- The paper establishes nearly tight mistake bounds for bandit feedback, demonstrating that randomized learners outperform deterministic ones in adversarial online multiclass settings.
- The study finds that adaptive adversaries can increase mistake bounds by a factor of Ω(k), significantly challenging online learning models.
- By extending the analysis to agnostic settings without prior inconsistency budget knowledge, the research broadens the practical applicability of online multiclass classifiers.
Bandit Feedback in Online Multiclass Classification: Analyzing Variants and Trade-offs
Randomized vs. Deterministic Learners and Adaptive vs. Oblivious Adversaries
In the field of online multiclass classification under the adversarial setting, key questions revolve around the performance differentials between randomized and deterministic learners, as well as between adaptive and oblivious adversaries, especially when only bandit feedback is available. This paper embarks on a comprehensive exploration of these dimensions, delineating nearly tight bounds that illuminate the inherent trade-offs and dynamics at play.
Key Findings
- Deterministic vs. Randomized Learners: Our investigation reveals that the optimal mistake bound for bandit feedback stands at most O(k) times higher than its full-information feedback counterpart, aligning with previously conjectured bounds. This result not only settles an open question but underscores the comparatively higher resilience of randomized strategies against adversarial inputs in the bandit feedback model.
- Adaptive vs. Oblivious Adversaries: The comparison between adaptive and oblivious adversaries in the bandit feedback scenario unveils a stark contrast: while oblivious adversaries exhibit restrained impact, adaptive adversaries can substantially escalate the learner's mistake bounds. Specifically, we establish that against an adaptive adversary, the mistake bound can increase by a factor of Ω(k), emphasizing the heightened challenge adaptive adversaries pose.
- The Role of Randomness: Interestingly, the examination into the efficacy of randomized versus deterministic learners underlines a nuanced dependence on randomness. In particular, for certain classes, we observe that randomness allows for bounds that are significantly tighter compared to deterministic approaches, especially when the adversary is adaptive. This divergence highlights randomness as a pivotal factor in mitigating adversarial influence.
- Implications in Agnostic and Realizable Settings: Extending our analysis to the agnostic setting—where a perfect hypothesis may not exist—we demonstrate that our results hold under the more general r-realizable assumption. Moreover, we introduce a method to circumvent the need for prior knowledge of the inconsistency budget r, further broadening the applicability of our findings.
Future Directions
This work opens up several avenues for future investigation. A noteworthy direction entails extending our analysis to the multilabel setting, potentially uncovering richer dynamics when multiple correct labels are permissible. Additionally, exploring alternative feedback models, like comparison feedback, could yield further insights into the landscape of online learning under partial information.
In summary, our paper provides a clearer understanding of the trade-offs between different learners and adversaries in online multiclass classification with bandit feedback. The nearly tight bounds we present not only resolve long-standing open questions but also pave the way for more nuanced explorations of adversarial online learning.