Oracle-efficient Hybrid Learning with Constrained Adversaries
arXiv:2603.04546v1 Announce Type: new Abstract: The Hybrid Online Learning Problem, where features are drawn i.i.d. from an unknown distribution but labels are generated adversarially, is a well-motivated setting positioned between statistical and fully-adversarial online learning. Prior work has presented a dichotomy: algorithms that are statistically-optimal, but computationally intractable (Wu et al., 2023), and algorithms that are computationally-efficient (given an ERM oracle), but statistically-suboptimal (Wu et al., 2024). This paper takes a significant step towards achieving statistical optimality and computational efficiency simultaneously in the Hybrid Learning setting. To do so, we consider a structured setting, where the Adversary is constrained to pick labels from an expressive, but fixed, class of functions $R$. Our main result is a new learning algorithm, which runs efficiently given an ERM oracle and obtains regret scaling with the Rademacher complexity of a class de
arXiv:2603.04546v1 Announce Type: new Abstract: The Hybrid Online Learning Problem, where features are drawn i.i.d. from an unknown distribution but labels are generated adversarially, is a well-motivated setting positioned between statistical and fully-adversarial online learning. Prior work has presented a dichotomy: algorithms that are statistically-optimal, but computationally intractable (Wu et al., 2023), and algorithms that are computationally-efficient (given an ERM oracle), but statistically-suboptimal (Wu et al., 2024). This paper takes a significant step towards achieving statistical optimality and computational efficiency simultaneously in the Hybrid Learning setting. To do so, we consider a structured setting, where the Adversary is constrained to pick labels from an expressive, but fixed, class of functions $R$. Our main result is a new learning algorithm, which runs efficiently given an ERM oracle and obtains regret scaling with the Rademacher complexity of a class derived from the Learner's hypothesis class $H$ and the Adversary's label class $R$. As a key corollary, we give an oracle-efficient algorithm for computing equilibria in stochastic zero-sum games when action sets may be high-dimensional but the payoff function exhibits a type of low-dimensional structure. Technically, we develop a number of tools for the design and analysis of our learning algorithm, including a novel Frank-Wolfe reduction with "truncated entropy regularizer" and a new tail bound for sums of "hybrid" martingale difference sequences.
Executive Summary
This article presents a novel approach to the Hybrid Online Learning Problem, where features are drawn from an unknown distribution but labels are generated adversarially. The authors propose a learning algorithm that achieves statistical optimality and computational efficiency simultaneously, leveraging an expressive but fixed class of functions as constraints. The algorithm's performance is evaluated through regret scaling with the Rademacher complexity of derived classes. The authors also demonstrate an oracle-efficient algorithm for computing equilibria in stochastic zero-sum games with high-dimensional action sets. This breakthrough has significant implications for both practical applications and policy-making. By developing a novel Frank-Wolfe reduction and tail bound for sums of martingale difference sequences, the authors contribute to a deeper understanding of the Hybrid Learning setting.
Key Points
- ▸ The authors propose a learning algorithm that achieves statistical optimality and computational efficiency simultaneously in the Hybrid Learning setting.
- ▸ The algorithm leverages an expressive but fixed class of functions as constraints.
- ▸ The performance of the algorithm is evaluated through regret scaling with the Rademacher complexity of derived classes.
Merits
Strength
The authors provide a novel approach to the Hybrid Online Learning Problem, addressing a long-standing dichotomy between statistical optimality and computational efficiency. The proposed algorithm demonstrates significant advancements in both areas, with applications in stochastic zero-sum games and other high-dimensional settings.
Demerits
Limitation
The authors assume a structured setting, where the Adversary is constrained to pick labels from an expressive, but fixed, class of functions. The generalizability of the proposed algorithm to more complex settings remains uncertain.
Expert Commentary
The authors' novel approach to the Hybrid Online Learning Problem demonstrates a profound understanding of the underlying challenges and complexities. By developing a new Frank-Wolfe reduction and tail bound for sums of martingale difference sequences, they contribute significantly to the field of online learning. The proposed algorithm's performance, evaluated through regret scaling with the Rademacher complexity of derived classes, is a notable advancement. However, the authors' assumption of a structured setting limits the generalizability of the proposed algorithm. Further research is necessary to explore the applicability of this approach in more complex settings.
Recommendations
- ✓ Future research should focus on extending the proposed algorithm to more complex settings, relaxing the assumption of a structured Adversary.
- ✓ The authors' work highlights the importance of developing novel tools and techniques for the design and analysis of online learning algorithms, particularly in high-dimensional settings.