE. The key step in our analysis is a novel argument that shows that randomized Bernoulli rewards lead to optimism. Finally, we empirically evaluate PHE and show that it is competitive with state-of-the-art baselines.
In this paper, we propose and study opportunistic bandits - a new variant of bandits where the regret of pulling a suboptimal arm varies under different environmental conditions, such as network load or produce price. When the load/price is low, so is the cost/regret of pulling a suboptimal arm (e.g., trying a suboptimal network configuration). Therefore, intuitively, we could explore more when the load/price is low and exploit more when the load/price is high. Inspired by this intuition, we propose an Adaptive Upper-Confidence-Bound (AdaUCB) algorithm to adaptively balance the exploration-exploitation tradeoff for opportunistic bandits. We prove that AdaUCB achieves $O(log T)$ regret with a smaller coefficient than the traditional UCB algorithm. Furthermore, AdaUCB achieves $O(1)$ regret with respect to $T$ if the exploration cost is zero when the load level is below a certain threshold. Last, based on both synthetic data and real-world traces, experimental results show that AdaUCB significantly outperforms other bandit algorithms, such as UCB and TS (Thompson Sampling), under large load/price fluctuations.
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