betekintés - Algorithms and Data Structures - # Multi-armed Bandits with Offline Data

Leveraging Offline Data in Multi-armed Bandits: Adaptive Policy for Biased Information

Q: How can the proposed approach be extended to other online learning settings beyond multi-armed bandits, such as linear bandits or reinforcement learning

The approach proposed in the paper can be extended to other online learning settings beyond multi-armed bandits by adapting the concept of leveraging biased historical data to different scenarios. For linear bandits, the valid bias bound can be constructed based on the difference between the offline and online reward distributions for each arm. The auxiliary input in MIN-UCB can be modified to incorporate this bias bound and adjust the decision-making process accordingly. In reinforcement learning, the historical data can be used to inform the exploration-exploitation trade-off, similar to how MIN-UCB leverages offline data in the multi-armed bandit setting. By adapting the algorithm to these settings and considering the specific characteristics of each problem, the principles of MIN-UCB can be applied effectively to improve learning performance in various online learning scenarios.

Q: What are some practical methods for constructing the valid bias bound, the auxiliary input required by MIN-UCB, in real-world applications

Constructing the valid bias bound, the auxiliary input required by MIN-UCB, in real-world applications can be achieved through various practical methods. One approach is to use domain knowledge and statistical techniques to estimate the potential distributional shift between the offline and online data sources. This can involve analyzing the historical data to identify patterns or trends that may indicate differences in the underlying distributions. Machine learning models can also be employed to learn the relationship between the offline and online data and predict the bias bound based on features extracted from the datasets. Additionally, cross-validation techniques can be used to validate the constructed bias bound and ensure its accuracy in capturing the distributional shift. By combining domain expertise, statistical analysis, and machine learning algorithms, a robust and reliable valid bias bound can be constructed for real-world applications.

Q: Can the ideas behind MIN-UCB be applied to other online learning problems with access to potentially biased historical data, beyond the multi-armed bandit setting

The ideas behind MIN-UCB can be applied to other online learning problems with access to potentially biased historical data beyond the multi-armed bandit setting by adapting the algorithm to suit the specific characteristics of each problem. In contextual bandits, where actions depend on contextual information, the bias bound can be constructed based on the difference in context-specific reward distributions. The auxiliary input in MIN-UCB can be tailored to incorporate this context-specific bias bound and guide decision-making in the learning process. In online model selection or dynamic pricing settings, where decisions are made based on changing environments, the concept of leveraging biased historical data can be utilized to improve decision-making under distributional shifts. By customizing the algorithm to address the unique challenges of each online learning problem, the principles of MIN-UCB can be extended to a wide range of applications beyond multi-armed bandits.

Alapfogalmak

The core message of this paper is to design an adaptive policy, MIN-UCB, that can effectively leverage offline data to improve online learning in stochastic multi-armed bandits, even when the offline data is biased and the difference between the offline and online reward distributions is unknown.

Kivonat

The paper considers a stochastic multi-armed bandit problem where the decision maker (DM) has access to an offline dataset before the online learning phase begins. The offline dataset is governed by a different probability distribution than the online rewards.

The key insights are:

The DM cannot outperform the vanilla UCB policy using any non-anticipatory policy without additional information about the difference between the offline and online reward distributions.
To bypass this impossibility result, the authors propose the MIN-UCB policy that adaptively chooses to utilize the offline data when they are deemed informative, and to ignore them otherwise. MIN-UCB requires an auxiliary input, a valid bias bound, which serves as an upper bound on the difference between the offline and online reward distributions.
The authors establish both instance dependent and instance independent regret bounds for MIN-UCB. They show that MIN-UCB outperforms the vanilla UCB when the offline and online reward distributions are "sufficiently close", and matches the performance of vanilla UCB when they are "far apart".
The authors also provide matching regret lower bounds, establishing the tightness of their analysis. In the special case when the offline and online reward distributions are identical, MIN-UCB achieves the optimal regret bound.
Numerical experiments corroborate the theoretical findings, demonstrating the robustness of MIN-UCB in adapting to the quality of the offline data.

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Forrás megtekintése

arxiv.org

Statisztikák

The paper does not contain any explicit numerical data or statistics. The analysis focuses on theoretical regret bounds.

Idézetek

"We leverage offline data to facilitate online learning in stochastic multi-armed bandits. The probability distributions that govern the offline data and the online rewards can be different."
"We show that no non-anticipatory policy can outperform the UCB policy by (Auer et al. 2002), even in the presence of offline data."
"MIN-UCB adaptively chooses to utilize the offline data when they are deemed informative, and to ignore them otherwise."

Főbb Kivonatok

Leveraging (Biased) Information: Multi-armed Bandits with Offline Data

by Wang Chi Che... : arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.02594.pdf

Leveraging (Biased) Information: Multi-armed Bandits with Offline Data

Mélyebb kérdések

How can the proposed approach be extended to other online learning settings beyond multi-armed bandits, such as linear bandits or reinforcement learning

The approach proposed in the paper can be extended to other online learning settings beyond multi-armed bandits by adapting the concept of leveraging biased historical data to different scenarios. For linear bandits, the valid bias bound can be constructed based on the difference between the offline and online reward distributions for each arm. The auxiliary input in MIN-UCB can be modified to incorporate this bias bound and adjust the decision-making process accordingly. In reinforcement learning, the historical data can be used to inform the exploration-exploitation trade-off, similar to how MIN-UCB leverages offline data in the multi-armed bandit setting. By adapting the algorithm to these settings and considering the specific characteristics of each problem, the principles of MIN-UCB can be applied effectively to improve learning performance in various online learning scenarios.

What are some practical methods for constructing the valid bias bound, the auxiliary input required by MIN-UCB, in real-world applications

Constructing the valid bias bound, the auxiliary input required by MIN-UCB, in real-world applications can be achieved through various practical methods. One approach is to use domain knowledge and statistical techniques to estimate the potential distributional shift between the offline and online data sources. This can involve analyzing the historical data to identify patterns or trends that may indicate differences in the underlying distributions. Machine learning models can also be employed to learn the relationship between the offline and online data and predict the bias bound based on features extracted from the datasets. Additionally, cross-validation techniques can be used to validate the constructed bias bound and ensure its accuracy in capturing the distributional shift. By combining domain expertise, statistical analysis, and machine learning algorithms, a robust and reliable valid bias bound can be constructed for real-world applications.

Can the ideas behind MIN-UCB be applied to other online learning problems with access to potentially biased historical data, beyond the multi-armed bandit setting

The ideas behind MIN-UCB can be applied to other online learning problems with access to potentially biased historical data beyond the multi-armed bandit setting by adapting the algorithm to suit the specific characteristics of each problem. In contextual bandits, where actions depend on contextual information, the bias bound can be constructed based on the difference in context-specific reward distributions. The auxiliary input in MIN-UCB can be tailored to incorporate this context-specific bias bound and guide decision-making in the learning process. In online model selection or dynamic pricing settings, where decisions are made based on changing environments, the concept of leveraging biased historical data can be utilized to improve decision-making under distributional shifts. By customizing the algorithm to address the unique challenges of each online learning problem, the principles of MIN-UCB can be extended to a wide range of applications beyond multi-armed bandits.