TL;DR#
Online learning aims to minimize cumulative loss when repeatedly choosing actions. This paper innovates by allowing the decision-maker to use “best-action queries,” which reveal the optimal action at a given time. However, using queries has cost, hence the decision-maker only allows a limited number of queries. This setting is important because predictive features are often expensive to acquire. Traditional online learning methods struggle with this constraint.
The paper addresses this challenge by establishing tight theoretical bounds on the performance of algorithms with access to a limited number of best-action queries. For full-feedback models, it shows that a sublinear number of queries substantially reduces regret. For label-efficient feedback, where feedback is only available during query times, it provides improved regret rates compared to standard label-efficient prediction. These findings highlight how limited, carefully-used queries substantially boost online learning performance, offering valuable insights for resource-constrained applications.
Key Takeaways#
Why does it matter?#
This paper significantly advances online learning by exploring the impact of limited best-action queries. It provides tight theoretical bounds on regret, showcasing the surprising multiplicative advantage of even a few queries. This opens avenues for designing efficient algorithms in scenarios where obtaining perfect predictions is costly, impacting various machine learning applications dealing with limited resources or time constraints.
Visual Insights#
🔼 This table presents the Hedge algorithm, which incorporates best-action queries. The algorithm uses a learning rate (η) that depends on the number of queries and the time horizon. It combines Hedge’s weights with a uniform query selection strategy. If a query is issued at time t, the algorithm selects the best action; otherwise, it samples an action probabilistically from the updated weights. This is then used for the proof of the minimax regret bounds in the full feedback case with best-action queries.
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Table 3.1: Hedge algorithm with k best-action queries
Full paper#
