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[2602.21328] Efficient Opportunistic Approachability
Summary
This paper presents an efficient algorithm for opportunistic approachability, improving upon previous methods by achieving faster approachability rates without the need for online calibration.
Why It Matters
The study addresses a significant challenge in machine learning related to approachability in adversarial settings. By providing a more efficient algorithm, it enhances the potential for applications in various fields, including game theory and decision-making processes, where understanding adversarial behavior is crucial.
Key Takeaways
- Introduces an efficient algorithm for opportunistic approachability.
- Achieves an approachability rate of O(T^{-1/4}) without online calibration.
- Demonstrates optimal rates of O(T^{-1/2}) for adversary action sets of dimension two.
- Builds on prior work by Bernstein et al. (2014), enhancing theoretical foundations.
- Offers insights into the implications for adversarial learning and decision-making.
Computer Science > Machine Learning arXiv:2602.21328 (cs) [Submitted on 24 Feb 2026] Title:Efficient Opportunistic Approachability Authors:Teodor Vanislavov Marinov, Mehryar Mohri, Princewill Okoroafor, Jon Schneider, Julian Zimmert View a PDF of the paper titled Efficient Opportunistic Approachability, by Teodor Vanislavov Marinov and 4 other authors View PDF HTML (experimental) Abstract:We study the problem of opportunistic approachability: a generalization of Blackwell approachability where the learner would like to obtain stronger guarantees (i.e., approach a smaller set) when their adversary limits themselves to a subset of their possible action space. Bernstein et al. (2014) introduced this problem in 2014 and presented an algorithm that guarantees sublinear approachability rates for opportunistic approachability. However, this algorithm requires the ability to produce calibrated online predictions of the adversary's actions, a problem whose standard implementations require time exponential in the ambient dimension and result in approachability rates that scale as $T^{-O(1/d)}$. In this paper, we present an efficient algorithm for opportunistic approachability that achieves a rate of $O(T^{-1/4})$ (and an inefficient one that achieves a rate of $O(T^{-1/3})$), bypassing the need for an online calibration subroutine. Moreover, in the case where the dimension of the adversary's action set is at most two, we show it is possible to obtain the optimal rate of $O(T^{-1/2})...
