Multi-dueling Bandits with Dependent Arms (1705.00253v1)

Abstract: The dueling bandits problem is an online learning framework for learning from pairwise preference feedback, and is particularly well-suited for modeling settings that elicit subjective or implicit human feedback. In this paper, we study the problem of multi-dueling bandits with dependent arms, which extends the original dueling bandits setting by simultaneously dueling multiple arms as well as modeling dependencies between arms. These extensions capture key characteristics found in many real-world applications, and allow for the opportunity to develop significantly more efficient algorithms than were possible in the original setting. We propose the \selfsparring algorithm, which reduces the multi-dueling bandits problem to a conventional bandit setting that can be solved using a stochastic bandit algorithm such as Thompson Sampling, and can naturally model dependencies using a Gaussian process prior. We present a no-regret analysis for multi-dueling setting, and demonstrate the effectiveness of our algorithm empirically on a wide range of simulation settings.

An Overview of "Multi-dueling Bandits with Dependent Arms"

The paper "Multi-dueling Bandits with Dependent Arms" addresses the challenges posed by the dueling bandits problem, an online learning framework that learns from pairwise preference feedback. It is particularly suited for contexts involving subjective or implicit human feedback, like information retrieval systems or recommendation systems. This paper extends the classical dueling bandits scenario by introducing multi-dueling bandits with dependent arms, capturing the intricacies of real-world applications more effectively. The proposed framework allows for both the simultaneous comparison of multiple arms and modeling of dependencies between them, which opens pathways for designing more efficient algorithms compared to traditional methods.

Key Contributions

This work makes several key contributions to the multi-dueling bandits problem:

1. Extension of Dueling Bandits: The authors extend the dueling bandits problem to accommodate multiple simultaneous duels and arm dependencies, enhancing capacity for realistic applications where these conditions are prevalent.
2. Algorithmic Framework: The paper proposes a novel algorithmic strategy that reduces the multi-dueling problem to a standard multi-armed bandit scenario. This reduction allows utilization of conventional bandit algorithms like Thompson Sampling, integrated with a Gaussian process prior to model dependencies.
3. No-regret Analysis: The paper presents a formal no-regret analysis for the multi-dueling bandits setting, a novel contribution to the literature on this topic.

Numerical Results and Claims

The authors demonstrate the efficacy of their proposed algorithm, named the algorithm, through comprehensive simulations. The algorithm showcases significant improvements in regret reduction across diverse experimental conditions compared to existing approaches. The simulations explore different preference functions and utility distributions, illustrating the algorithm's robustness and superiority over other state-of-the-art methods like Sparring or BOPPER. Their results substantiate the claim that the algorithm yields significant reductions in regret, particularly with increasing numbers of arms being simultaneously played.

Implications

The paper's findings exhibit substantial implications in both theoretical and practical domains. Theoretically, it fills a crucial gap in multi-dueling bandits literature by providing a framework that combines multi-dueling and dependency modeling in a unified approach. Practically, the algorithm can significantly enhance systems requiring efficient arm selections in environments where multidimensional dependencies are intrinsic.

Future Directions

From the results and discussions presented, several future research avenues can be extrapolated:

• Refinement of Theoretical Analysis: The paper suggests that a more detailed, finite-time regret analysis could be a beneficial extension. Such an analysis might offer tighter bounds and a deeper understanding of the algorithm's performance under various conditions.
• Extension to Other Feedback Mechanisms: Further exploration of different feedback mechanisms tailored for varying practical applications could enhance adaptability and usability in real-world scenarios.
• Real-world Application Testing: Although the algorithm demonstrates superior performance in simulations, testing in real-world datasets beyond the MSLR-30K environment would validate its applicability and efficiency further.

In conclusion, "Multi-dueling Bandits with Dependent Arms" proposes an innovative framework and algorithm that bring significant advancements to the field of preference-based learning. Its potential to handle multi-dueling scenarios with inherent dependencies marks an essential step towards more comprehensive and adaptable online learning algorithms.